Prediction of a risk of an event

Abstract

The disclosure provides a method for training a cause-specific Cox proportional hazards model to predict at least a risk of an event, a method for predicting a risk of an event, computer systems and computer programs.

Description

PREDICTION OF A RISK OF AN EVENTTECHNICAL FIELD

[0001] This disclosure relates to a computer-implemented method for risk assessment of an event.BACKGROUND

[0002] Cox proportional hazards models, also known as Cox regression or Cox model, include regression models implementing statistical techniques used in medical research to investigate the association between patients' survival time and one or more predictor variables. A Cox proportional hazards model assumes that the hazard rate or probability of an event occurring at a given time, given survival up to that time, is proportional across different levels of the predictor variables.

[0003] Cause-specific Cox may refer to a Cox regression analysis where the focus is on modeling the hazard for specific causes of events. The hazard for specific causes of events may be relevant in situations where multiple potential causes are being studied and where an objective is to understand how different predictors or variables affect the hazard for each specific cause. Causespecific Cox regression may involve fitting separate Cox models for each cause of interest, with potentially different sets of predictor variables for each cause. This approach allows for a more nuanced understanding of how different factors, or covariates, influence the risk of specific outcomes.

[0004] There are currently no solutions for providing clinically meaningful and accurate models in a clinical context that account for competing events. Examples of the present disclosure seek to reduce at least partially one or more of the aforementioned problems.SUMMARY

[0005] In a first aspect, the present disclosure provides a computer-implemented -Cl- method for training a cause-specific Cox proportional hazards model to predict at least a risk of an event, wherein the event comprises one of a risk of mortality, a risk of mechanical ventilation, and a risk of ICU -Intensive Care Unit- admission, by mapping the risk of the event to a raw set of variables comprising demographic information variables, comorbidity variables, and blood marker variables; the computer-implemented method comprising: selecting, from the raw set of variables, a set of training variables and a set of validation variables, the training variables and the validation variables comprising at least: a risk of the event, a demographic information variable, a comorbidity variable and a blood marker variable; inputting the set of training variables into a cause-specific Cox proportional hazards model so that the cause-specific Cox proportional hazards model is trained to output therisk of the event by mapping the risk of the event to at least a demographic information variable, the at least a comorbidity variable and the at least a blood marker variable, providing thereby a prediction function of the cause-specific Cox proportional hazards model; applying a fitness function to the prediction function on a set of validation variables, the fitness function combining calibration and discrimination, obtaining thereby a fitness value; selecting, by a stochastic optimization method and based on the fitness value, a subset of variables from the set of training variables; iteratively:- inputting the subset of variables into the cause-specific Cox proportional hazards model so that the cause-specific Cox proportional hazards model is updated to map the risk of the event to the subset of variables, providing thereby a further prediction function of the cause-specific Cox proportional hazards model;- applying the fitness function to the further prediction function on a subset of validation variables, the subset comprising the subset selected by the stochastic optimization method, obtaining thereby a further fitness value; and- selecting, by the stochastic optimization method and based on the further fitness value, a further subset of variables from the set of training variables; until a termination criterion is met.

[0006] The Cl method for training of the present disclosure allows providing a prediction model of at least a risk of an event, wherein the event may comprise one of a risk of mortality, a risk of mechanical ventilation, and a risk of ICU -Intensive Care Unit- admission. The Cl method of training provides a model for predicting risks in response to a raw set of variables comprising demographic information variables, comorbidity variables, and blood marker variables. In some examples further variables such as “time to event" is also included as a training variable, “time to event” refers to a duration between a defined starting point (e.g., hospital admission) and the occurrence of a specific critical health event (e.g., event of mortality, event of mechanical ventilation, or event of ICU admission. “Time to event” is a component in survival analysis, enabling the prediction of when a patient is likely to experience mortality, require ICU admission, or need mechanical ventilation.

[0007] The Cl method for training comprises an iterative update of the cause-specific Cox proportional hazards model and an iterative update of the selection of the subset of variables from the set of training variables, thereby providing two nested optimization loops. An internal loop optimizes the cause-specific Cox proportional hazards model -or cause-specific regression-, and an outer loop calculates the fitness function -or cost function- that involves discrimination and calibration. The stochastic optimization method selects the subset of features so that the cause-specific model provides the best model with calibration and discrimination. By employing two nested optimization loops, with the internal loop optimizing the cause-specific regression model and the outer loop optimizing the overall model performance through a stochastic optimization method based on feature or variable selection, the approach ensures that the model is both well- calibrated and capable of discriminating between different risk levels.

[0008] The Cl method for training comprises selecting a set of training variables from a raw set of variables. This step may be referred to as feature selection or initial feature selection. Highly correlated variables may be eliminated in the initial feature selection to provide stability to the method and to the system where the method may be implemented. The condition number of a matrix in regression models measures the sensitivity of the solution to changes in the input data. High multicollinearity among input variables or features can lead to a high condition number, making the model's predictions unstable and unreliable. Feature selection may comprise removing highly correlated and redundant features, thus lowering the condition number and enhancing the model's numerical stability. Stability refers to the model's ability to produce consistent predictions across different subsets of the data. High-dimensional data with multicollinearity and sparse categories can lead to overfitting, where the model performs well on the training data but poorly on unseen data. Feature selection improves stability by retaining only the most informative features, leading to more generalizable and robust models. In this context, sensitivity refers to how sensitive the model's predictions are to small changes in the input data. Multicollinearity and sparse categories can amplify this sensitivity, causing significant fluctuations in predictions with minor variations in the data. Feature selection reduces sensitivity by eliminating features that are not meaningful information, thus leading to more reliable and interpretable predictions. Convergence is the model's ability to find an optimal solution during training. Highdimensional data with multicollinearity and sparsity issues can slow down or prevent convergence. By selecting a subset of relevant features, feature selection simplifies the optimization problem, facilitating faster and more reliable convergence.

[0009] The Cl method for training further comprises inputting the set of training variables into the cause-specific Cox proportional hazards model so that the cause-specific Cox proportional hazards model is trained to map the risk of the event to at least a demographic information variable, the at least a comorbidity variable and the at least a blood marker variable, providing thereby a prediction function of the cause-specific Cox proportional hazards model. The causespecific Cox proportional hazards model represents the internal Loop: The internal loop aims at optimizing the parameters or coefficients of the cause-specific Cox regression model or parameters or coefficients of the prediction function. This involves adjusting the model coefficients to fit the training data best and accurately predict the risk of an event, for example, mortality, and / or ICU admission, and / or mechanical ventilation.

[0010] The Cl method for training receives at least one variable in each of the categories ofvariables: demographic information variables, comorbidity variables, and blood marker variables. The three categories of variables allow accurately assessing the risk of mortality, or the risk of ICU admission, or the risk of mechanical ventilation. Each type contributes uniquely and synergistically to the model, improving the model's effectiveness. While blood markers might often carry significant weight due to their dynamic nature, including all three types ensures the most comprehensive and reliable risk assessment.

[0011] For training, variables of subjects recorded at hospital admission may be used. Data collected from the two preceding months may be used as input. The method may also be trained with the outcomes of the subjects, for example, from the Hospital Information System (HIS), such as ground truth or predicted event.

[0012] The Cl method for training further comprises applying a fitness function to the prediction function on a set of validation variables, the fitness function combining calibration and discrimination, thereby obtaining a fitness value. For example, the validation set may be used with the prediction function, and an associated fitness value may be calculated with the fitness function. For example, the fitness function results from the sum of the discrimination and calibration values; for example, the area under the curve plus the coefficient R2, or ALIC+R2.

[0013] The set of validation variables is different from the set of training variables, and the set of validation variables comprises at least one demographic information variable, at least one comorbidity variable, and at least one blood marker variable.

[0014] The Cl method for training further comprises selecting a subset of variables from the set of training variables by a stochastic optimization method based on the fitness value. The selection by the stochastic optimization method may be referred to as "Feature Selection via the stochastic optimization method" and represents the outer loop of the method. The outer loop allows for selecting an optimal feature subset from the available training variables. By exploring various combinations of features, the stochastic optimization method identifies a subset that maximizes the fitness value by combining both discrimination and calibration. This process includes only the most relevant and informative features or variables, enhancing the model's predictive power and robustness. Feature Selection via the stochastic optimization method provides for developing a robust and reliable cause-specific Cox regression model. It addresses issues such as multicollinearity, stability, sensitivity, and convergence, ultimately leading to improved prediction outcomes.

[0015] The stochastic optimization method, for example, a Swarm Intelligence (SI) algorithm such as Ant Colony Optimization (ACO), Artificial Bee Colony (ABC), Cuckoo Search (CS), or Particle Swarm Optimization (PSO) selects a subset of features, making that the cause-specific model provides the best model or method with calibration and discrimination. The stochastic optimization method represents the outer loop in the presented method. The outer loop optimizes the overall model performance by evaluating a cost function that includes discrimination measures -or howwell the model distinguishes between different risk levels-, and calibration -or how accurately the predicted risks reflect actual outcomes. The outer loop ensures that the model fits the training data well and generalizes effectively to new, unseen data.

[0016] The Cl method for training further comprises iteratively inputting the subset of variables into the cause-specific Cox proportional hazards model so that the cause-specific Cox proportional hazards model is updated to map the risk of the event to the subset of variables, providing thereby a further prediction function of the cause-specific Cox proportional hazards model; applying the fitness function to the further prediction function on a subset of validation variables, where the subset of validation variables are updated as the subset of variables - selected by the stochastic optimization method- obtaining thereby a further fitness value; and selecting, by the stochastic optimization method and based on the further fitness value, a further subset of variables from the set of training variables; until a termination criterion is met.

[0017] The iteration of steps makes it possible for the Cl method for training to continue updating the coefficients of the prediction function and the selection of the subset of variables by the feature selection in the outer loop so that the model performance converges to an optimal solution. When the optimization converges to a local minimum and the termination criterion is set, then the model may be considered trained.

[0018] The risk of the event given the subset of variables may be a value between 0 to 100, in examples represented as a continuous variable.

[0019] The termination criterion may comprise that the subset of variables selected by the stochastic optimization method, also referred to as the "global best of the optimization method", does not change in 100 iterations. The termination criterion may comprise a maximum number of iterations reached, for example, 1000. The termination criterion may comprise a maximum number of iterations reached without the fitness function changing a predefined number of times. For example, the termination criterion depends on the fitness value. As seen, the termination of the iterations depends both on the internal loop and the outer loop since the outer loop selects significant variables depending on the fitness value, and the internal loop updates the coefficients of the prediction function based on such parameters.

[0020] In a further aspect of the invention, a computer system comprising means for carrying out the computer-implemented method for training a cause-specific Cox proportional hazards model to predict at least a risk of an event is provided.

[0021] In a further aspect of the invention, there is provided a computer-implemented -Cl- method for predicting a risk of an event, the method comprising obtaining a prediction of the risk of the event by providing input variables of a subject to a cause-specific Cox proportional hazards model which has been trained by the method for training according to the present disclosure and obtaining a risk of the event by the cause-specific Cox proportional hazards model. The risk of the event may comprise a risk of the subject's mortality, the risk of ICU admission, or the risk ofmechanical ventilation. The prediction may be a 2-month forecast.

[0022] In clinical investigations, there may be situations where several known quantities or covariates potentially affect a patient's prognosis. Supposing a comparison between two groups of patients, the first group with a specific genotype and the second group without the specific genotype, if one of the groups contains older individuals, any difference in survival may be attributable to genotype or age or both. Hence, when investigating survival in relation to any one covariate, the impact of others may be adjusted. Multivariate statistical modeling is a tool to analyze survival with respect to several covariates simultaneously. Additionally, multivariate statistical models provide the effect size for each covariate. The Cox proportional-hazards model is one of the methods used to model survival analysis data. The purpose of the Cox proportionalhazards model is to simultaneously evaluate several covariates' effects on survival. In other words, it allows for examining how specified factors influence the rate or probability of a particular event (e.g., infection, mortality) at a particular point in time. The probability is commonly referred to as the hazard rate. Predictor variables or factors are usually termed covariates in the survivalanalysis literature.

[0023] The cause-specific Cox proportional hazard model is a variant of the Cox proportional hazards model specifically designed to handle competing risk data. Competing risks occur when individuals are exposed to the risk of experiencing one of multiple possible types of events, and the occurrence of one type of event precludes the occurrence of the others. In the present disclosure, competing events may include ICU admission, mechanical ventilation, and "discharge alive" when "hospital death" is an event of interest.

[0024] In traditional survival analysis, the Kaplan-Meier estimator and the Cox proportional hazards model treat censoring as the only reason for an individual to leave the study without experiencing the event of interest. However, in the presence of competing risks, individuals may leave the study due to experiencing a different type of event, leading to informative censoring. The cause-specific Cox proportional hazard models address this issue by focusing on modeling the hazard of the event of interest while treating other types of events as censoring events. This allows researchers to estimate the hazard associated with each specific cause of failure while accounting for the presence of competing risks. The cause-specific hazard function for the j-th event is typically denoted by AJ(t|x), where t represents time, x represents covariates or predictor variables, and j indexes the different types of events. The cause-specific cox proportional hazard model is assumed to follow a proportional hazards form or a closed-form equation, AJ(t|x) = A_Oj(t) * exp(Px), where A_Oj(t) is the baseline hazard function for the j-th event, and p is a vector of regression coefficients representing the effect of the covariates on the hazard for the j-th event. For example, for a first event "mortality" (event 1), a baseline hazard function or prediction function may take the form: A1 (t)=A01 (t)*exp(0.03xage+0.5xsex+0.4xdiabetes). For example, for a second event "hospital discharge" (event 2), a prediction function may take the form:A2(t)=A02(t)*exp(-0.02xage-0.3xsex-0.2xdiabetes). A01 (t) and A02(t) are baseline hazards for the first and second events. The baseline hazard is the hazard function when all covariates (predictors) in the model are set to zero. It represents the underlying hazard rate of the event happening (e.g., death, failure) over time for an individual with baseline (reference) characteristics.

[0025] In the present disclosure, the covariates may comprise demographic information, comorbidity, and blood marker variables.

[0026] Evaluating the risk of an event may comprise evaluating the risk of mortality, or the risk of mechanical ventilation, or the risk of ICU -Intensive Care Unit- admission. Mortality risk assessment, and / or risk assessment of ICU admission, and / or risk assessment of mechanical ventilation may be provided or evaluated over a projected time, for example, for two months from a current date. The computer-implemented method may provide a valuable healthcare planning and patient management tool. Mortality risk assessment or, and / or risk assessment of ICU admission, and / or risk assessment of mechanical ventilation allow medical professionals to apply personalized treatment plans and interventions or may allow professionals to categorize patients based on the severity of their condition and potential needs. Risk assessment enables early identification of patients at increased risk, ensuring timely and appropriate care, such as specialized monitoring or early mechanical ventilation, can be provided. Furthermore, risk assessment may aid professionals in resource allocation, as predicting the need for ICU beds and ventilators.

[0027] The Cl method for training the disclosure's cause-specific cox proportional hazard model includes a fitness function, also referred to as cost function, combining discrimination and calibration. The fitness function determines how the quality of a model is assessed. Discrimination or "model discrimination" may comprise the ability of the model to differentiate between different outcomes, e.g., survival versus mortality. Models may correctly distinguish high-risk from low-risk individuals. Using discrimination as part of the fitness function ensures that the model is evaluated based on correctly classifying individuals according to their risk. Calibration or "model calibration" assesses how well the predicted probabilities align with the observed frequencies. A well- calibrated model ensures that if the model predicts a 30% risk of mortality, then around 30% of the patients with that risk prediction should experience the event. Calibration thus captures the reliability of the model's predictions, ensuring that the probabilities are meaningful.

[0028] In the context of risk assessment of mortality and / or mechanical ventilation and / or ICU admission, defining the fitness function based on a combination of model discrimination and calibration provides at least the following advantages:

[0029] Clinical relevance: combining discrimination and calibration captures two relevant aspects in a clinical context: correctly identifying high-risk individuals (discrimination) and the reliability of the risk predictions (calibration). This ensures that the model's predictions are both accurate andclinically meaningful, aligning with the goals of mortality risk assessment and / or risk assessment of ICU admission and / or risk assessment of mechanical ventilation.

[0030] Avoiding overfitting: traditional MSE - Mean Squared Error - minimization can sometimes lead to overfitting, where the model fits the training data too closely and performs poorly on unseen data. By combining discrimination and calibration, the fitness function allows the model to capture the underlying risk structure without fitting the noise in the data. This can lead to better generalization to new data.

[0031] Risk stratification: Mortality risk assessment or, and / or risk assessment of ICU admission, and / or risk assessment of mechanical ventilation often requires stratifying patients into different risk categories, e.g., low, medium, high risk. A fitness function combining discrimination and calibration allows the model to provide meaningful risk stratification, aligning with the clinical need to identify and manage different risk groups. MSE does not inherently allow meaningful risk stratification.

[0032] Alignment with decision-making: clinical decision-making based on mortality risk assessment and / or risk assessment of ICU admission and / or risk assessment of mechanical ventilation requires accurate identification of high-risk individuals (discrimination) and reliable risk predictions (calibration). A fitness function that captures both aspects ensures the model is aligned with the decision-making process, potentially leading to better patient management.

[0033] Holistic evaluation: using both discrimination and calibration provides a more holistic evaluation of the model, capturing different aspects of model quality, which may provide a more nuanced and comprehensive understanding of how well the model is performing compared to MSE, which provides a more one-dimensional assessment.

[0034] In summary, defining the fitness function for mortality risk assessment or, and / or risk assessment of ICU admission, and / or risk assessment of mechanical ventilation based on a combination of model discrimination and calibration ensures that the model is evaluated based on its ability to both correctly classify individuals according to risk and provide reliable risk predictions. This aligns more closely with the clinical goals of mortality risk assessment and / or risk assessment of ICU admission and / or risk assessment of mechanical ventilation and provides a more comprehensive and meaningful evaluation of model quality than traditional MSE minimization.

[0035] In some approaches, a model is usually designed, then discrimination is analyzed, and in some cases, calibration is also analyzed. If the model is not good in validation, then variables may be manually changed, and different trials will be performed until the model is suitable.

[0036] The Cl method for training of the disclosure provides an automatic procedure, with the combination of discrimination and calibration in the model design.

[0037] The Cl method for training, incorporating a fitness function combining discrimination and calibration, provides advantages compared to other solutions, including "Steyerberg EW,Vergouwe Y. Towards better clinical prediction models: seven steps for development and an ABCD for validation" (Eur Heart J. 2014)", or “Bias by censoring for competing events in survival analysis”, (BM J 2022; 378, published on 13th September 2022), which focus primarily on developing and validating clinical prediction models but do not explicitly address the simultaneous assessment of multiple risks (mortality, mechanical ventilation, ICU admission) over a projected time period.

[0038] The Cl method for training integrates the evaluation of multiple critical risks over a defined period (e.g., two months), providing a comprehensive tool for healthcare planning and patient management. The integration goes beyond standard prediction model development, addressing the multifaceted nature of patient care in a hospital setting.

[0039] Typical prediction models assess immediate or near-term risks without a specified future time frame. The Cl method of the present disclosure provides the ability to evaluate risks over a specified future period (e.g., two months) and adds a significant layer of foresight, allowing for better resource allocation and personalized care planning.

[0040] Some approaches may be based on model discrimination, but they do not emphasize its application in the context of multiple risk assessments for diverse outcomes (mortality, mechanical ventilation, ICU admission). The Cl method for training of the present disclosure applies discrimination to ensure accurate classification across multiple outcomes, enhancing the model's utility in a real-world clinical environment where different risks must be managed concurrently. The calibration aspect is often treated separately and not integrated into a holistic fitness function for multiple risk outcomes. Integrating calibration into the fitness function ensures that the model's predictions are reliable and actionable. The method enhances clinical decision-making accuracy by ensuring that predicted probabilities align closely with observed frequencies across different risk assessments.

[0041] The example development steps outlined in Steyerberg and Vergouwe do not specifically address implementing personalized treatment plans based on combined risk assessments. By enabling early identification of high-risk patients and facilitating personalized interventions, the disclosed method offers a tailored approach to patient care. A personalized treatment plan based on a combination of risk assessments enhances patient outcomes and optimizes healthcare resources.

[0042] In a further aspect of the disclosure, a computer program comprising instructions is provided, which, when a computer executes the program, causes the computer to carry out the computer-implemented method for training of the disclosure. The computer or processor may comprise a single processing core or multiple processing cores on a single processor chip or multiple processor chips, in direct communication with each other or in a distributed processing system, executing computer instructions, dedicated hardware, or a combination thereof. Although various operations are described as being performed sequentially or iteratively, in someimplementations, such operations may be executed fully or partially in parallel rather than in sequential iterations. The computer program may be stored in a non-transitory storage unit.

[0043] In a further aspect of the disclosure, a computer program comprising instructions is provided, which, when a computer executes the program, causes the computer to carry out the computer-implemented method for predicting risk of an event according to the disclosure.

[0044] The aspects of the present disclosure allow an improvement of clinical outcomes. The methods and systems disclosed implement statistical techniques and machine learning algorithms to analyze patient data, which enhances clinical decision-making by providing improved patient outcomes. The methods and systems disclosed may integrate with existing medical devices and EHR -electronic health record- systems for continuous data collection and analysis, may employ real-time data processing techniques to assess the risk of patients relating to e.g., mortality, using cause-specific Cox regression models and cumulative incidence functions. The solutions in the disclosure provide accurate risk assessments improving clinical outcomes by providing precise and timely risk assessments. The solutions of the present disclosure may implement automation of risk assessments and integration with existing healthcare systems, reducing the manual effort required by clinicians, allowing them to focus on patient care and leveraging advanced statistical and machine learning techniques. The cited advantages may contribute to enhance patient monitoring, decision-making, and resource allocation in hospitals. The focus on real-time data processing, integration with medical devices, and improvement of clinical workflows underscores the technical nature of the innovation.

[0045] The advantages described in relation to any of the above-mentioned aspects may analogously apply to the rest of the aspects.FIGURES

[0046] Figure 1 shows an example of a computer system comprising means for carrying out the computer-implemented method for training a cause-specific Cox proportional hazards model.

[0047] Figure 2 shows an example calibration plot.

[0048] Figure 3 shows an example computer system 300.

[0049] Figure 4 shows an example risk chart.

[0050] Figure 5 shows the method steps of a computer-implemented method 500 for predicting a risk of an event.

[0051] Figure 6 shows the discrimination of an example prediction model (ROC plot of the mortality prediction model).

[0052] Figure 7 shows the calibration of the example prediction model of figure 6.

[0053] Figure 8 shows the effect of time on the estimated mortality risks for the following times: one week, two weeks, three weeks, four weeks, and two months.DETAILED DESCRIPTION

[0054] Figure 1 shows an example of a computer system 100 comprising means or modules for carrying out the computer-implemented method for training a cause-specific Cox proportional hazards model to predict at least a risk of an event according to the disclosure. The computer system 100 comprises a feature selection module 101 , a -specific Cox proportional hazards module 102, a fitness module 103, a termination criterion module 104, and an optimization module 105. The module 101 may be configured to implement feature selection as described in the present disclosure, for example, configured to select, from a raw set of variables, a set of training variables and a set of validation variables, the set of training variables and the set of validation variables comprising same variables and the same variables being at least: a risk of the event, a demographic information variable, a comorbidity variable and a blood marker variable. A raw set of variables may be fed into the feature selection module 101. The feature selection module may be configured to select a set of variables from which a part may be used as the set of training variables to be input into a cause-specific Cox proportional hazards module 102 configured to implement the cause-specific Cox proportional hazards model. The model may be trained so that a prediction function is provided. A fitness module 103 may be configured to implement a fitness function combining discrimination and calibration. A set of validation variables may be input into fitness module 103 to validate the cause-specific Cox proportional hazards module 102 prediction function. A discrimination value and a calibration value may be computed by the fitness module 103 by using the prediction function with the set of validation variables. The fitness module 103, based on the combination of the discrimination and calibration values, may implement the fitness function to provide a fitness value. A termination criterion may be evaluated by a termination criterion module 104. If a termination criterion is not met, an optimization module 105 may be configured to select a subset of variables, for example, from the set of training variables, to improve the fitness value at a further iteration. At a further iteration, the cause-specific Cox proportional hazards module 102 may receive the subset of variables selected by optimization module 105 to iterate the provision of a new prediction function with new parameters of coefficients. The new prediction function may be evaluated with a subset of validation variables comprising the subset of variables selected by the optimization module, obtaining thereby a further fitness value by the fitness module 103, and a new fitness value may be computed. Once again, if the termination criterion is not met, the optimization module may then select a new subset of variables to improve the fitness value further iteratively. Once the termination criterion is met, the computer-implemented training method may end. Computer means may be provided so that steps can be iterated. The computer means may be in communication with the modules described in the disclosure. The steps of the Cl method may be iterated by the modules described in the present disclosure, where the modules are in wired or wireless communication or may be part of a set of instructions to implement the different modules.

[0055] The raw set of variables

[0056] In examples, the raw set of variables or input variables or input variables dataset are part of a group comprising SEMI-COVID dataset in a hospital. The input variables dataset may not be public and may be located on secure servers. In examples, the standard IEEE Standard Association, "IEEE Recommended Practice for the Quality Management of Datasets for Medical Artificial Intelligence", IEEE Engineering in Medicine and Biology Society, IEEE Std 2801-2022, May 2022 may be followed to create and manage the input database.

[0057] In examples, some of the input variables may be nominal or binary, such as a) demographic information, which may comprise sex, and others may be numerical such as demographic information, which may further comprise one or more of sex, age and body mass index -BMI-; and / or b) Comorbidities, which may further comprise one or more of Hypertension, Diabetes Mellitus, Chronic Kidney Disease, Cardiovascular Disease, Autoimmune Diseases, and Charleston Comorbidity Index -CCI-; and / or c) blood markers which may comprise one or more of: neutrophils, lymphocytes, platelets, dehydrogenase -LDH-, C-reactive protein -CRP-, D-dimer, Albumin, oxygen saturation -SpO2-, Ferritin, Blood Urea Nitrogen -BUN-, Creatinine, Erythrocyte Sedimentation Rate -ESR-, Neutrophil-to-Lymphocyte Ratio -NLR-, Platelet-to-Lymphocyte Ratio -PLR-, Lymphocyte-to-C-Reactive Protein Ratio -LCR- and Systemic Immune-Inflammation Index -SII-; and / or d) dates or times which may comprise one or more of a time to the event, where the event may comprise discharge or death. For example, other "time" variables may comprise date of admission into hospital, date of ICU admission, date of using mechanical Ventilation, date of exit from hospital, date of discharge and date of death.

[0058] In an example, in-hospital data from the previous two months for mortality risk assessment are analyzed. During this period, the patients experienced one of three outcomes: some patients died (event of interest), some patients were discharged alive (competing event), and some patients were still hospitalized by the end of the study period (censored). Excluding censored subjects or patients still hospitalized, selection bias is introduced because all the available data is not being used, leading to inaccurate estimates of the risk of death or discharge. On the other hand, if patients who were discharged alive (competing event) are not considered competing risks bias is introduced because the discharge event impacts the probability of the death event and ignoring it would overestimate the risk of death. Cause-specific Cox regression is designed to handle these complexities effectively. It naturally handles censored data by including censored patients in the risk set-up to the point they are censored, using all available information without introducing selection bias. It also fits separate Cox models for each type of event (death and discharge), accounting for the fact that a patient can only experience one event, thus avoiding competing risk bias by properly incorporating the discharge event's impact on the risk. In contrast, logistic regression is unsuitable for this type of survival analysis because it does not account forthe timing of events, cannot handle censored data appropriately, and typically models only one binary outcome at a time, making it challenging to incorporate competing risks without complex modifications. Therefore, cause-specific Cox regression ensures that all available data is used effectively, providing accurate and unbiased risk estimates for each event type in the context of in-hospital patient outcomes.

[0059] Blood markers offer critical insights into the patient's inflammatory response, coagulation status, organ function, and immune response. Blood markers provide a comprehensive understanding of a disease's severity and progression, enabling risk stratification and outcome prediction. Input variables may comprise SpO2 and CCI, which provide valuable information. SpO2 and CCI may be combined with other input variables to predict in-hospital mortality for patients such as COVID-19 accurately. A model incorporating blood markers along with SpO2 and CCI provides a robust and reliable prediction of COVID-19 mortality. SpO2 provides a snapshot of the patient's respiratory status but does not reflect the underlying physiological processes or the dynamic changes occurring over time. SpO2 does not provide information on inflammation, organ function, or the body's immune response, which are critical in COVID-19 progression and outcomes. Charlson Comorbidity Index -CCI- is useful for assessing the general risk associated with pre-existing conditions but does not account for the acute severity of COVID- 19 or the specific impact of the virus on different organ systems. CCI is a static measure that does not reflect changes in real-time patient conditions. Importance of Blood Markers: Inflammation Indicators: C-Reactive Protein (CRP) and Ferritin: Elevated levels of CRP and ferritin indicate systemic inflammation, which is a critical factor in the severity and progression of COVID-19. Interleukin-6 (IL-6): High levels of IL-6 are associated with severe inflammatory responses and can predict the likelihood of complications such as cytokine storms. Immune Response Markers: Lymphocyte Count: Lymphopenia (low lymphocyte count) is commonly observed in severe COVID-19 cases and is associated with poorer outcomes. Neutrophil-to-Lymphocyte Ratio (NLR): A high NLR is a marker of systemic inflammation and has been shown to correlate with disease severity and mortality. Organ Function Markers: Liver Enzymes (ALT, AST): Elevated liver enzymes can indicate liver dysfunction or damage, which may be associated with poor outcomes in COVID-19. Kidney Function (Creatinine, Blood Urea Nitrogen - BUN): Kidney dysfunction significantly predicts mortality in COVID-19 patients.

[0060] In examples, the input variables comprise sex, age, BMI, CCI, neutrophils, lymphocytes, platelets, LDH, CRP, D-dimer, albumin, and oxygen saturation. The ground truth result may comprise a risk of death, a risk of ICU admission, or a risk of mechanical ventilation.

[0061] For training the model, input variables comprising outliers or missing features may be excluded.

[0062] Some input variables may be provided ranging within predetermined intervals, for example, numerical values of neutrophils, lymphocytes, platelets, LDH, CRP, D-dimer, andalbumin may be categorized. Categorization avoids the normalization of data.

[0063] In some examples, the training of the Cl method of the disclosure was performed by providing as input variables age and oxygen saturation categories from "Petrilli CM, Jones SA, Yang J, Rajagopalan H, O'Donnell L, Chernyak Y, Tobin KA, Cerfolio RJ, Francois F, Horwitz LI: Factors associated with hospital admission and critical illness among 5279 people with coronavirus disease 2019 in New York City: prospective cohort study. BMJ 2020, 369:m1966" and "Mejia F, Medina C, Cornejo E, Morello E, Vasquez S, Alave J, Schwalb A, Malaga G: Oxygen saturation as a predictor of mortality in hospitalized adult patients with COVID-19 in a public hospital in Lima, Peru. PLOS ONE 2021 , 15(12):e0244171". In some examples CCI was dichotomized as low or high to minimize the (Error-Rate) ER-criteria of the Receiver operating characteristic curve (ROC) for optimal mortality discrimination: "Tuty Kuswardhani RA, Henrina J, Pranata R, Anthonius Lim M, Lawrensia S, Suastika K. Charlson comorbidity index and a composite of poor outcomes in COVID-19 patients: A systematic review and meta-analysis. Diabetes Metab Syndr. 2020; 14(6) :2103-9".

[0064] In examples, input variables data become available in sequential order.

[0065] The Cl method for training of the present disclosure may comprise receiving, as a raw set of variables, variables categorized in the three categories: demographic information variables, comorbidity variables, and blood marker variables. Using the three categories provides different advantages:

[0066] Demographic Information Variables include age, sex, and other sociodemographic factors. They can significantly influence the likelihood of adverse health outcomes. For instance, older age and male sex are well-known risk factors for higher mortality and severe disease outcomes.

[0067] Comorbidity Variables: These account for pre-existing health conditions, such as diabetes, hypertension, or heart disease. Comorbidities are critical for assessing risk because they can exacerbate the severity of an illness and increase the likelihood of poor outcomes, such as ICU admission or the need for mechanical ventilation.

[0068] Blood Marker Variables: Blood markers provide objective, quantifiable data about the patient's current health status, including markers of inflammation, organ function, and other critical physiological parameters or variables. These biomarkers can offer early indications of deterioration, guiding timely interventions.

[0069] Using the three categories of variables enhances the model's predictive power. Each variable type contributes unique information: Demographic variables offer baseline risk stratification. Comorbidity variables add context about chronic disease burden. Blood markers provide real-time insights into acute physiological changes.

[0070] Using the three categories allows the model to capture a more comprehensive picture of the patient's health status, leading to more accurate predictions for mortality, ICU admission, andmechanical ventilation.

[0071] Using the three categories of variables allows for capturing diverse aspects of patient health:

[0072] Demographic Information: Reflects broader population-level risk trends and individual baseline risks.

[0073] Comorbidity: Highlights chronic vulnerabilities that may predispose patients to worse outcomes.

[0074] Blood Markers: Indicate acute physiological responses and immediate health status.

[0075] The interaction between these variables can reveal complex health dynamics that a single type of variable might miss.

[0076] Using the three categories allows holistic patient assessment:

[0077] Using all three types of variables ensures a holistic assessment of patient risk. Healthcare decisions, especially in critical care, require comprehensive information to tailor interventions effectively. Omitting any category could lead to an incomplete risk assessment and potentially suboptimal care decisions.

[0078] Using the three categories allows for obtaining clinical relevance:

[0079] In routine practice, clinicians use demographic information, comorbidities, and blood markers to assess patient risk and make treatment decisions. A model that integrates these variables aligns with clinical workflows and decision-making processes, making it more practical and applicable in real-world settings.

[0080] Using the three categories allows interdependencies and synergistic effects:

[0081] The combined use of these variables can capture interdependencies and synergistic effects. For example, an elderly patient (demographic) with diabetes (comorbidity) and elevated inflammatory markers (blood marker) might have a much higher risk of adverse outcomes than indicated by any single variable alone. The model can learn these interactions to provide more nuanced risk predictions.

[0082] Including demographic information, comorbidity variables, and blood marker variables in your model is essential for a thorough and accurate risk assessment. Each type of variable contributes uniquely to understanding patient risk, and their combined use ensures a comprehensive, clinically relevant, and highly predictive model. Th Cl method of the disclosure incorporating these diverse data points outperform models using fewer types of variables, providing robust and reliable predictions for various health outcomes.

[0083] Feature selection by the feature selection module 101

[0084] In examples, selecting a set of training variables from the raw set of variables is performed by eliminating highly correlated variables. The remaining variables, i.e., variables that are not eliminated, may be used as training variables. In other examples, The remaining variables, i.e.,variables that are not eliminated, may be distributed in a set of training variables and a set of validation variables.

[0085] In examples, the raw set of variables is used for feature selection of future data at each step or iteration, where feature selection comprises:- performing univariate analysis to assess the relationship of each feature with the outcome,- using statistical tests (e.g., chi-square tests for categorical variables),- computing a generalized correlation matrix for the input features,- identifying pairs of features with high correlation,- removing redundant features: for highly correlated pairs, retaining the feature that has a stronger univariate association with the outcome or is more clinically relevant,- multicollinearity check: calculating variance inflation factor (VIF) for each feature in the model,- removing features with VIF > 5 to reduce multicollinearity.

[0086] In examples, the feature selection comprises implementing steps A to E as follows:

[0087] A: Redundant feature elimination: Performing univariate analysis to assess the relationship of each feature with the outcome.

[0088] B: Eliminate Highly Correlated Variables: Assess the correlations between variables and remove highly correlated variables to enhance model stability and reduce multicollinearity.- assess association for continuous-continuous variables: use the Pearson correlation coefficient to measure the strength of the linear relationship between continuous variables.- assess association for continuous-ordinal variables: use Kendall’s tau-b coefficient or the spearman rank correlation coefficient if the ordinal variable has many levels.- assess association for continuous-nominal variables: use the point-biserial correlation coefficient for binary nominal variables or calculate point-biserial correlations for each pair of levels if the nominal variable has more than two levels.- assess association for ordinal-ordinal variables: use Kendall’s tau-b coefficient to measure the strength of the relationship between two ordinal variables, if both ordinal variables have many levels, consider using the spearman rank correlation coefficient.- assess association for ordinal-nominal variables: use the rank-biserial correlation coefficient to measure the association between an ordinal variable and a nominal variable.- assess association for nominal-nominal variables: use the phi coefficient for 2x2 contingency tables, and goodman and Kruskal’s lambda for variables with more than two levels.

[0089] C: check for sparse categories: identify features with sparse categories that may contribute to overfitting:- identify features with sparse categories that have very few observations, which can lead to overfitting:- use frequency counts or histograms to detect sparse categories.- set a threshold (e.g., categories with fewer than 5% of total observations) to identify sparse categories.

[0090] D address sparsity issues: combine or transform sparse categories to ensure robust feature representation.

[0091] E: calculate condition number: measure the condition number of the matrix formed by the training variables to ensure numerical stability:- a high condition number (e.g., >30) indicates potential multicollinearity issues.- if the condition number is high, indicating potential multicollinearity issues, repeat steps B to D to remove more highly correlated or redundant features until an acceptable condition number is achieved.

[0092] When a feature set is found, the cause-specific Cox proportional hazard model is updated until the fitness value combining discrimination and calibration is acceptable.

[0093] In examples, stratified random sampling may be used to reduce sampling error in cases where patients can be partitioned into subgroups (i.e., events of interest).

[0094] Given a raw set of variables, and given that highly correlated variables may be eliminated, then a resulting set of variables may be obtained from which 70%-80%, for example 75% of the resulting set of variables may be selected as set of training variables, whereas a 30%-20%, for example, 25%, of the resulting set of variables, may be selected as set of validation variables. Using the same dataset for both training the cause-specific regression model and assessing its performance (based on discrimination and calibration) can lead to overfitting. Separate training and validation sets: to mitigate overfitting, it is essential to use separate datasets for training and validation. The training set fits the model and optimizes its parameters, while the validation set assesses the model's performance independently. This approach ensures that the model's evaluation metrics (discrimination and calibration) reflect its ability to generalize to new data, thereby providing a more accurate and reliable measure of its real-world performance.

[0095] The cause-specific Cox proportional hazard model implemented by the cause-specific Cox proportional hazard module 102

[0096] The cause-specific Cox proportional hazard model, compared to other models for mortality risk assessment (i.e., cox regression models), provides identification of specific causes of failure: traditional survival models typically consider the time until the first occurrence of an event, ignoring the fact that there might be different causes for the failure. In contrast, cause-specific Cox proportional Hazard models allow for identifying and estimating the hazard for each specific cause, allowing for an understanding of the different risks involved. Handling competing risks:cause-specific Cox proportional Hazard models are particularly useful when dealing with competing risks. Competing risks occur when there are multiple potential events or 'causes' that could prevent the occurrence of the event of interest. Traditional survival models might provide biased estimates in the presence of competing risks, whereas cause-specific Cox proportional Hazard models can provide more accurate estimates by addressing each cause separately. Model flexibility: cause-specific Cox proportional Hazard models allow for incorporating timedependent covariates and complex interactions between covariates. This can make the models more flexible and able to handle complex data structures, thus providing a more tailored fit to the data. Better interpretability: by modeling the hazard function for each specific cause, the results can be more easily interpreted in terms of the risk factors for different events, which may help identify specific factors that contribute to different risks, which is valuable in making informed decisions in areas like medical treatment planning. Inclusion of censoring and truncation: like other survival analysis techniques, cause-specific hazard models can also handle right-censored and left-truncated data, which is common in survival analysis. This means that these models can handle situations where the event of interest has not occurred for all subjects during the study period, or subjects entered the study after a time of origin. Potential for enhanced prediction: by understanding the risks associated with different causes, it is possible to provide more targeted predictions and interventions. For example, in a medical context, understanding the specific hazards associated with different diseases can lead to more targeted treatment plans. Avoiding assumption of independence: traditional survival models might require the assumption that competing risks are independent of each other, which might not be the case in many real-world scenarios. Cause-specific Cox proportional hazard models can consider the dependencies between competing risks, providing more robust estimates. In conclusion, cause-specific Cox proportional Hazard models offer a more detailed and accurate approach to risk assessment of mortality and / or mechanical ventilation and / or ICU admission by allowing for the consideration of multiple failure causes, handling competing risks, offering model flexibility, and providing better interpretability. These characteristics often make them more suitable for complex survival data with competing risks than traditional survival models.

[0097] Cause-specific Cox proportional hazard models for mortality risk assessment of in-hospital data provide the following advantages compared to machine learning methods, including logistic regressions: modeling time-to-event data: cause-specific Cox proportional hazard models are specifically designed to model time-to-event data, considering censoring and the timing of events. Machine learning models, like logistic regression, typically model a binary outcome and do not naturally incorporate time-to-event information, leading to a loss of valuable temporal information. Interpretability: cause-specific Cox proportional hazard models provide hazard ratios and survival probabilities that clearly interpret risks over time. Machine learning methods can be more challenging to interpret, especially more complex models like neural networks. For healthprofessionals, understanding how variables relate to survival is often crucial. Handling of censored data: in survival analysis, patients may leave the study or remain event-free at the end of the observation period, leading to censored data. Cause-specific Cox proportional hazard models can handle this right-censoring, whereas most traditional machine learning models, including logistic regression, do not have built-in mechanisms to deal with censoring. Ignoring censored observations can lead to biased estimates. Competing risks: cause-specific Cox proportional Hazard models allow for considering competing risks and the ability to model the hazard for each specific cause. This is important in the context of in-hospital data, where different causes of mortality may be at play. Machine learning methods might not be naturally suited to handle competing risks without additional modifications. Proven methodology: survival analysis, including cause-specific cox proportional hazard models, has a long history in medical statistics and has been extensively validated in the context of mortality risk assessment. This can make health professionals more comfortable using these models, whereas machine learning methods may be viewed as more experimental in this context. Assumption flexibility: cause-specific Cox proportional hazard models can be constructed to accommodate various underlying assumptions regarding the hazards, allowing more flexible modeling of different data types. While machine learning methods can capture complex patterns, they may require more data and might be prone to overfitting, especially when dealing with the relatively small sample sizes often encountered in clinical studies. Predictive accuracy: although machine learning methods are often praised for their predictive accuracy, in the context of survival data with censoring, competing risks, and complex time-dependent covariates, cause-specific Cox proportional hazard models may provide predictions that are just as accurate or even more so. Integration with clinical practice: causespecific Cox proportional hazard models often align better with how health professionals think about risks over time and can be more easily integrated into clinical decision-making processes. Machine learning models might require more specialized knowledge to interpret and apply. Regulatory acceptance: in some jurisdictions, regulatory bodies may have guidelines favoring statistical methods with well-understood properties like cause-specific Cox proportional hazard models, especially in the context of medical research and healthcare. In summary, the preference for cause-specific Cox proportional hazard models over machine learning methods for mortality risk assessment in in-hospital data often comes down to their ability to model time-to-event data accurately, their interpretability, handling of censored data, flexibility in modeling assumptions, and alignment with clinical and regulatory considerations. While machine learning methods have a role to play in predictive modeling, the unique characteristics of survival data often make causespecific Cox proportional hazard models a more natural choice.

[0098] The cause-specific cox proportional hazard model avoids "competing risk bias" compared with the traditional survival analysis models and "selection biases" compared with machine learning methods.

[0099] In examples, the cause-specific Cox proportional hazard model of the disclosure acquires any of the following forms: For example, for a first event "mortality" (event 1), a prediction function may take the form: A1(t)=A01 (t)*exp(0.03xage+0.5xsex+0.4xdiabetes). For example, for a second event "hospital discharge" (event 2), a prediction function may take the form: A2(t)=A02(t)*exp(-0.02xage-0.3xsex-0.2xdiabetes).

[0100] The fitness function implemented by the fitness module 103

[0101] The fitness function is a combination of discrimination and calibration. The fitness evaluation's objective is to maximize the model's predictive performance (cause-specific cox proportional hazard model).

[0102] In some examples, the fitness function evaluates each particle's fitness (see optimization module below) based on a performance metric, for example, AUC+R2, on a validation dataset or set of validation variables.

[0103] In some examples, the discrimination comprises the area under the curve -AUC- or area under the ROC - Receiver Operating Characteristic- curve on the validation dataset for any one of the mentioned risks.

[0104] In examples, the discrimination is calculated as the area under the curve (AUC) of the receiver operator curve (ROC) and may be used to assess accuracy for discrimination between patients discharged alive and dead. The AUC may be computed as:where:

[0106] m is the number of patients who died, n is the number of patients discharged alive, Pi and Pj are the estimated mortality risks of the data points i and j, and l Pi > Pj 0.5 Pi = Pj0 Pi < Pj

[0108] In examples the fitness function is AUC+R2, where AUC is the goodness-of-fit of the model in terms of discrimination and R2is the goodness-of-fit of the calibration plot.

[0109] In examples, the computer-implemented method combines different goodness-of-fit measures, such as g=f1+alpha*f2; where f1 is a primary function and f2 is a secondary function. If the coefficient alpha is one, then they are as important as each other. If the coefficient alpha is less than one, the primary function f1 is the focus of the optimization, while the secondary function f2 may be marginally optimized. In examples, f1 is the AUC of the prediction model tested on the validation set. In examples, R2is the goodness-of-fit of the calibration plot on the validation set.

[0110] Figure 2 shows an example calibration plot. The example calibration plot is a graphical representation used to assess the calibration of a probabilistic prediction system. Calibrationrefers to the agreement between observed outcomes and predictions. A well-calibrated model means that if it predicts an event with a 70% probability, then that event should happen roughly 70% of the time across all instances with that prediction. An example method to create a calibration plot may comprise:- binning predicted probabilities, which may comprise dividing a range of predicted probabilities (typically [0,1]) into bins (e.g., [0, 0.1], [0.1 , 0.2], ... [0.9, 1]); optionally, a bin size may be selected, for example, 10 bins for binary classification problems;- computing observed frequencies: for each bin, calculating the fraction of actual positive outcomes, providing an observed frequency for each bin;- plotting, which may comprise plotting the predicted probabilities, for example, in an x- axis, against the observed frequencies, for example, in a y-axis. Optionally, a midpoint of the bin's range may be used as its x-value for each bin.

[0111] For example, a well-calibrated model may result in points lying along a 45-degree diagonal line, meaning that predicted probabilities match observed frequencies.

[0112] Optionally, visualization enhancements may be performed, such as plotting the 45-degree diagonal line from [0,0] to [1 ,1] on the calibration plot. The line represents perfect calibration.

[0113] In the case where non-uniform bin sizes have been used, the number of samples in each bin may be represented. This can be done using point sizes or added as an extra metric on the side.

[0114] An interpretation of such plot may comprise that points or curves above the diagonal line suggest under-prediction; the model tends to be conservative in its predicted probabilities for those bins. An interpretation of such a plot may comprise points or curves below the diagonal line, indicating over-prediction; the model overestimates the probability of the positive classification for those bins.

[0115] A calibration plot may be used in conjunction with other tools to comprehensively assess a predictive model. In examples, other more sophisticated binning strategies and smoothing techniques, like isotonic regression or beta calibration, may be applied to improve the visualization and interpretation of calibration plots.

[0116] In the example, calibration is applied by estimating the goodness of fit R2of the calibration plot on the validation set.

[0117] In examples the calibration is computed as R2calculation of the calibration plot:

[0118] The cause-specific Cox proportional hazard model outputs risk values (pi) for each variable in the set of validation variables (validation dataset). The risk values pi may be divided into k bins (e.g., deciles; k=10). For each bin (j): the mean risk values pj may be calculated; and the observed frequency, y7, of the risk values may be calculated. Then regression analysis may be performed by for example fitting a simple linear regression model yj=0O+ pipj + ej, with: yObserved frequency of the risk values in bin j; ( p7): Average risk values in bin j; (PO): Intercept of the regression line; (pi): Slope of the regression line; and (ej ): Error term.

[0119] Then the R2value may be given by:

[0120] R2= 1 -_ — ; with (ypred,j predicted value from the regression model for bin j;(y j y) y : overall mean of the observed risk values. In the expression given for / ?2, the numerator is the sum of squared residuals, i.e., the differences between observed and predicted values; and the denominator is the total sum of squares, i.e., the differences between observed values and the mean observed value.

[0121] Termination criterion evaluated by the termination criterion module 104

[0122] The computer-implemented method for training the model is iterated until either: a maximum number of iterations, for example 1000, is reached or until a fitness value increment between consecutive interactions is less than a predefined threshold for a predefined number of consecutive iterations or in other words, until the improvement in the global best fitness falls below a predefined threshold, for example 1e-5, for 100 consecutive iterations.

[0123] Optimization model implemented by the optimization module 105

[0124] In examples, Particle Swarm Optimization (PSO) is implemented as a stochastic optimization method. PSO is an optimization algorithm inspired by the social behavior of birds flocking or fish schooling. It is used to find optimal solutions by iteratively improving candidate solutions with regard to a given measure of quality or fitness. In this context, PSO is used to select variables for the model.

[0125] Parameters and Initialization. Number of Particles: 20+2* K. Each particle is a K bit number (1 bit for each variable). For example, a system with ( =16) variables has 28 particles. Each selected feature is represented as a bit. The PSO selects a set of variables having best fitness value based on calibration and discrimination.

[0126] Particle Representation: Each particle represents a solution encoded as a K-bit binary string, where K is the number of variables available. In the binary string: Each bit indicates a variable's inclusion (1) or exclusion (0) in the model. Population initialization: Initialize a population of 20+2* K randomly.

[0127] Velocity: Each particle has a velocity that determines how its position (solution) is updated.

[0128] Position Update: The velocity of a particle is updated based on three components: 1. Its current velocity. 2. The difference between its current and personal best positions (the best position it has achieved so far). 3. The difference between its current position and the global best position (the best position achieved by any particle in the swarm).

[0129] The position of a particle is updated by applying a transformation to its velocity, convertingit into a probability. This probability is then compared to a random value to decide whether a bit in the binary string will flip (change from 0 to 1 or from 1 to 0).

[0130] An example of the Cl method for training and implementing the optimization model may comprise:- 1. Initialization:Initialize the positions (binary strings) and velocities of all particles randomly,Evaluate the initial fitness of each particle,Identify the initial personal best position for each particle and the global best position,- 2. Iteration: For each particle:- update its velocity using its current velocity, the difference between its current position and personal best, and the difference between its current position and the global best, and update its position based on the updated velocity by determining the probability of each bit flipping and comparing it to a random value,- Evaluate the new fitness of the particle,- update the particle's personal best position if its new fitness is better than its previous best,- update the global best position if any particle's new position has a better fitness than the current global best,- 3. Stopping Criteria: Iterate until either: a maximum number of iterations, for example 1000, is reached; or until a fitness value increment between consecutive interactions is less than a predefined threshold, for a predefined number of consecutive iterations, or in other words, until the improvement in the global best fitness falls below a predefined threshold, for example 1e-5, for 100 consecutive iterations.

[0131] In examples, 10 variables are used, so K = 10. The particles may be represented as:

[0132] - Particle 1 : [1 , 0, 1 , 1 , 0, 0, 1 , 0, 1 , 0]

[0133] - Particle 2: [0, 1 , 0, 1 , 1 , 0, 0, 1 , 0, 1]

[0134] - ...

[0135] In each iteration, the particles' velocities and positions may be updated based on their personal best and global best positions, and their fitness is evaluated on the validation dataset.

[0136] The hyperparameters

[0137] In some examples a final calibration is applied by multiplying a hyperparameter, or coefficient, by any calibrations computed as described herein.

[0138] The computer-implemented method may be implemented using Shiny R.

[0139] Further examples

[0140] Figure 3 shows an example computer system 300. The computer system 300 comprises a feature selection module 301 , a cause-specific Cox proportional hazards module 302, a fitnessmodule 303, a termination criterion module 304 and an optimization module 305. A raw set of variables may be fed into the feature selection module 301 and the raw set of variables may comprise sex, and others may be numerical such as demographic information comprising one or more of the following or all of the following variables or parameters: Age, sex, Body Mass Index (BMI); Comorbidities comprising one or more of the following or all of the following variables or parameters: Hypertension, Diabetes Mellitus, Chronic Kidney Disease, Cardiovascular Disease, Autoimmune Diseases, Charlson Comorbidity Index (CCI); Blood markers comprising one or more of the following or all of the following variables or parameters: Oxygen Saturation (SatO2), C-Reactive Protein (CRP), D-dimer, Lactate Dehydrogenase (LDH), Ferritin, Blood Urea Nitrogen (BUN), Creatinine, Albumin, Erythrocyte Sedimentation Rate (ESR), Neutrophil, Lymphocyte, Platelet, Neutrophil-to-Lymphocyte Ratio (NLR), Platelet-to-Lymphocyte Ratio (PLR)m, Lymphocyte-to-C-Reactive Protein Ratio (LCR), Systemic Immune-Inflammation Index (Sil).

[0141] The feature selection module 301 may be configured to categorize and select the raw input variables into a set of variables from which at least a part may be used as set of training variables to be input into the cause-specific Cox proportional hazards module 302 configured to implement the cause-specific Cox proportional hazards model. The cause-specific Cox proportional hazards model is trained so that a prediction function for "risk of mortality" -first eventtakes the form: A1(t)=A01 (t)*exp(0.03xage+0.5xsex+0.4xdiabetes+ 0.6 x CRP) with CRP being the blood marker C-reactive protein measured in mg / L. For a second event the prediction function for "hospital discharge" (event 2) takes the form: A2(t)=A02(t)*exp(-0.02xage-0.3xsex-0.2xdiabetes- 0.5 x CRP). A set of validation variables "age", sex" and "diabetes" may be input into the fitness module 303 to validate the prediction function "risk of mortality(t)=) fo‘ Ai(u) x exp[- fou(Ai(s) + A2(s)) ds ] du. The prediction model is validated for mortality risk -first event-. Such a prediction may imply estimation of A01 (t) and A02(t), as illustrated in a particular example below, so both the event and the competing event may be used in the calculation.

[0142] The fitness module 303 computes AUC+R2 using the prediction function with the validation variables. A termination criterion may be evaluated by the termination criterion module 404. If a termination criterion is not met, an optimization module based on Particle Swarm Optimization (PSO) 305 selects a subset of variables from the set of training variables to improve the fitness value AUC+R2at a further iteration. At a further iteration, the cause-specific Cox proportional hazards module 302 receives the subset of variables selected by the optimization module PSO 305 to iterate the provision of a new prediction function with new parameters of coefficients. The new prediction function may be evaluated with a subset of validation variables, the subset which corresponds to the subset of variables selected by the PSO, by the fitness module 303, and a new fitness value may be computed. Once again, if the termination criterion is not met, then the optimization module may select a new subset of variables to further improvethe fitness value iteratively with a new set of variables at each iteration, the set of variables optimized by the PSO. Once the termination criterion is met, the computer-implemented method for training ends at 306.

[0143] Once the model is trained, for example, after 2 months, hospital personnel may use the prediction function with variables extracted from a particular subject or patient. The Cl method of the disclosure may provide information, for example, in a graphical user interface -GUI- about the prediction function or variables needed for predicting a particular risk so that the hospital personnel can input the variables into the prediction function to obtain a risk.

[0144] The Cl method for training of the invention may comprise plotting a risk chart. Figure 4 shows an example risk chart. The example risk chart shows risks of mortality within 58 days of hospitalization for a specific sex, for different ages, for different saturation levels and for different CCI. The risk chart may be output by the Cl method for training of the disclosure or by the computer system 100, 300 of the disclosure after the training once relevant predictors or variables for the prediction function are determined by the Cl method for training. For example, the chart may be provided in a graphical user interface -GUI-. The chart represents a guide for hospital personnel to estimate the risk of an event for a particular subject or patient given, for example and in view of figure 4, his / her age, sex, CCI and oxygen saturation.

[0145] Figure 5 shows the method steps of a computer-implemented method 500 for predicting a risk of an event, the event being a specific event being one of: risk of mortality and / or risk of mechanical ventilation, and / or risk of ICU -Intensive Care Unit- admission, the method comprising, in block 501 : providing input variables -the variables which are relevant for the prediction function for the specific event- of a subject to a cause-specific Cox proportional hazards model trained by the Cl method for training according to the disclosure; and, in block 502, obtaining a prediction of the risk of the specific event by the cause-specific Cox proportional hazards model.

[0146] An example use in hospital

[0147] An example hospital may be provided with a computer system 100, 300 with means to train a model as disclosed herein. The hospital may input training variables as described herein and, after a training period, for example 2 months, one or more prediction functions may be obtained by the trained system(s) or model(s). The hospital personnel may start using the trained model(s) to predict different risks for different patients by inputting the variables selected as relevant by the prediction function for each subject. The system(s) or model(s) may continuously be trained in the hospital since, as time evolves, diseases and environmental conditions evolve so that a model that has been trained during a first period may not be useful for a further period. For example, the model(s) in hospital may be trained overnight with new training data compiled during the previous day. The model(s) in hospital may be trained once per month with new training data compiled during the previous month, for example.

[0148] Examples and advantages of different trainings for different risks

[0149] In examples, the present disclosure discloses a computer-implemented method for predicting risk of mortality and / or risk of mechanical ventilation, and / or risk of ICU -Intensive Care Unit- admission, the method comprising implementing the method of training of the disclosure using a first model to predict the risk of mortality, and / or a second model to predict the risk of mechanical ventilation, and / or a third model to predict the risk of ICU admission.

[0150] Therefore, the Cl method for predicting a risk can be run three times, each time with different outputs: mortality, ICU admission, and Intubation. Different features may be selected as relevant for each output so that different prediction functions are obtained.

[0151] A computer system or a computer-implemented method may iterate the training of 3 different models trained to output 3 different risks, providing thereby a first model to predict the risk of mortality, and / or a second model to predict the risk of mechanical ventilation, and / or a third model to predict the risk of ICU admission. Evaluating the three risks may provide several advantages:

[0152] Mortality risk relates to patient survival. Assessing the risk of mortality may be essential for making informed decisions about treatment plans and end-of-life care. ICU Admission Risk: Predicting the likelihood of ICU admission helps in resource allocation and preparedness. Knowing this risk allows hospitals to manage ICU capacity better and ensure that high-risk patients receive timely and appropriate care. Mechanical Ventilation Risk: Mechanical ventilation is a significant intervention with substantial resource implications and potential complications. Predicting this risk aids in planning for necessary eguipment and personnel and discussing treatment options with patients and families.

[0153] The three risks may be interrelated. For example, patients at high risk of ICU admission may also be at high risk of reguiring mechanical ventilation and potentially at higher risk of mortality. An integrated model that assesses all three risks simultaneously may capture the interdependencies more accurately than separate models. A method that assesses all three risks provides a more comprehensive patient risk profile. This holistic view is essential for clinicians to develop more tailored and effective treatment plans rather than relying on fragmented information from separate models. By having a method that includes all three outcomes, clinicians can make more informed decisions about triage, treatment prioritization, and resource allocation. This is particularly important in situations where healthcare resources are limited, such as during a pandemic or in resource-constrained settings. Combining multiple related outcomes into a single model can improve the predictive accuracy of the risk assessment. The model can learn from the correlations between the outcomes, leading to better overall performance compared to using separate models for each outcome. A comprehensive risk assessment helps better communicate with patients and their caregivers about potential future scenarios. This can aid in setting realistic expectations and planning for different outcomes, thereby improving patient care and satisfaction.A method simultaneously assessing multiple outcomes can provide valuable insights for further research and development. It allows for a deeper understanding of the factors influencing each outcome and their interactions, potentially leading to improved medical interventions and risk stratification techniques.

[0154] In summary, integrating the assessment of mortality, ICU admission, and mechanical ventilation risks into a single method is essential for providing a comprehensive, accurate, and actionable risk profile. This holistic approach enhances patient management, optimizes resource allocation, and improves overall healthcare outcomes.

[0155] In a particular example, mortality risk assessment may be provided as follows:

[0156] A data frame of a hospital was analyzed starting from the previous two months. Among1727 subjects, 981 were discharged alive -competing event-, 311 died -event-, and 435 were still hospitalized (censored) when. Selected variables by the PSO were sex, age, body mass index (BMI), Oxygen saturation (SatO2), Neutrophil-to-Lymphocyte Ratio (NLR), and Charlson Comorbidity Index (CCI).

[0157] The absolute mortality risk assessment of COVID-19 patients using Cause-specific Cox regression, where Hazard Raio (HR) or mortality probability equals the exponential of Cox regression coefficients (HRj=exp(Pj)); for j=1 ,... ,K (number of variables).

[0158] The results comprises the probabilities shown in Table 1 :

[0159] Table 1 :

[0160] Table 1 represents the effect of each input variables compared with their own reference value or category. The HR or mortality probability value for each variable only shows increase or decrease of risk compared to the reference interval. The hazard ratio is a measure used in survival analysis to compare the hazard (or risk) of a specific event occurring at any given point in time between two groups. HR = 12 may comprise that an example age group has a 12 times higherhazard (or risk) of an event occurring compared to the reference group. The age group with an HR of 12 has a significantly increased risk of the event (e.g., mortality, hospitalization) compared to the reference age group. Specifically, the event is 12 times more likely to occur in this age group than in the reference group. If the reference group is, for example, individuals aged 30-39, and the age group with HR = 12 is individuals aged 70-79, then individuals aged 70-79 may be 12 times more likely to experience the event compared to those aged 30-39. A hazard ratio of 12 suggests that the age group in question is at a substantially higher risk and may need more intensive monitoring, preventive measures, or treatment to mitigate the risk.

[0161] Figure 6 shows the discrimination of the prediction model, or The ROC plot of the mortality prediction model. Figure 7 shows the calibration of the mortality prediction model. The performance indices of the model are: AUC (c-statistics) = 0.87 [Cl 95%: 0.85-0.89], The risk prediction with a cut-off of 0.32 has a sensitivity and Specificity of 79.4 [Cl 95%: 74.5 - 83.8] and 80.02 [Cl 95%: 77.4 - 82.5] in percentage, respectively. Sensitivity is the ability of the system to correctly identify individuals who died, while Specificity is the ability to identify individuals who were discharged alive correctly. Calibration in the large: -0.1. Calibration slope: 0.98. R2of calibration: 0.46

[0162] Some examples from mortality risk assessment comprise the following data:

[0163] A 74-year-old male patient with an oxygen saturation of 97%, an NLR of 27.57, a CCI of 3, and a BMI of 29.98 was estimated to have an absolute mortality risk of 62%. This patient died after 18 days of hospitalization.

[0164] An 82-year-old female patient with an oxygen saturation of 70%, an NLR of 12.30, a CCI of 2, and a BMI of 24.13 was estimated to have an absolute mortality risk of 93%. This patient died after 18 days of hospitalization.

[0165] A 73-year-old female patient with an oxygen saturation of 90%, an NLR of 12.88, a CCI of 0, and a BMI of 33.39 was estimated to have an absolute mortality risk of 27%. This patient was discharged alive after 60 days of hospitalization.

[0166] A 45-year-old male patient with an oxygen saturation of 89%, an NLR of 2.27, a CCI of 0, and a BMI of 26.58 was estimated to have an absolute mortality risk of 3%. This patient was discharged alive after 13 days of hospitalization.

[0167] In a particular example, the step-by-step formulas for calculating the risk of mortality comprise:

[0168] Step 1: Cause-Specific Hazard Function

[0169] For each cause], the cause-specific hazard function is given by: A,(t I x) = AOj(t)exp(xp7), where: AOj(t) is the baseline hazard for cause j; x is the vector of covariates; j is the vector of regression coefficients for cause j.

[0170] Step 2: Cumulative Hazard Function: The cumulative hazard function for cause ] is: Ay(t Ix)ds, which may be estimated as: Aj(t > where Y(tk) isthe number of individuals at risk just before time tk and dNy(tk) is the number of events of cause j at times tk .

[0171] Step 3: Overall Survival Function

[0172] where K is the number of competing events.

[0173] Step 4: Cumulative Incidence Function (CIF) for Cause-Specific Event

[0174] F (t I x ) can be estimated as: Fj(t I x) = 2k:tfc<ts(tkwhere S(tkI x)is the overall survival function just before time tk. The Cumulative Incidence Function (CIF) for a cause-specific event represents the predicted risk of that specific event occurring by a given time, accounting for competing risks. In the context of competing risks, the CIF quantifies the probability that a particular event (e.g., mortality) will occur before a specified time, given that other types of events might also happen. In the disclosure, j=1 is the event of interest (e.g., mortality), and j=2,... ,K are other competing events (e.g., discharged alive). The calculations required to reach the probabilities is the result of step 4. The covariates (variables for each patient) and the coefficients in addition to time are used in the above formulas to calculate the risk for each subject.

[0175] A combination of the above formulas may provide the following closed-form formula:

[0176] where:- t: Time- x: Vector of covariates- tk: Time points- tp Discrete time points for numerical approximation- tp Time interval between tj and tj-i- dNj tk)'. Number of events of cause j at times tk- Y(tk): Number of individuals at risk just before time tk-Om(ti): Baseline hazard function for cause m at discrete time tj- pm. Vector of regression coefficients for cause m.

[0177] Using j=1 , as the event of interest, the outer sigma is calculated as k-. tk< t. Thus, the time parameter affects a calculated mortality risk. Figure 8 shows the effect of time on the estimated mortality risks for the following times: one week, two weeks, three weeks, four weeks, and two months. Figure 8 shows results using pair-wise Wilcoxon signed-rank tests. In particular, Figure 8 represents a box plot of the predicted mortality risks for different hospitalization times (week 1 , week 2, week 3, week 4, two months). Significant differences with p<0.001 are marked by ***.

[0178] As can be derived from the disclosure, the solutions disclosed in this patent application allow enhancing clinical decision-making and patient care through advanced real-time data processing and integration with medical systems rather than hospital management logistics. The disclosed methods and systems implement statistical techniques and machine learning algorithms to analyze patient data, thereby providing precise and timely risk assessments. The focus on predicting risks such as mortality, mechanical ventilation, and ICU admission directly supports clinical interventions and resource allocation to improve patient outcomes. The solutions allow to continuously collect and process data from existing medical devices and EHR systems, automate risk assessments, and integrate seamlessly into clinical workflows, significantly reducing manual effort required by clinicians and allowing them to prioritize patient care. Thus, these solutions' core objective and application are to advance medical treatment and patient management through data-driven technologies.

[0179] Any of the modules described in any of the computing systems of the disclosure may comprise electronic means, that is, electronic configuration, and / or may be a programmable electronic device such as a Complex Programmable Logic Device, CPLD, a Field Programmable Gate Array, FPGA or an Application-Specific Integrated Circuit, ASIC.

[0180] Examples of a module may be a computer system, which may comprise a memory and a processor, the memory is adapted to store a set of computer program instructions, and the processor is adapted to execute these instructions stored in the memory in order to generate the various events and actions for which the control module has been programmed.

[0181] Examples of a module may comprise specific hardware configured to perform a specific routine or subroutine of a program.

[0182] The memory may be comprised in the processor, e.g. an EEPROM, or may be external. In the case of an external memory, it can be, for example, data storage means such as magnetic disks, e.g., hard disks, optical disks, e.g., DVD or CD, memory cards, flash memory, e.g., pen drives, or solid-state drives, SSD based on RAM, based on flash, etc. Such storage means may be part of the modules of the disclosure and I or arranged remotely, wired or wirelessly connected. In the case of being remotely arranged, the communication established between the modules of the disclosure and the storage means can be ensured by, for example, username I password, cryptographic keys and / or by an SSL tunnel established in the communicationbetween the module and the storage means.

[0183] A set of computer program instructions may be executable by the processor, such as a computer program, and may be stored in a physical storage means, such as those mentioned, but may also be carried by a carrier wave or the carrier medium. The carrier medium can be any entity or device capable of carrying the program, such as electrical or optical, which can be transmitted via electrical or optical cable or by radio or other means. In this way, when the computer program is contained in a signal that can be transmitted directly by means of a cable or other device or means, the carrier medium can be constituted by said cable or another device or means.

[0184] The computer program may be in the form of source code, object code, a code intermediate source and object code such as in partially compiled form or in any other form suitable for use in implementing the method. The carrier may be any entity or device capable of carrying the computer program.

[0185] When the computer program is embodied in a signal that may be conveyed directly by a cable or other device or means, the carrier may be constituted by such cable or other device or means.

[0186] Alternatively, the carrier may be an integrated circuit in which the computer program is embedded, the integrated circuit being adapted for performing, or for use in the performance of, the relevant methods.

[0187] Any one of the modules may be based on a low-power hardware device like a microcontroller, a System-On-Chips, SOC, a Programmable SoC, PSoC or an ASIC, although, in some scenarios, it may be possible to use other hardware like an FPGA, a CPLD or a Digital Signal Processor, DSP. Any one of the modules may also contain different types of embedded memories to store data and program instructions. In addition, any one of the modules may include other electronic components like oscillators or programming interfaces, e.g., JTAG, ICSP.

[0188] Any one of the modules may also be implemented by using different types of electronic devices. Such devices include Central Processing Units, CPUs, microcontrollers, FPGAs, ASIC, or SOCs. CPUs are powerful but consume too much energy for small battery-powered devices. Microcontrollers are usually used for low-power systems because they consume less energy, can be reprogrammed easily, and are powerful enough to carry out the tasks to be performed. FPGAs can be powerful for performing certain deterministic demanding tasks, but development is not as easy as with microcontrollers and they consume more power than other devices due to the need for powering the used logic continuously. ASICs are designed explicitly for specific applications and thus they are extremely powerful, since they have been optimized for such applications, their power consumption can be minimized. However, the cost of developing an ASIC is high, in the order of millions of U.S. dollars, and it may only compensate when a relatively high number of devices are produced. Regarding SoCs, they integrate in a single integrated circuit a powerfulmicrocontroller and several peripherals, e.g., wireless transceivers, what makes them consume more power than traditional microcontrollers.

[0189] The scope of protection is defined in the claims.List of references cited in the disclosure- IEEE Recommended Practice for the Quality Management of Datasets for Medical Artificial Intelligence, IEEE Engineering in Medicine and Biology Society, IEEE Std 2801- 2022, May 2022.- Steyerberg EW, Vergouwe Y. Towards better clinical prediction models: seven steps for development and an ABCD for validation (Eur Heart J. 2014).- Maarten Coemans, et al. Bias by censoring for competing events in survival analysis. BMJ 2022; 378, published on 13th September 2022.- Petrilli CM, Jones SA, Yang J, Rajagopalan H, O'Donnell L, Chernyak Y, Tobin KA, Cerfolio RJ, Francois F, Horwitz LI: Factors associated with hospital admission and critical illness among 5279 people with coronavirus disease 2019 in New York City: prospective cohort study. BMJ 2020, 369:m1966.- Mejia F, Medina C, Cornejo E, Morello E, Vasquez S, Alave J, Schwalb A, Malaga G: Oxygen saturation as a predictor of mortality in hospitalized adult patients with COVID-19 in a public hospital in Lima, Peru. PLOS ONE 2021 , 15(12):e0244171.- Tuty Kuswardhani RA, Henrina J, Pranata R, Anthonius Lim M, Lawrensia S, Suastika K. Charlson comorbidity index and a composite of poor outcomes in COVID-19 patients: A systematic review and meta-analysis. Diabetes Metab Syndr. 2020;14(6):2103-9.

Claims

CLAIMS1. A computer-implemented method for training a cause-specific Cox proportional hazards model to predict at least a risk of an event, wherein the event comprises one of a risk of mortality, a risk of mechanical ventilation, and a risk of ICU -Intensive Care Unit- admission, by mapping the risk of the event to a raw set of variables comprising demographic information variables, comorbidity variables, and blood marker variables; the computer-implemented method comprising: selecting, from the raw set of variables, a set of training variables and a set of validation variables, the set of training variables and the set of validation variables comprising same variables and the same variables being at least: a risk of the event, a demographic information variable, a comorbidity variable and a blood marker variable; inputting the set of training variables into a cause-specific Cox proportional hazards model so that the cause-specific Cox proportional hazards model is trained to output the risk of the event by mapping the risk of the event to at least a demographic information variable, the at least a comorbidity variable and the at least a blood marker variable, providing thereby a prediction function of the cause-specific Cox proportional hazards model; applying a fitness function to the prediction function on the set of validation variables, the fitness function combining calibration and discrimination, obtaining thereby a fitness value; selecting, by a stochastic optimization method and based on the fitness value, a subset of variables from the set of training variables; and iteratively:- inputting the subset of variables into the cause-specific Cox proportional hazards model so that the cause-specific Cox proportional hazards model is updated to map the risk of the event to the subset of variables, providing thereby a further prediction function of the cause-specific Cox proportional hazards model;- applying the fitness function to the further prediction function on a subset of validation variables, the subset of validation variables comprising the subset of variables selected by the stochastic optimization method, obtaining thereby a further fitness value; and- selecting, by the stochastic optimization method and based on the further fitness value, a further subset of variables from the set of training variables;- until a termination criterion is met.

2. The computer-implemented method of claim 1 wherein "selecting, from the raw set of variables, a set of training variables and a set of validation variables" is performed by eliminating at least part of correlated variables from the raw set of variables.

3. The computer-implemented method of claim 1 or 2 wherein the termination criterion comprises one or more of the following criteria:- a maximum number of iterations is reached; or- a fitness value between consecutive interactions is less than a predefined threshold, for a predefined number of consecutive iterations.

4. The computer-implemented method of any one of Claims 1 to 3, wherein the calibration is calculated by a method comprising:- outputting, by the cause-specific cox proportional hazard model, risk values, pi, for each variable in the set of validation variables;- dividing the risk values pi into k bins;- for each bin, j, calculating a mean risk values p7;- calculating an observed frequency , y7, of each mean risk values p7;- performing regression analysis by equating y7to the regression line 00+ 01pj + ej, with: y7observed frequency of the risk values in bin j; p7: mean risk values in bin j; 0: intercept of the regression line; pi : Slope of the regression line; and (ej ): Error term; and- computing R2value as: R2= 1 -2; with ypred,j predicted value from the y i y) regression line for bin j; y : overall mean of the risk values.

5. The computer-implemented method of any one of claims 1 to 4 further comprising plotting a risk chart.

6. The computer-implemented method of any one of claims 1 to 5 implemented for training a first model to predict a risk of mortality, and / or for training a second model to predict a risk of mechanical ventilation, and / or for training a third model to predict a risk of ICU -Intensive Care Unit- admission, providing thereby a first trained model and / or a second trained model and / or a third trained model.

7. A computer system (100) comprising means for carrying out the computer- implemented method for training a cause-specific Cox proportional hazards model to predict at least a risk of an event according to any one of claims 1 to 6.

8. The computer system (100, 300) of claim 7 wherein the means comprise at least:- a feature selection module (101 , 301) configured to select a set of training variables and a set of validation variables from a raw set of variables;- a cause-specific Cox proportional hazards module (102, 302), in communication with the feature selection module (101 , 301), the cause-specific Cox proportional hazards module (102, 302) configured to be trained to map the risk of the event to a set of training variables, the set of training variables comprising at least a demographic information variable, at least a comorbidity variable and at least a blood marker variable, providing thereby a prediction function of a cause-specific Cox proportional hazards model;- a fitness module (103,303) in communication with the cause-specific Cox proportional hazards module (102, 301), the fitness module (103, 303) configured to apply a fitness function to the prediction function on the set of validation variables providing thereby a fitness value;- a termination criterion module (104, 304) configured to evaluate a termination criterion; and- an optimization module (105, 305) in communication with the fitness module (103, 303) and with the termination criterion module (104, 304), the optimization module (105, 302) configured to select by a stochastic optimization method and based on the fitness value, a subset of variables from the set of training variables to optimize the fitness value.

9. A computer-implemented method for predicting a risk of an event, the method comprising obtaining a prediction of the risk of the event by providing input variables of a subject to a cause-specific Cox proportional hazards model trained by the method for training according to any of claims 1 to 6 and obtaining a risk of the event by the causespecific Cox proportional hazards model.

10. The computer-implemented method for predicting a risk of an event of claim 9 wherein the cause-specific Cox proportional hazards model outputs the risk of the event comprising one of: the risk of mortality of the subject, or the risk of ICU admission, or the risk of mechanical ventilation.11 . The computer-implemented method for predicting a risk of an event of claim 9 or 10 wherein the prediction is a 2-month forecast.

12. A computer-implemented method for predicting risk of mortality and / or risk of mechanical ventilation, and / or risk of ICU -Intensive Care Unit- admission, the method comprising implementing the method of any one of claims 9 to 11 when they depend on claim 6 and using the first model to predict the risk of mortality, and / or the second model to predict the risk of mechanical ventilation, and / or the third model to predict the risk of ICU admission.

13. A computer program comprising instructions which, when the program is executed by a computer, causes the computer to carry out the computer-implemented method for training a cause-specific Cox proportional hazards model to predict at least a risk of an event according to any one of claims 1 to 6.

14. A computer program comprising instructions which, when the program is executed by a computer, causes the computer to carry out the computer-implemented method for predicting a risk of an event according to any one of claims 9 to 12.

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