A nomogram model construction method for predicting the risk of sepsis pleural effusion

Abstract

The application discloses a nomogram model construction method for predicting the risk of sepsis pleural effusion, collects clinical and biochemical indexes of sepsis patients, includes MMP8 as a prediction variable, adopts single factor Logistic regression and support vector machine recursive feature elimination (SVM-RFE) double algorithm fusion to screen variables, takes common variables to fit a multi-factor Logistic regression model and draw a nomogram, and finally includes five variables of plasma MMP8, albumin, blood urea nitrogen, lactic acid and APACHE II score. The application firstly applies MMP8 to the risk prediction of sepsis pleural effusion, improves the robustness of variable selection through double algorithm fusion screening, and realizes visual risk assessment by using a nomogram.

Description

Technical Field

[0001] This invention belongs to the field of medical data analysis, specifically relating to a method for constructing a nomogram model to predict the risk of sepsis pleural effusion. Background Technology

[0002] Sepsis is a life-threatening organ dysfunction caused by a dysregulated host response to infection and is one of the leading causes of death in ICU patients. Pleural effusion, a common complication of sepsis with an incidence of 30%-50%, significantly increases the duration of mechanical ventilation, ICU stay, and mortality. Pleural effusion is essentially a clinical manifestation of vascular leakage caused by sepsis-induced impairment of the pulmonary vascular endothelial barrier. Early identification of high-risk patients with pleural effusion is of significant clinical importance for timely intervention and improved patient prognosis.

[0003] Currently, existing technologies for predicting the risk of sepsis pleural effusion mainly include the following categories: (a) Prediction using a single biomarker Traditional inflammatory markers such as C-reactive protein (CRP) and procalcitonin (PCT) have limited predictive power, with AUCs mostly between 0.65 and 0.72. In recent years, matrix metalloproteinase-8 (MMP8) has attracted attention as a sepsis-related biomarker. Studies have shown that MMP8 expression is elevated in sepsis and is associated with poor prognosis in sepsis patients. MMP8 can promote the adhesion of leukocytes to endothelial cells and is a potential therapeutic target for sepsis. However, existing research mainly focuses on the application of MMP8 in the diagnosis or prognostic assessment of sepsis, and there are no reports of using MMP8 to predict the specific complication of pleural effusion in sepsis.

[0004] (ii) Prediction based on scoring system The APACHE II score and SOFA score are commonly used tools for assessing the severity of sepsis. However, these scoring systems integrate multiple physiological parameters and laboratory indicators, aiming to comprehensively assess the patient's condition rather than being specifically designed for pleural effusion. Their predictive power is moderate (AUC 0.70-0.75), and they cannot provide clinicians with individualized risk assessment for pleural effusion.

[0005] (III) Existing nomogram prediction models Nomograms, as a visual predictive tool, have been widely used to predict the risk of sepsis-related complications. For example, studies have developed nomogram predictive models for postoperative intra-abdominal hypertension in sepsis patients (AUC 0.793), bloodstream infection in sepsis patients, acute respiratory distress syndrome (ARDS) in sepsis, and acute kidney injury in sepsis. However, these models all use intra-abdominal hypertension, bloodstream infection, ARDS, or acute kidney injury as predictive endpoints, and none address the specific complication of pleural effusion in sepsis.

[0006] In addition, existing studies have combined MMP8 with other biomarkers in diagnostic prediction models for sepsis, but these studies have not addressed the specific application of MMP8 in predicting the risk of sepsis-related pleural effusion.

[0007] In summary, the main shortcomings of the existing technology include: I. Mismatch of prediction endpoints: Existing sepsis prediction models are mostly aimed at the diagnosis, prognosis or other complications of sepsis itself (such as intra-abdominal hypertension, bloodstream infection, ARDS, acute kidney injury), and there is no nomogram model specifically for predicting the risk of sepsis pleural effusion. Second, the variable selection method is too simple: most existing models only use univariate logistic regression or LASSO regression for variable selection, which easily misses important nonlinear relationships and interactions between variables. III. Lack of Mechanistic Support for Biomarker Selection: Although some studies suggest that MMP8 is associated with sepsis, no studies have yet linked it to the specific complication of sepsis-induced pleural effusion, and there is a lack of a complete translation from molecular mechanisms to clinical prediction. Summary of the Invention

[0008] Therefore, this invention provides a nomogram model construction method for predicting the risk of sepsis pleural effusion, to overcome the shortcomings of existing technologies such as mismatched prediction endpoints, single variable screening methods, and lack of mechanism-supported biomarker selection, including the following steps: Step S1: Screen candidate variables based on univariate logistic regression to obtain preliminary screening variables. The candidate variables are collected from clinical data of sepsis patients, including demographic characteristics, physiological parameters, laboratory indicators, and scoring systems. Step S2: The candidate variables are screened based on support vector machine recursive feature elimination to obtain the optimal feature subset; Step S3: Determine the key variables for the final input regression model based on the initial screening variables and the optimal feature subset; Step S4: Based on the results of fitting the key variables to the multivariate logistic regression model, determine the regression coefficients of the key variables, and construct a nomogram model based on the regression coefficients to calculate the probability of pleural effusion in individual patients.

[0009] Further, in step S1, the demographic characteristics, physiological parameters, laboratory indicators, and scoring system include: The demographic characteristics include age and sex; The physiological parameters include heart rate, mean arterial pressure, respiratory rate, and body temperature; The laboratory indicators include white blood cell count, neutrophil percentage, lymphocyte percentage, platelet count, creatinine, blood urea nitrogen, total bilirubin, albumin, lactate, C-reactive protein, procalcitonin, and plasma MMP8 concentration. The scoring system includes the Acute Physiology and Chronic Health Score II and the Sequential Organ Failure Score.

[0010] Further, in step S1, the process of determining the initial screening variable includes: Based on the results of univariate logistic regression analysis of each candidate variable, with the occurrence of pleural effusion as the dependent variable, the regression coefficient and corresponding significance probability value between each candidate variable and the dependent variable are calculated to determine the candidate variable that meets the condition as the initial screening variable. The dependent variable is a state variable that marks pleural effusion, which is assigned a value of 1 when pleural effusion occurs and a value of 0 when it does not occur.

[0011] Furthermore, in step S2, the support vector machine recursive feature elimination involves using 10-fold cross-validation to evaluate the predictive performance of different feature subsets, so as to determine the feature subset with the smallest cross-validation error as the optimal feature subset.

[0012] Furthermore, in step S3, the key variable is determined based on the intersection of the initial screening variable and the optimal feature subset.

[0013] Further, in step S4, the process of constructing the nomogram model includes: Based on the regression coefficients of key variables, the score corresponding to the range of values ​​for each variable is determined. The score distribution of each variable is directly proportional to the absolute value of its regression coefficient. For variables with positive regression coefficients, higher scores correspond to higher variable values; for variables with negative regression coefficients, higher scores correspond to lower variable values.

[0014] The total score is determined based on the sum of the scores. Based on the correlation between the total score and the probability of pleural effusion, the probability of pleural effusion in an individual patient is determined.

[0015] Further, in step S4, the process of determining the regression coefficients of the key variables includes: Input the key variables into a multivariate logistic regression model to output the fitting results; The model is fitted using the maximum likelihood estimation method to determine the regression coefficient β values ​​for each variable.

[0016] Furthermore, the process of determining the score corresponding to the range of values ​​of the key variable includes: The maximum value of the absolute value of the regression coefficient of the key variable is set as 100 points, and the score range of the other variables is reduced proportionally to the absolute value of their regression coefficients and the maximum value.

[0017] Furthermore, the process of determining the correspondence between the total score and the probability of pleural effusion includes: The key variables are input into a multivariate logistic regression model to output the predicted probabilities.

[0018] Based on the predicted probability, the correspondence between the total score obtained by summing the scores corresponding to the key variable values ​​and P is determined, so that each total score value corresponds to a unique probability of pleural effusion.

[0019] Furthermore, in step S4, the risk type of the pleural effusion is determined based on the probability of the pleural effusion occurring. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating the steps of the nomogram model construction method for predicting the risk of sepsis pleural effusion in this embodiment.

[0021] Figure 2 This is a flowchart of the key variable screening process in this embodiment.

[0022] Figure 3 This is a flowchart illustrating the construction process of the line graph model in this embodiment.

[0023] Figure 4 This is a nodal graph-based clinical application decision-making flowchart in this embodiment. Detailed Implementation

[0024] To make the objectives and advantages of the present invention clearer, the present invention will be further described below with reference to embodiments; it should be understood that the specific embodiments described herein are merely for explaining the present invention and are not intended to limit the present invention.

[0025] Please see Figure 1As shown, it is a flowchart of the steps of the nomogram model construction method for predicting the risk of sepsis pleural effusion in this embodiment.

[0026] This embodiment describes a method for constructing a nomogram model to predict the risk of sepsis-induced pleural effusion, including: Step S1: Candidate variables are screened based on univariate logistic regression to obtain preliminary screening variables. The candidate variables are collected from clinical data of sepsis patients, including demographic characteristics, physiological parameters, laboratory indicators, and scoring systems.

[0027] In the univariate logistic regression, the occurrence of pleural effusion is used as the dependent variable (1 is assigned to the occurrence and 0 is assigned to the absence). The odds ratio, 95% confidence interval and significance probability (p-value) of each candidate variable are calculated. The candidate variable that meets the condition of p-value less than 0.1 is determined as the initial screening variable.

[0028] Specifically, in step S1, the demographic characteristics, physiological parameters, laboratory indicators, and scoring system include: The demographic characteristics include age and sex; The physiological parameters include heart rate, mean arterial pressure, respiratory rate, and body temperature; The laboratory indicators include white blood cell count, neutrophil percentage, lymphocyte percentage, platelet count, creatinine, blood urea nitrogen, total bilirubin, albumin, lactate, C-reactive protein, procalcitonin, and plasma MMP8 concentration. The scoring system includes the Acute Physiology and Chronic Health Score II and the Sequential Organ Failure Score.

[0029] In this embodiment, the plasma MMP8 concentration can be determined by ELISA, chemiluminescence immunoassay, or other equivalent quantitative detection methods. As long as the detection result is expressed in ng / mL, it meets the input requirements of the model of this invention. The detection sample is peripheral venous serum collected within 24 hours of admission of sepsis patients. The APACHE II score is calculated based on the patient's age, 12 physiological indicators (body temperature, mean arterial pressure, heart rate, respiratory rate, oxygenation status, arterial blood pH, serum sodium, serum potassium, creatinine, hematocrit, white blood cell count, and Glasgow Coma Scale) and chronic health status within 24 hours of admission to the ICU. The SOFA score is calculated by summing the functional status of six organ systems within 24 hours of admission to the ICU: respiratory system (oxygenation index), coagulation system (platelet count), liver (total bilirubin), cardiovascular system (mean arterial pressure and dosage of vasoactive drugs), nervous system (Glasgow Coma Scale), and kidneys (creatinine and urine output) from 0 to 4 points respectively.

[0030] Understandably, in the clinical context of treating sepsis patients in the emergency department or ICU, by incorporating a multi-dimensional candidate variable pool that covers demographic characteristics, physiological parameters, laboratory indicators (including plasma MMP8), and scoring systems during the clinical data collection phase, the technical problems of inconsistent candidate variable selection standards and easy omission of key predictive indicators in existing technologies are solved. This achieves the technical effect of comprehensively covering multi-dimensional clinical information of sepsis patients and providing a complete data foundation for subsequent dual-algorithm screening.

[0031] Specifically, step S1, the process of determining the initial screening variable, includes: Based on the results of univariate logistic regression analysis of each candidate variable, with the occurrence of pleural effusion as the dependent variable, the regression coefficient and corresponding significance probability value between each candidate variable and the dependent variable are calculated to determine the candidate variable that meets the condition as the initial screening variable. The dependent variable is a state variable that marks pleural effusion, which is assigned a value of 1 when pleural effusion occurs and a value of 0 when it does not occur.

[0032] In this embodiment, in the univariate logistic regression analysis, the occurrence of pleural effusion is used as the dependent variable, and a logistic regression equation is constructed for each candidate variable: ; Where P is the probability of pleural effusion, β0 is the intercept, βᵢ is the regression coefficient of the i-th candidate variable, and Xᵢ is the measured value of the i-th candidate variable.

[0033] The significance probability value p corresponding to the regression coefficients of each candidate variable is calculated using the Wald test. The χ² statistic of the Wald test is calculated using the following formula: ; Where SE(βᵢ) is the standard error of the regression coefficient βᵢ, and this χ² statistic follows a chi-square distribution with 1 degree of freedom. The p-value is calculated accordingly. When p < 0.1, it is determined that there is a statistically significant association between the candidate variable and the occurrence of pleural effusion, and it is included in the initial screening variable set.

[0034] Understandably, when clinical researchers are faced with a large number of candidate variables and need to screen out those related to the occurrence of pleural effusion, univariate logistic regression is used to perform statistical tests on each candidate variable one by one. This solves the technical problem that single screening methods rely on subjective judgment or clinical experience and lack unified quantitative standards. It achieves the technical effect of objectively screening initial screening variables based on statistical significance thresholds and providing a candidate set for subsequent secondary screening.

[0035] Step S2: The candidate variables are screened based on support vector machine recursive feature elimination to obtain the optimal feature subset.

[0036] The Support Vector Machine Recursive Feature Elimination (SVM-RFE) method employs 10-fold cross-validation to evaluate the predictive performance of different feature subsets, determining the optimal feature subset as the feature subset with the smallest cross-validation error. SVM-RFE recursively sorts features based on the absolute value of their weights after each SVM classifier training iteration, successively removing the features with the smallest weights until all features are removed. The 10-fold cross-validation error of the feature subsets in each iteration is calculated, and the feature subset with the smallest error is selected as the optimal feature subset.

[0037] Specifically, in step S2, the support vector machine recursive feature elimination involves using 10-fold cross-validation to evaluate the predictive performance of different feature subsets, so as to determine the feature subset with the smallest cross-validation error as the optimal feature subset.

[0038] In this embodiment, in the Support Vector Machine Recursive Feature Elimination (SVM-RFE), the entire candidate variable dataset is randomly divided into 10 equal subsets using 10-fold cross-validation. Nine subsets are then selected as the training set and one subset as the validation set, repeated 10 times, ensuring each subset is evaluated once as a validation set. The average cross-validation error of the 10 validation results is used as the prediction performance evaluation metric for the current feature subset. SVM-RFE uses a recursive approach; assuming the entire feature set is F0, in the t-th iteration, based on the current feature subset F... t Train an SVM classifier, calculate the weight wⱼ for each feature j, and calculate the importance score Rⱼ = wⱼ for each feature. ² , where wⱼ is the weight coefficient of the j-th feature in the SVM classification hyperplane, and the larger its absolute value, the greater its contribution to the classification decision. Features are sorted in ascending order according to their importance scores Rⱼ, and the features with the lowest scores (i.e., the least important) are successively removed to obtain F. t+1 The iteration process is repeated until the number of features is 1. The 10-fold cross-validation error of the feature subset in each iteration is calculated, and the feature subset with the smallest average cross-validation error is selected as the optimal feature subset. After SVM-RFE screening, the optimal feature subset contains 11 candidate indicators: potassium ions, creatinine, lactate, blood urea nitrogen, fibrinogen, APACHE II score, hematocrit, albumin, interleukin-6, SOFA score, and plasma MMP8.

[0039] Understandably, when clinical researchers face a large number of candidate variables and need to further screen for variables with high discriminative power, using SVM-RFE combined with 10-fold cross-validation for feature selection and model evaluation solves the technical problem that single statistical test methods are difficult to capture nonlinear relationships and interactions between variables and cannot effectively control the risk of model overfitting. This achieves the technical effect of objectively screening out a subset of features with the best predictive power from high-dimensional data.

[0040] Please see Figure 2 This is a flowchart of the key variable screening process in this embodiment.

[0041] Step S3: Take the intersection of the initial screening variables and the optimal feature subset as the key variable to be input into the final regression model.

[0042] In this embodiment, based on the result of the intersection operation between the initial screening variable set and the optimal feature subset, the intersection is determined to be the key variable finally included in the regression model. After taking the intersection, the initial screening variables (albumin, blood urea nitrogen, lactate, APACHE II score, MMP8, C-reactive protein) and the optimal feature subset (potassium ions, creatinine, lactate, blood urea nitrogen, fibrinogen, APACHE II score, hematocrit, albumin, interleukin-6, SOFA score, and plasma MMP8) share five common variables: plasma MMP8, albumin (Alb), blood urea nitrogen (BUN), lactate (Lac), and APACHE II score.

[0043] Understandably, in the modeling scenario where clinical researchers need to determine the final set of variables to be included in the regression model after completing the initial screening by univariate logistic regression and the secondary screening by SVM-RFE, taking the intersection of the two screening methods as the final key variable solves the technical problem that a single screening method may introduce false positive variables or miss important variables. This achieves the technical effect of utilizing the complementary advantages of the two methods to improve the robustness and reliability of the key variable screening results.

[0044] Please see Figure 3 This is a flowchart of the construction process of the line graph model in this embodiment.

[0045] Step S4: Based on the fitting results of the multivariate logistic regression model to the key variables, determine the regression coefficients of the key variables, and construct a nomogram model based on the regression coefficients to calculate the probability of pleural effusion in individual patients. The fitting result is a multivariate logistic regression equation. The five key variables determined in S3 (plasma MMP8, albumin (Alb), blood urea nitrogen (BUN), lactate (Lac), and APACHE II score) are included in the multivariate logistic regression model. Maximum likelihood estimation is used for fitting, and the regression coefficients are solved using iterative weighted least squares. The fitted multivariate logistic regression equation is then obtained.

[0046] Specifically, in step S4, the process of constructing the nomogram model includes: Based on the regression coefficients of key variables, the score corresponding to the range of values ​​for each variable is determined. The score distribution of each variable is directly proportional to the absolute value of its regression coefficient. For variables with positive regression coefficients, higher scores correspond to higher variable values; for variables with negative regression coefficients, higher scores correspond to lower variable values.

[0047] The total score is determined based on the sum of the scores. Based on the correlation between the total score and the probability of pleural effusion, the probability of pleural effusion in an individual patient is determined.

[0048] In this embodiment, the scores of each variable in the noctilinear plot model are determined in the following way: Let |β| max The maximum value among the absolute values ​​of the regression coefficients of all key variables is given, with each variable's score ranging from 0 to (βᵢ / |β|). max The score range is calculated as 100 points, where the variable with the largest absolute value of its regression coefficient receives the full score of 100 points, and the score ranges for other variables are reduced proportionally. Based on the regression coefficients of each variable determined by the multifactor logistic regression equation in claim 6, |β| max =0.18 (absolute value of the regression coefficient of MMP8). The score distribution for each variable is as follows: MMP8 regression coefficient absolute value is 0.18, obtaining a full score range of 0-100; Lac regression coefficient absolute value is 0.12, with a score range of 0-67; APACHE II regression coefficient absolute value is 0.11, with a score range of 0-61; Alb regression coefficient absolute value is 0.09, with a score range of 0-50; BUN regression coefficient absolute value is 0.08, with a score range of 0-44. The total score is obtained by summing the scores of each variable, with a total score range of 0-425, corresponding to a probability of pleural effusion of 0.05-0.95.

[0049] Understandably, in clinical scenarios where emergency room or ICU doctors need to quickly assess the risk of pleural effusion based on patient test values, this step establishes a correspondence between the total score and the probability of occurrence by converting the regression coefficients of each variable into intuitive scores and summing them to obtain a total score. This solves the technical problem of complex regression formulas in existing technologies being inconvenient for rapid clinical use, and achieves the technical effect of transforming mathematical models into intuitive scoring tools that can be operated at the bedside.

[0050] Specifically, in step S4, the process of determining the regression coefficients of the key variables includes: Input the key variables into a multivariate logistic regression model to output the fitting results; The model is fitted using the maximum likelihood estimation method to determine the regression coefficient β values ​​for each variable.

[0051] In this embodiment, the five key variables (plasma MMP8, albumin, blood urea nitrogen, lactate, and APACHE II score) determined in step S3 are used as independent variables, and the status of pleural effusion (occurrence is assigned a value of 1, absence is assigned a value of 0) is used as the dependent variable to construct a multivariate logistic regression model. The model expression is: ; Where P is the probability of pleural effusion, β0 is the intercept term, and β1 to β n The regression coefficients for each key variable are X1 to X... n These are the measured values ​​of each key variable.

[0052] The model is fitted using the maximum likelihood estimation method, and the regression coefficients are estimated by maximizing the following likelihood function: ; Where Yᵢ is the value of the dependent variable (1 or 0) of the i-th sample, Xᵢ is the vector of measured values ​​of each variable of the i-th sample, and β is the vector composed of all regression coefficients.

[0053] The likelihood function is solved using an iterative weighted least squares method. Iteration stops when the change in regression coefficients between two consecutive iterations is less than a preset convergence threshold. During model fitting, a forward stepwise regression method (based on the AIC criterion) is first used to perform a secondary screening of the five key variables to eliminate variables that do not make significant independent contributions in the multifactor model, ensuring the simplicity of the final model. Simultaneously, the variance inflation factor (VIF) of each variable is calculated to assess multicollinearity among the independent variables. A VIF value less than 5 indicates the absence of significant multicollinearity, and the model estimation results are stable and reliable. Based on the fitting results, the regression coefficient β values ​​and corresponding standard errors (SE) of each key variable are output. The significance probability (p-value) of each coefficient is calculated according to the Wald test, and the Wald test statistic χ² is used. 2 =(β / SE) 2 This statistic follows a chi-square distribution with 1 degree of freedom.

[0054] Understandably, when modeling researchers have completed the screening of key variables and need to quantify the independent contribution of each variable to the risk of pleural effusion, fitting a multivariate logistic regression model using the maximum likelihood estimation method solves the technical problems of univariate analysis being unable to control confounding effects among variables and accurately assessing the independent effects of each variable. It achieves the technical effect of solving the regression coefficients of each variable by maximizing the likelihood function, quantifying the independent contribution of each key variable, and assessing its statistical significance.

[0055] Specifically, the process of determining the score corresponding to the range of values ​​of the key variable includes: The maximum value of the absolute value of the regression coefficient of the key variable is set as 100 points, and the score range of the other variables is reduced proportionally to the absolute value of their regression coefficients and the maximum value.

[0056] In this embodiment, the regression coefficients of the key variables are determined by fitting a multifactor logistic regression model using the maximum likelihood estimation method, assuming |β| max The maximum value among the absolute values ​​of the regression coefficients of all key variables is used. The range of scores for each key variable is determined according to the following formula: ; Where βᵢ is the regression coefficient of the i-th key variable, |β| max The value of |β| is the maximum absolute value among all regression coefficients; the variable with the largest absolute value of its regression coefficient receives the full score of 100, and the scores of the other variables are determined by the ratio of their absolute regression coefficients to |β|. max The proportion is linearly reduced. For any specific value of each variable within its range, linear interpolation is used to determine the corresponding score, ensuring a linear correspondence between the variable's value and its score. Specifically, let the minimum value of a variable be X. minCorresponding score P min The maximum value is X max Corresponding score P max Then, the score p corresponding to any value x of the variable is determined by the following linear interpolation formula: ; The sum of the scores for each variable is the total score. The larger the range of scores for a variable, the greater its contribution to the total score. This reflects that the larger the absolute value of the regression coefficient of that variable, the stronger its influence on the probability of pleural effusion, thus obtaining a wider range of score scales in the nomogram.

[0057] Understandably, in the process of drawing nomograms, it is necessary to standardize the regression coefficients of each variable to construct a unified scoring scale. By normalizing the scoring based on the maximum absolute value of the regression coefficient, the technical problem of different variables being unable to be uniformly quantitatively compared in the same nomogram due to the different dimensions and ranges of the regression coefficients is solved. This achieves the technical effect of ensuring that the contribution of each variable to the total score is proportional to its actual influence on the probability of pleural effusion, and that the relative proportion of the scores of each variable in the nomogram accurately reflects its statistical weight.

[0058] Specifically, the process of determining the correspondence between the total score and the probability of pleural effusion includes: The key variables are input into a multivariate logistic regression model to output the predicted probabilities.

[0059] Based on the predicted probability, the correspondence between the total score obtained by summing the scores corresponding to the key variable values ​​and P is determined, so that each total score value corresponds to a unique probability of pleural effusion.

[0060] In this embodiment, the intercept term β0 and regression coefficients β1 to β2 of the multifactor logistic regression model determined by fitting are used. n The total score corresponds to the linear predicted value as follows: (The formula is missing from the original text.) Let the score of the i-th variable be Pointsᵢ, then the total score Total Points = ΣPointsᵢ. According to the score calculation formula, Pointsᵢ = (βᵢ / |β| max The total score and Logit(P) show a linear relationship: 100 × (normalized contribution corresponding to the variable value). ; Where C is a constant determined by the normalized contribution of each variable value during the nomogram design. Substituting the above Logit(P) into the Logistic regression probability transformation formula: ; The probability P of pleural effusion can then be uniquely calculated from the total score. Based on the above formula, a one-to-one correspondence is established between the total score and P, ensuring that each total score value corresponds to a unique probability of pleural effusion.

[0061] Understandably, when clinicians make clinical decisions based on the corresponding risk probabilities derived from the patient's total score, establishing a one-to-one correspondence between the total score and the probability of pleural effusion based on the inverse function of logistic regression solves the technical problem that the total score in the nomogram cannot be directly converted into a clinically understandable risk probability and that clinicians have difficulty comparing the score results with the decision threshold. This achieves the technical effect of transforming the nomogram from a scoring tool into a clinical decision support tool that can directly quantify individual risk probabilities.

[0062] Specifically, step S4 further includes determining the risk type of the pleural effusion based on the probability of its occurrence.

[0063] The probability P of pleural effusion output by the nomogram model is a continuous value between 0 and 1, which itself is a quantitative estimate of the likelihood of pleural effusion in an individual patient. To achieve stratified guidance for clinical decision-making, this embodiment presets three risk levels—low risk, medium risk, and high risk—based on the range of predicted probability P: low risk when P < 0.5, medium risk when 0.5 ≤ P < 0.75, and high risk when P ≥ 0.75. This risk level threshold is determined based on the Youden exponent maximization principle, ensuring that each predicted probability P can be uniquely mapped to its corresponding risk level. Thus, based on the predicted probabilities output by the nomogram model, the continuous probability values ​​are discretized into risk stratification results that are easy to operate clinically.

[0064] Understandably, in ICU clinical decision-making scenarios, existing technologies only provide continuous probability values ​​and lack risk level classification standards, making it difficult for clinicians to directly formulate differentiated treatment strategies based on probability results. This solution maps continuous probabilities to three risk levels: low, medium, and high, realizing the transformation from probability values ​​to actionable decision recommendations. This enables clinicians to quickly formulate corresponding imaging examination plans and intervention measures based on risk levels, improving the clinical operability and decision-making efficiency of the model output.

[0065] Example 1: Variable Selection and Model Building (1) Research subjects Forty sepsis patients admitted to the ICU of a tertiary hospital from January 2023 to June 2024 were collected, along with 12 healthy individuals as a control group. The sepsis patients were divided into two groups based on whether pleural effusion (confirmed by ultrasound or chest X-ray) occurred within 72 hours of ICU admission: ① Pleural effusion group (n=25): 14 males and 11 females, with an average age of (62.3±12.8) years; ② No pleural effusion group (n=15): 8 males and 7 females, with an average age of (58.7±14.2) years.

[0066] (2) Candidate variables The initial selection included 32 candidate variables, including: ① Demographic characteristics: age, sex; ② Physiological parameters: heart rate, mean arterial pressure, respiratory rate, body temperature; ③ Laboratory indicators: white blood cell count, neutrophil percentage, lymphocyte percentage, platelet count, creatinine (Cr), blood urea nitrogen (BUN), total bilirubin (TBil), albumin (Alb), lactate (Lac), C-reactive protein (CRP), procalcitonin (PCT), and plasma MMP8. ④ Scoring systems: APACHE II scoring, SOFA scoring.

[0067] (3) Variable selection results ① Univariate Logistic Regression Screening (p<0.1): Six variables were retained—Alb (OR=0.82, 95%CI 0.74-0.91, p<0.001), BUN (OR=1.15, 95%CI 1.06-1.25, p=0.002), Lac (OR=1.28, 95%CI 1.12-1.47, p=0.001), APACHE II (OR=1.12, 95%CI 1.05-1.20, p=0.001), MMP8 (OR=1.18, 95%CI 1.08-1.29, p<0.001), and CRP (OR=1.02, 95%CI 1.00-1.04, p=0.058). ②SVM-RFE screening (10-fold cross-validation): The optimal feature subset contains 5 variables—Alb, BUN, Lac, APACHE II, and MMP8; ③ Intersection: The final variables included in the model are 5 – Alb, BUN, Lac, APACHE II, and MMP8.

[0068] (4) Construction of nomogram model Based on the above five variables, a multivariate logistic regression model was fitted, and the results are as follows: MMP8: β=0.18, OR=1.20 (95%CI 1.08-1.33), p=0.001; Alb: β=-0.09, OR=0.91 (95%CI 0.85-0.97), p=0.004; BUN: β=0.08, OR=1.08 (95%CI 1.01-1.16), p=0.028; Lac: β=0.12, OR=1.13 (95%CI 1.03-1.24), p=0.012; APACHE II: β=0.11, OR=1.12 (95%CI 1.04-1.20), p=0.003.

[0069] Regression coefficients, standard errors, and Wald χ² for each variable 2 The values ​​and p-values ​​are as follows: MMP8 (β=0.18, SE=0.055, χ²) 2 =10.71, p=0.001), Alb (β=-0.09, SE=0.031, χ 2 =8.43, p=0.004), BUN (β=0.08, SE=0.036, χ 2 =4.94, p=0.028), Lac (β=0.12, SE=0.048, χ 2 =6.25, p=0.012), APACHE II (β=0.11, SE=0.037, χ 2 =8.84, p=0.003). The VIF values ​​for all variables are <5, indicating that there is no significant multicollinearity.

[0070] Model formula:

[0071] The model AUC was 0.821 (95% CI 0.72–0.91).

[0072] (5) Drawing of line graphs Use the `rms` package in R to create a line graph. The score assignment for each variable is as follows: MMP8 (ng / mL): 5→0 points, 10→25 points, 15→50 points, 20→75 points, 25→100 points; Alb (g / L): 20→100 points, 25→75 points, 30→50 points, 35→25 points, 40→0 points; BUN (mmol / L): 2→0 points, 5→25 points, 10→50 points, 15→75 points, 20→100 points; Lac (mmol / L): 1→0 points, 2→25 points, 4→50 points, 6→75 points, 8→100 points; APACHE II (scores): 5→0, 10→25, 15→50, 20→75, 25→100.

[0073] The scores of each variable between adjacent assignment points are determined by linear interpolation, as shown in the following formula: ; in The variable to be scored is the detected value (e.g., MMP8 = 12 ng / mL). This is the lower limit of the interval containing this variable (10 ng / mL). This represents the upper limit of the interval containing this variable (15 ng / mL). The score corresponding to the lower limit (25 points) This is the score corresponding to the upper limit (50 points). The score of the variable to be calculated For example, when the MMP8 detection value is 12 ng / mL, the score is calculated linearly between 10 ng / mL (25 points) and 15 ng / mL (50 points) = 25 + (12-10) / (15-10) × (50-25) = 35 points.

[0074] A total score of 0-425 corresponds to a probability of pleural effusion of 0.05-0.95.

[0075] Example 2: Model Validation and Evaluation (1) Internal validation (Bootstrapping) Due to the limited sample size (40 cases) in this embodiment, the bootstrapping method (1000 resampling times) was used for internal validation. The original dataset was not split into training and validation sets to fully utilize the limited sample size to evaluate the model's optimism bias and generalization ability. The original AUC was 0.821, the corrected AUC was 0.809, and the optimism bias was 0.012. The model shows no significant overfitting and exhibits good generalization ability.

[0076] (2) Calibration assessment The calibration curves show good agreement between the predicted probability and the actual incidence: Hosmer-Lemeshow test: χ² 2 =8.23, p=0.412, indicating good calibration; The mean absolute error (MAE) of 0.032 indicates that the deviation between the predicted probability and the actual occurrence rate is small.

[0077] (3) Clinical utility analysis (DCA) The DCA curve shows that, within the threshold probability range of 0.2-0.8, the net benefit of the noctilinear plot model is higher than that of the "ALL" and "NONE" strategies. When the threshold probability is 0.5, the model's net benefit is 0.35, meaning that using this model for every 100 patients can avoid 35 unnecessary interventions.

[0078] (4) Determination of risk stratification threshold In this embodiment, the risk stratification threshold is determined based on the following method: First, a receiver operating characteristic (ROC) curve is plotted using the total score as the test variable and the occurrence of pleural effusion as the state variable. The Youden Index (sensitivity + specificity - 1) is calculated for different total score cutoff points, and the total score cutoff point corresponding to the maximum Youden Index is selected as the optimal threshold for distinguishing between 'high risk' and 'low risk'. Calculations show that the total score corresponding to the maximum Youden Index is 300 (corresponding to a prediction probability of approximately 0.75), meaning that the model's overall effectiveness in distinguishing between the occurrence and absence of pleural effusion is optimal when the total score is >300. Simultaneously, referring to the results of decision curve analysis (DCA), the model exhibits a positive net benefit within the threshold probability range of 0.2-0.8. Based on the combined results of Youden's Index maximization and DCA analysis, and taking into account the clinical practice logic of 'high-risk requires active intervention, and medium-risk requires close monitoring,' this embodiment defines a total score >300 as high risk, 200-300 as medium risk, and <200 as low risk. This threshold determination method balances statistical optimality with clinical operability, ensuring the scientific validity and clinical applicability of risk stratification.

[0079] (5) Recommendation of decision threshold Based on the overall score of the nomogram, the following decision thresholds are recommended: Low risk: Total score <200 points (predicted probability <0.5), close observation is recommended, no special treatment required; Medium risk: Total score 200-300 (predicted probability 0.5-0.75), it is recommended to have a follow-up ultrasound within 24-48 hours; High risk: Total score > 300 points (predicted probability > 0.75), it is recommended to have an ultrasound immediately to confirm and consider preventive intervention.

[0080] Comparative Example 2-1: Univariate Prediction Model vs. Multivariate Noctilinear Plot Model The univariate predictive model containing only MMP8 had an AUC of 0.783 (95% CI 0.67–0.89), significantly lower than the AUC of 0.821 of the multivariate nomogram model (DeLong test p = 0.028). Furthermore, the univariate model cannot provide clinicians with a comprehensive risk assessment, while the nomogram model can integrate information from multiple indicators, providing a more comprehensive risk prediction.

[0081] Comparative Example 2-2: Using only Logistic Regression to screen variables versus using a dual-algorithm fusion screening. If only univariate logistic regression (p<0.1) is used to screen variables, six variables will ultimately be included (including C-reactive protein). The constructed model has an AUC of 0.798, slightly lower than the model screened using the dual-algorithm fusion (AUC=0.821). Furthermore, CRP was removed from the multivariate model (p=0.312). This indicates that the dual-algorithm fusion screening can effectively avoid including insignificant variables, improving the model's simplicity and interpretability.

[0082] The model performance comparison is shown in Table 1, which lists the model performance metrics. Table 1: Model Performance Metrics

[0083] Please see Figure 4 This is a nodal graph representing the clinical application decision-making process in this embodiment.

[0084] Example 3: Clinical decision validation of risk stratification using a nomogram model Example 3-1: Management of Low-Risk Patients Patient Zhang, male, 52 years old, was admitted to the hospital due to sepsis secondary to community-acquired pneumonia. Upon admission to the ICU, peripheral venous blood was collected, and plasma MMP8 was 8.5 ng / mL, Alb was 35 g / L, BUN was 5.2 mmol / L, Lac was 1.8 mmol / L, and APACHE II score was 10. The values ​​of these five variables were input into a nomogram model. MMP8 corresponded to approximately 20 points, Alb approximately 25 points, BUN approximately 15 points, Lac approximately 10 points, and APACHE II approximately 20 points. The sum of the variable scores yielded a total score of 90 points. According to the risk stratification criteria, a total score of 90 points < 200 points was considered low risk. The clinicians adopted a close observation strategy, without special treatment, and continued anti-infection and organ support therapy according to the standard sepsis protocol. The patient underwent a follow-up chest CT scan on the 3rd day after admission to the ICU, which showed no pleural effusion. The patient's condition gradually improved, and the patient was transferred out of the ICU on the 7th day.

[0085] Example 3-2: Management of intermediate-risk patients Patient Li, male, 65 years old, was admitted to the hospital due to biliary tract infection complicated by sepsis. Upon admission to the ICU, peripheral venous blood was collected, and plasma MMP8 was 16.2 ng / mL, Alb was 28 g / L, BUN was 14.5 mmol / L, Lac was 3.8 mmol / L, and the APACHE II score was 18. The values ​​of these five variables were input into a nomogram model. MMP8 corresponded to approximately 55 points, Alb approximately 50 points, BUN approximately 65 points, Lac approximately 45 points, and APACHE II approximately 60 points. The sum of all variable scores yielded a total score of 275 points. According to the risk stratification criteria, a score of 200 ≤ 275 ≤ 300 points was classified as medium risk. Based on this, the clinician arranged a bedside chest ultrasound examination within 24 hours. The ultrasound showed a small amount of pleural effusion on the right side (about 2.5 cm deep). Because the amount of effusion was small and the patient did not have obvious respiratory distress, thoracentesis was not performed at the time. The patient continued to be closely observed and a follow-up ultrasound was performed 48 hours later. The effusion did not increase significantly and the patient's condition was stable.

[0086] Example 3-3: Management of High-Risk Patients Patient Wang, male, 71 years old, was admitted to the hospital due to urinary tract infection complicated by sepsis. Upon admission to the ICU, peripheral venous blood was collected, and plasma MMP8 was 22.5 ng / mL, Alb was 22 g / L, BUN was 18.2 mmol / L, Lac was 6.5 mmol / L, and the APACHE II score was 24. The values ​​of these five variables were input into a nomogram model. MMP8 corresponded to approximately 90 points, Alb approximately 80 points, BUN approximately 85 points, Lac approximately 80 points, and APACHE II approximately 85 points. The sum of all variable scores yielded a total score of 420 points. According to the risk stratification criteria, a total score of 420 points > 300 points, indicating a high risk. The clinician immediately arranged a bedside chest ultrasound, which revealed moderate bilateral pleural effusion (approximately 5.5 cm on the right and 4.8 cm on the left). The patient also presented with tachypnea (RR 28 breaths / min) and decreased oxygenation (PaO2 / FiO2 = 220 mmHg). Based on the ultrasound results and clinical symptoms, a right thoracentesis was immediately performed, draining approximately 450 mL of bloody fluid. Postoperatively, the patient's dyspnea and oxygenation significantly improved.

[0087] Comparative Example 3-1: High-risk patients did not receive model-guided delayed treatment A patient named Zhao (another sepsis patient admitted to the ICU in the same batch, with an APACHE II score of 23, MMP8 21.8 ng / mL, Alb 23 g / L, BUN 17.5 mmol / L, and Lac 5.9 mmol / L upon admission to the ICU) with similar baseline characteristics to Wang in the example was selected. Zhao's total score was 405, which should have been considered high-risk and recommended immediate ultrasound examination. However, the clinician did not use a nomogram model for risk assessment, but only followed the routine treatment procedure, performing daily vital sign monitoring and chest X-ray examinations every three days. On the second day after admission to the ICU, the patient developed shortness of breath (RR 30 breaths / min) and a decreased oxygenation index (PaO2 / FiO2 = 195 mmHg). Bedside ultrasound showed bilateral massive pleural effusion (approximately 7.5 cm deep on the right side). Emergency thoracentesis was performed, draining approximately 800 mL of hemorrhagic fluid. Compared to Example 3, the patients in this comparative example experienced delayed intervention, resulting in a significant progression of pleural effusion, with drainage volume nearly doubling (800 mL vs 450 mL). They also exhibited marked respiratory impairment and their ICU stay extended to 13 days. Comparative Example 3-2: Risk Stratification Comparison between Single Indicator MMP8 and Nodal Chart Model A sepsis patient, Mr. Sun, was selected. Upon admission to the ICU, his plasma MMP8 level was 18.5 ng / mL. Further testing revealed other indicators: Alb was 32 g / L, BUN was 6.8 mmol / L, Lac was 2.1 mmol / L, and his APACHE II score was 12, with a total score of only 165, indicating a low-risk diagnosis. Subsequent clinical observation confirmed that the patient did not develop pleural effusion.

[0088] The above embodiments and comparative examples demonstrate that using the nomogram model constructed in this invention to stratify sepsis patients by risk and adopting differentiated clinical treatment strategies based on risk levels can achieve the following beneficial effects: (1) High-risk patients: Through model early warning and timely imaging examinations, pleural effusion can be detected and intervened in the early stage, avoiding the situation of passive treatment only after the effusion has progressed to a large extent, reducing drainage volume and hospitalization time, and improving prognosis; (2) Medium-risk patients: By identifying patients through the model and completing imaging re-examination within 24-48 hours, it is possible to promptly detect pleural effusions that require intervention and avoid unnecessary invasive procedures on negative patients, thus achieving accurate monitoring; (3) Low-risk patients: By excluding high-risk patients through model assessment, unnecessary imaging examinations and waste of medical resources are avoided, which is in line with the principles of precision medicine and health economics; (4) Multivariate model is superior to single indicator: The 5-variate nomogram model including MMP8 has higher specificity than the single MMP8 indicator. While ensuring sensitivity, it significantly reduces the false positive rate and avoids unnecessary medical intervention.

[0089] The technical solution of the present invention has been described above with reference to the preferred embodiments shown in the accompanying drawings. However, it will be readily understood by those skilled in the art that the scope of protection of the present invention is obviously not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will all fall within the scope of protection of the present invention.

Claims

1. A method for constructing a nomogram model to predict the risk of sepsis-induced pleural effusion, characterized in that, Includes the following steps: Step S1: Screen candidate variables based on univariate logistic regression to obtain preliminary screening variables. The candidate variables are collected from clinical data of sepsis patients, including demographic characteristics, physiological parameters, laboratory indicators, and scoring systems. Step S2: The candidate variables are screened based on support vector machine recursive feature elimination to obtain the optimal feature subset; Step S3: Determine the key variables for the final input regression model based on the initial screening variables and the optimal feature subset; Step S4: Based on the results of fitting the key variables to the multivariate logistic regression model, determine the regression coefficients of the key variables, and construct a nomogram model based on the regression coefficients to calculate the probability of pleural effusion in individual patients.

2. The method for constructing a nomogram model for predicting the risk of sepsis-induced pleural effusion according to claim 1, characterized in that, In step S1, the demographic characteristics, physiological parameters, laboratory indicators, and scoring system, include: The demographic characteristics include age and sex; The physiological parameters include heart rate, mean arterial pressure, respiratory rate, and body temperature; The laboratory indicators include white blood cell count, neutrophil percentage, lymphocyte percentage, platelet count, creatinine, blood urea nitrogen, total bilirubin, albumin, lactate, C-reactive protein, procalcitonin, and plasma MMP8 concentration. The scoring system includes the Acute Physiology and Chronic Health Score II and the Sequential Organ Failure Score.

3. The method for constructing a nomogram model for predicting the risk of sepsis-induced pleural effusion according to claim 2, characterized in that, In step S1, the process of determining the initial screening variable includes: Based on the results of univariate logistic regression analysis of each candidate variable, with the occurrence of pleural effusion as the dependent variable, the regression coefficient and corresponding significance probability value between each candidate variable and the dependent variable are calculated to determine the candidate variable that meets the condition as the initial screening variable. The dependent variable is a state variable that marks pleural effusion, which is assigned a value of 1 when pleural effusion occurs and a value of 0 when it does not occur.

4. The method for constructing a nomogram model for predicting the risk of sepsis-induced pleural effusion according to claim 1, characterized in that, In step S2, the support vector machine recursive feature elimination involves using 10-fold cross-validation to evaluate the predictive performance of different feature subsets, so as to determine the feature subset with the smallest cross-validation error as the optimal feature subset.

5. The method for constructing a nomogram model for predicting the risk of sepsis pleural effusion according to claim 1, characterized in that, In step S3, the key variable is determined based on the intersection of the initial screening variable and the optimal feature subset.

6. The method for constructing a nomogram model for predicting the risk of sepsis pleural effusion according to claim 1, characterized in that, In step S4, the process of constructing the nomogram model includes: Based on the regression coefficients of key variables, the score corresponding to the range of values ​​for each variable is determined, where the score distribution of each variable is directly proportional to the absolute value of its regression coefficient; for variables with positive regression coefficients, higher scores correspond to higher variable values; for variables with negative regression coefficients, higher scores correspond to lower variable values. The total score is determined based on the sum of the scores. Based on the correlation between the total score and the probability of pleural effusion, the probability of pleural effusion in an individual patient is determined.

7. The method for constructing a nomogram model for predicting the risk of sepsis pleural effusion according to claim 6, characterized in that, In step S4, the process of determining the regression coefficients of the key variables includes: Input the key variables into a multivariate logistic regression model to output the fitting results; The model is fitted using the maximum likelihood estimation method to determine the regression coefficient β values ​​for each variable.

8. The method for constructing a nomogram model for predicting the risk of sepsis-induced pleural effusion according to claim 7, characterized in that, The process of determining the score corresponding to the range of values ​​of the key variable includes: The maximum value of the absolute value of the regression coefficient of the key variable is set as 100 points, and the score range of the other variables is reduced proportionally to the absolute value of their regression coefficients and the maximum value.

9. The method for constructing a nomogram model for predicting the risk of sepsis-induced pleural effusion according to claim 8, characterized in that, The process of determining the correspondence between the total score and the probability of pleural effusion includes: Input the key variables into a multivariate logistic regression model to output the predicted probabilities; Based on the predicted probability, the correspondence between the total score obtained by summing the scores corresponding to the key variable values ​​and P is determined, so that each total score value corresponds to a unique probability of pleural effusion.

10. The method for constructing a nomogram model for predicting the risk of sepsis-induced pleural effusion according to claim 6, characterized in that, In step S4, the risk type of the pleural effusion is determined based on the probability of the pleural effusion occurring.

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