Computer-implemented method to predict individual reference change values

Abstract

A computer-implemented non-parametric method for estimating the upper and lower bounds of an Individual Reference Change Value, I-RCV, for a measured test value of a subject, said method using a longitudinal data set of corresponding test values for said subject and at least three different independent subjects, and applying two I-RCV models on said longitudinal data to estimate said upper and lower bounds with a symmetry property between said upper and lower bounds, characterized in that the two I-RCV models include the observed time lags between consecutive measurements in the longitudinal data as a covariate in the model to determine a difference between the two consecutive measurements on the same subject.

Description

[0001] Computer-implemented method to predict Individual Reference Change Values Field of Invention ^e field of the invention relates to a computer-implemented method to predict Individual Reference Change Values, I-RCV. Particular embodiments relate to a use of models used in predicting the I-RCV to determine whether a measured change of a test value is within or outside of the I-RCV of said subject. Background In clinical practice, current symptoms, historical health records, results of laboratory tests, among others, are commonly incorporated for drawing patients’ diagnosis. From this list, laboratory tests play a crucial role in translating the symptoms present in a patient. In the current routine, the numerical results of the tests are usually compared with a Population Reference Interval, abbreviated as PRI, which represents a range that is expected from a healthy population. In addition to this PRI, medical professionals are often also interested in analyzing the clinical importance of the changes between multiple test results. The analysis of changes between test results can provide valuable information about the presence or progression of a disease and the analysis can indicate whether a particular therapy is achieving the desired outcome. The interpretation of the PRI reading and the observation of those important changes, if any, would then help translating the test results and link them to the reported symptoms and health records. Therefore, diagnoses and decision-making regarding treatment adjustment can be made more accurately. As the PRI only provides a healthy reference range without looking into the measurement changes, the concept of Reference Change Value, abbreviated as RCV, had been previously proposed so that it can describe an important change between two successive results of a clinical test [1]. Such changes can be clinically important and should be ’flagged’ for further examination, yet they possibly cannot be detected by the PRI and they may be ignored by the medical professionals. The use of the RCV helps medical professionals to differentiate between random fluctuations and true changes in patients’ laboratory test results. Figure 1 presents an illustration of two consecutive laboratory albumin test results in different scenarios with the PRI and RCV interpretations. In Figure 1b, three situations are illustrated for interpreting the new test (the 2ndtest result) with reference to the previous test (the 1sttest result); i) the new test is not clinically important and it is also still within the PRI, in ii) the new test is within the PRI but is considered clinically important based on the RCV, and in iii) the new test is clinically important and outside the PRI. The new test results in both ii) and iii) are subject to further examination by the medical professionals. The earliest version of the RCV estimation involves the computation of the within-subject variability across individuals, where the variance is assumed to follow a log-normal distribution [2]. Over the past decades, various RCV calculation procedures have been developed and improved [3, 4]. Currently, the simplified-traditional version is widely used. This procedure takes into account the within-subject biological variability and measurement uncertainty associated with a specific laboratory test, and it relies on the standard normal distribution. It is defined as where τ is the desired coverage probability (if τ = 95%, use z0.975), CVI and CVA are the coefficients of variation related to the within-subject biological variation and the analytical imprecision, respectively [5, 6]. The RCV of a clinical test is usually given in a percentage change (%RCV ). As an example, suppose that two successive clinical tests of an individual are available, y11 and y12; when the absolute percentage change between the two tests relative to the first test ( 100) is greater than the %RCV , the change can be considered clinically important. Although it is possible that both test results still lie within the PRI. In this traditional RCV, the information of CVA would commonly be obtained from the laboratory while CVI is computed from data with repeated measurements; for some clinical outcomes, CVI is available in an external database[7]. Both the underlying distributional assumptions and the required variability information in the RCV formulation in (formula 1) imposes at least two potential drawbacks: 1) that the method heavily relies on the distributional assumptions, and 2) the available database of CVI is limited to certain frequently-measured clinical outcomes. Moreover, the traditional RCV aims to produce a single %RCV that is applicable to all individuals in the population, offering less individualized interpretation of the measurement changes. The time differences between clinical tests are also not incorporated and therefore the %RCV threshold is the same regardless the clinical tests temporal interval. The individualized health concept in clinical laboratory outcomes and omics measurements has also been discussed in the recent studies of Individual Reference Intervals, abbreviated as IRI [8, 9]. From the same studies, the subject variances computed from a longitudinal data have been shown to vary between individuals, implying that each person may have a different definition of ”healthy” or ”diseased”. When taking into account this variability, the RCV could also be better interpreted and give a more precise reading, specific to each person. Only a few prior studies discussed the potential approach for obtaining individualized Reference Change Value, also referred to as the Individual Reference Change Value, abbreviated as I-RCV. These studies still rely on the CVAand the availability of a CVIdatabase, and they assume that the changes between clinical test to follow a Gaussian distribution[10, 11]. Summary ^e object of embodiments of the present invention is to provide a method to obtain individualized subject-based indicators representative for a substantial variation. According to a first aspect a computer-implemented non-parametric method for estimating the upper and lower bounds of an Individual Reference Change Value, I-RCV, for a measured test value of a subject is provided. Said computer-implemented non-parametric method using a longitudinal data set of corresponding test values for said subject and at least three different independent subjects, and applying two I-RCV models on said longitudinal data to estimate said upper and lower bounds with a symmetry property between said upper and lower bounds, characterized in that the two I-RCV models include the observed time lags between consecutive measurements in the longitudinal data as a covariate in the model to determine a difference between the two consecutive measurements on the same subject. I-RCV stands for Individual Reference Change Value, which is a change interval that allows for direct comparison of observed changes in the same unit as the clinical test. It is a measure of the magnitude of change required to indicate a clinically important change in a clinical test result for an individual. A clinically important change refers to a change in a clinical test result that is considered to be clinically meaningful or important. ^e definition of what constitutes a clinically important change can vary depending on the specific clinical test being used and the context in which it is being applied. However, in general, a clinically important change is one that indicates a meaningful difference in the health status or condition of an individual. Longitudinal data set refers to a collection of data that is gathered over a period of time, typically with multiple observations of the same subject or group of subjects at different points in time. A longitudinal data set of corresponding test values for said subject and at least three different independent subjects means that the data set includes at least three observations of the same test values for the subject over time, as well as test values for at least three other independent subjects over the same time period. In other words, the data set includes a set of test values for the subjects being analyzed. ^ese test values are taken at corresponding time points, so that changes in the test values over time can be compared and analyzed. ^is approach allows for a more accurate estimation of the I-RCV for the subject, as the I-RCV is calculated based on the longitudinal data of healthy subjects. Applying two I-RCV models on said longitudinal data to estimate said upper and lower bounds with a symmetry property between said upper and lower bounds means that two models are used to estimate the upper and lower bounds of the I-RCV for the subjects being analyzed. ^ese models are applied to the longitudinal data set of corresponding test values for the subject and at least three different independent subjects. ^e two models are designed to have a symmetry property between the upper and lower bounds, meaning that during the observed time of study, the upper and lower bounds of the I-RCV are estimated to be equidistant from the null point i.e. when the observed time lag is equal to zero or when there are no differences between two consecutive measurements. ^e two I- RCV models include the observed time lags between two consecutive measurements in the longitudinal data as a covariate in the model to determine a difference between the two consecutive measurements on the same subject, which means that the two models used to estimate the upper and lower bounds of the I-RCV take into account the time interval between consecutive measurements of the same subject in the longitudinal dataset. ^e covariate is a variable that is not of primary interest but is included in the model to adjust for its effect on the response variable, in this case, the I-RCV. By including the observed time lags between consecutive measurements as a covariate, the models can more accurately estimate the I-RCV by taking into account the time- dependent nature of the longitudinal data. ^e symmetry property between the upper and lower bounds ensures that the I-RCV is estimated in a consistent and reliable manner, as the upper and lower bounds are estimated to be equidistant from the null point. It can be said that the symmetry property is assumed for the sake of simplicity. ^is approach ensures that any changes in the test values over time, that fall within the estimated upper and lower bounds, are considered to be within the range of normal clinical change, while changes outside this range are considered to be clinically substantial. One advantage of this method for calculating I-RCV is that contrary to the conventional RCV which provides a threshold in percentage changes, the I-RCV estimate offers a change interval in the same unit as the clinical test by using longitudinal data of healthy subjects, enabling direct comparison of observed changes. ^is method thus follows a non-parametric approach that does not rely on distributional assumptions, and for which only relatively short time- series from multiple subjects are needed. Both the variation within and between subjects are included in the model, and all model parameters can be directly estimated from the data. Hence no external database is required. Another advantage of the method is that it utilizes the observed time lags between consecutive measurements in the longitudinal data as a covariate in the model to determine a difference between the two consecutive measurements on the same subject. ^is approach enables the model to take into account the time-dependent nature of the longitudinal data, which allows for a more accurate estimation of the I-RCV. In conclusion, the computer- implemented non-parametric method for estimating the upper and lower bounds of an Individual Reference Change Value, I-RCV, for a measured test value of subjects provides a novel approach to calculating I-RCV using longitudinal data of healthy subjects. ^e method utilizes a non- parametric approach that does not rely on distributional assumptions, and for which only relatively short time-series from multiple subjects are needed. ^e method also utilizes the observed time lags between consecutive measurements in the longitudinal data as a covariate in the model to determine a difference between the two consecutive measurements on the same subject, enabling a more accurate estimation of the I-RCV. Preferably, the two I-RCV models of the non-parametric method include two subject- specific parameters shared amongst the two I-RCV models. ^e two subject-specific parameters are shared between the two I-RCV models, meaning that they are used in both models to estimate the upper and lower bounds of the I-RCV. ^ese parameters are also referred to as subject-specific effects or subject-specific estimates in the equations used to calculate the I-RCV. Including subject- specific parameters in the models allows for a more personalized and accurate estimation of the I- RCV for each subject, as the models can account for any individual differences in the test results that may not be captured by the population-level parameters. By sharing the subject-specific parameters between the two models, the method can estimate the I-RCV with a higher degree of performance. It in addition, simplifies the parameter estimation procedures and as such enables the I-RCV parameter estimation on a small number of test results. In the equations hereinafter these subject-specific parameters are also referred to as subject-specific effects, or subject-specific estimates. Preferably, the subject-specific parameters are determined using an iterative penalised estimation procedure using two penalty terms. ^is means that in the preferred embodiment of the non-parametric method, the subject-specific parameters are estimated using an iterative penalized estimation procedure that uses two penalty terms to estimate the subject-specific parameters. ^e first penalty term is used to control the location of the estimated I-RCV over time, while the second penalty term is used to ensure that the width of the estimated I-RCV are consistent with the overall population-level clinical change. By using these two penalty terms, the estimation procedure can balance the need for the location and width of the estimated I-RCV, while still allowing for individual differences between subjects to be accounted for. More preferably, the selection of the penalty terms includes splitting the longitudinal data set into test data and training data, wherein the test data contains the measurement changes between the last test value and the previous corresponding test values of all subjects in the longitudinal data set; and wherein the training data are all measurement changes, but the measurement changes between the last test value and the previous corresponding test values of all subjects in the longitudinal data set; and performing a parameter estimation procedure using the training data, and subsequently use the test data for evaluating the obtained interval. ^is means that in an even more preferred embodiment of the non- parametric method, the selection of the penalty terms involves dividing the longitudinal data set into two separate sets of data: training data and test data. ^e training data includes all measurement changes in the longitudinal data set, except for the measurement changes between the last test value and the previous corresponding test values of all subjects in the data set. ^e test data, on the other hand, includes only the measurement changes between the last test value and the previous corresponding test values of all subjects in the data set. Using this approach, the parameter estimation procedure is performed using the training data, while the test data is used to evaluate the performance of the estimated I-RCV intervals. By splitting the data set into training and test data, the method can more accurately estimate the subject-specific parameters and penalty terms, while also ensuring that the estimated I-RCV intervals are reliable and can be used in clinical practice. More preferably, the optimal penalty terms are selected by fitting a binary logistic regression model with the observed time lags on the test data as covariate and the probability of having the changes in the test data to be within the I-RCV bounds as response, and by determining the Euclidean distance between the origins 0,0 and the slope and intercept estimates of said fitted binary logistic regression model; and computing the Time Empirical Coverage, abbreviated as TEC, the proportion or the frequency to have the changes in the test data to be within the I-RCV bounds, and wherein the penalty terms with the largest TEC and the smallest Euclidean distance are selected. ^e thus obtained optimal and selected penalty terms are used to estimate the parameters including the subject-specific estimates, of the two I-RCV models. Preferably the two I-RCV models use quantile function for obtaining respectively the lower Q_i (τ_1;δ) bound and upper Q_i (τ_2;δ) bound for subject i corresponds to ^^^^^; ^^ = −^^− ^^+ ^^^^^^^^(2) ^^^^^; ^^= ^^+ ^^+ ^^^^^^^^(3) where τ_1 and τ_2 denote the probability of the lower and the upper I-RCV bounds, respectively, and τ_2-τ_1 denote the true coverage probability of the estimated I-RCV, δijk denotes the time difference or time lag (in day units) of subject i between the j-th and the k-th measurement i.e. δijk = tik −tij, β0 denotes the fixed intercept, β1 denotes the fixed slope specific to the lower bound, β2 denotes the fixed slope specific to the upper bound, ui and vi denote the subject-specific parameters that are shared among the two models. The lower bound of the I-RCV is estimated using the quantile function in equation (2), which takes into account the time difference or time lag between consecutive measurements for each subject. The upper bound of the I-RCV is estimated using the quantile function in equation (3), which also takes into account the time difference or time lag between consecutive measurements for each subject. The parameters β0, β1, and β2 are fixed intercept and slopes that are specific to the lower and upper bounds of the I-RCV, respectively. The parameters ui and vi are subject-specific parameters that are shared between the two models, and are used to adjust for individual differences in the test results or response to treatment that may be present between subjects. The probabilities τ_1 and τ_2 denote the probability of the lower and upper I-RCV bounds, respectively, and τ_2-τ_1 denotes the true coverage probability of the estimated I-RCV. By using the quantile function and taking into account the time difference or time lag between consecutive measurements, the method can estimate the I-RCV with a high degree of performance, while also accounting for individual differences between subjects. More preferably, the optimal and selected penalty terms are used to estimate the β-parameters and the subject-specific parameters ui and vi of the two I-RCV models. By using the optimal and selected penalty terms, the method can estimate the β-parameters and the subject-specific parameters with a high degree of accuracy and reliability, while also ensuring that the estimated I-RCV intervals have good coverage. This approach ensures that the method can accurately estimate the I-RCV intervals while also providing a reliable measure of clinical significance. In a second aspect the use of the aforementioned method in determining whether a measured change of a test value is within or outside of the I-RCV of said subject is provided. For example, in case the subject is a human or non-human animal and the test value is a (clinical) biochemical test value, such as frequently measured in clinical laboratories, the method as herein provided, can be used to determine whether an observed change in test value, i.e. a change in a clinical (biochemical) test value, is within or outside of the I-RCV of said subject. A sample outside of the subject’s I-RCV can thus be identified as an important change that may require further investigation. To the same extend, changes within the I-RCV can be qualified as healthy changes in the test value of said subject, and as such monitoring the I-RCV allows to follow-up the healthy evolution of a test value over time, i.e. taking into account the aging of the subject. It will be apparent to the skilled person that this method can be applied to any subject of investigation and any parameter of such a subject of investigation for which a longitudinal data set exists. It will be understood by the skilled person that the features and advantages disclosed hereinabove with respect to various embodiments of the method may also apply, mutatis mutandis, to various embodiments of the use. According to yet another aspect of the present invention, there is provided a computer program product comprising a computer-executable program of instructions for performing, when executed on a computer, the steps of the method of any one of the method embodiments described above. It will be understood by the skilled person that the features and advantages disclosed hereinabove with respect to embodiments of the method may also apply, mutatis mutandis, to embodiments of the computer program product. According to yet another aspect of the present invention, there is provided a digital storage medium encoding a computer-executable program of instructions to perform, when executed on a computer, the steps of the method of any one of the method embodiments described above. It will be understood by the skilled person that the features and advantages disclosed hereinabove with respect to embodiments of the method may also apply, mutatis mutandis, to embodiments of the digital storage medium. According to yet another aspect of the present invention, there is provided a device programmed to perform a method comprising the steps of any one of the methods of the method embodiments described above. According to yet another aspect of the present invention, there is provided a method for downloading to a digital storage medium a computer-executable program of instructions to perform, when executed on a computer, the steps of the method of any one of the method embodiments described above. It will be understood by the skilled person that the features and advantages disclosed hereinabove with respect to embodiments of the method may also apply, mutatis mutandis, to embodiments of the method for downloading. Brief description of the figures ^e accompanying drawings are used to illustrate presently preferred non-limiting exemplary embodiments of devices of the present invention. ^e above and other advantages of the features and objects of the present invention will become more apparent and the present invention will be better understood from the following detailed description when read in conjunction with the accompanying drawings, in which: Figure 1 is an illustration of a) albumin test results distribution in a healthy population, the grey area indicates the 95% PRI, and b) three scenarios of two consecutive albumin test results, the 95% PRI is also shown in the grey shaded area and the RCVs (also at 95% probability) are indicated by the arrows in the 1st test; Figure 2 shows a method performance of I-RCV at the 95% nominal coverage level. Data were generated from different error term and random effect distributions, with either constant or subject-specific variances. The TEC and SEC were calculated for all scenarios with four different number of repeated measurements n, in N = 30 and N = 50 subjects. Figure 3 shows I-RCV median coverages for the I-RCV intervals. Data were generated with time series of n = 3 and n = 5 observations, with different numbers of subjects, ranging from N = 3 to N = 200. The dashed lines refer to the nominal coverage level of 0.95, with 0.025 deviation around the nominal coverage; Figure 4: I-RCV of blood serum creatinine in 15 male participants of IAM Frontier study (in dark lines). Training data of seven clinical tests (small grey dots) from each subject are used to estimate the I-RCV. The test data at the 8th time point is taken and plotted against the time differences. The time differences between this data and all creatinine results in the training data are also computed, hence multiple orange dots in one subject. The changes toward the closest time point (between the 8th and the 7th), indicating the changes between two successive test results, are shown in dark grey dots. The published creatinine RCV (12.7%) is also plotted in the shaded grey area; Figure 5 shows IRI of blood serum creatinine in 15 male participants of IAM Frontier study (blue lines); Training data of seven clinical tests from each subject are used to estimate the IRIs (grey dots). The test data at the 8th time point is taken (dark grey dots) and plotted against the measurement times (in month). The published creatinine PRI is also plotted in the shaded grey area. The IRIs should be used for interpreting the test data. Figure 6 shows a method performance based on the simulation study of I-RCV computed using the I-RCV model at the 95% nominal coverage; Figure 7 shows I-RCV of blood serum creatinine in 15 female participants of IAM Frontier study (in dark lines). Training data of seven clinical tests (small grey dots) are used to estimate the I-RCV The published creatinine RCV (12.7%) is plotted in the shaded grey area. Figure 8 shows IRI of blood serum creatinine in 15 female participants of IAM Frontier study (dark lines); and . The published creatinine PRI is plotted in the shaded green area. Figure 9 shows a flow diagram of an exemplary embodiment of a computer-implemented non-parametric method for estimating the upper and lower bounds of an Individual Reference Change Value. Detailed Description Figure 9 shows a flow diagram of an exemplary embodiment of a computer-implemented non-parametric method for estimating the upper and lower bounds of an Individual Reference Change Value for a measured test value of a subject. Some example of potential subjects are athletes in an anti-doping program (athletes’ biological passport, ABP) and athletes’ performance monitoring. In the context of monitoring athletes for doping, the IRCV method can be used to identify abnormal changes in biological markers that could indicate the use of performance- enhancing drugs. The Athlete Biological Passport (ABP) introduced by WADA for longitudinally monitoring biological features over time in athletes can benefit from the IRCV method, given that the athletes must perform regular and consistent testing to obtain their ABP, allowing for a longitudinal data with rather long time series. The IRCV method can also help in tailoring training programs that adapt dynamically to an athlete's specific condition and progress compared to their peers, aiding in optimizing performance and reducing injury risks. Other examples may include applications in drug response monitoring, personalized nutrition and fitness programs, veterinary medicine, air quality monitoring or even detection of machine or equipment malfunctions or failures. In drug response monitoring, the IRCV method can be utilized to monitor and predict individual responses to medications, facilitating personalized medicine practices that optimize drug efficacy and minimize adverse effects. The longitudinal measurements come from patients that are being prescribed with specific medications, in a population of patients with the same prescriptions and probably similar demographic features. In personalized nutrition and fitness, the IRCV can help in developing personalized diet and fitness programs by monitoring the individual's responses to different interventions compared to similar profiles, ensuring the diet and exercises are optimally effective. In veterinary medicine, the implementation of the IRCV method would enable veterinarians to predict health issues in individual animals early by utilizing their historical biological data together with the peers (other animals from the same species or breeds, and similar health status), leading to more precise diagnosis and / or more effective interventions. In air quality monitoring, the IRCV method can be used to assess air quality changes in real-time, improving responses to pollution incidents. The longitudinal data of AQI of several air quality monitoring tools, collected over time, spread within one city can be used to estimate the IRCV. In industrial applications, the IRCV method can provide an early detection of machine or equipment malfunctions or failures. This would allow for timely maintenance and optimizing the production process. Several possible parameters that can be measured longitudinally by individual specific machines within one same factory or one production line, such as the machine temperatures, noise levels, energy consumption, production speed, etc., can be used to estimate the IRCV. Figure 9 shows the steps of an exemplary embodiment of the computer-implemented method which will be elucidated and validated in relation to figure 2-8 and the experimental section described below. In a first step, the computer-implemented non-parametric method may comprise inputting a longitudinal data set of at least three corresponding test values and at least three different independent subjects. A longitudinal data set refers to a collection of data that is gathered over a period of time, usually with multiple observations of the same subject or group of subjects at different points in time. In this context, the longitudinal data set consists of test values, which are typically clinical or medical measurements, such as blood pressure, heart rate, or cholesterol levels, that are taken at multiple time points over a period of time. Corresponding test values may refer to measurements taken for corresponding tests for each subject. For example, if the longitudinal data set includes measurements of blood pressure taken at four different time points for a subject, the corresponding test values would be the blood pressure measurements taken at at least three different time points each of the other independent subjects. Not all subject need to have the same number of time points, as long as for each subject at least three time points are available. This also implies that the time points amongst the different subjects are not necessarily the same in time and date. As mentioned, not all subjects need to have exactly the same number of time points, abbreviated as TP. For example, subject 1 may have 4 TP, subject 2 may have 3 TP, subject 3 may have 3 TP, and so on. It is important to note that at least 3 TP for each subject are provided. The exact time and date can also be different between subjects. Independent subjects refer to subjects who are different to the subject being analysed, and who are typically not part of the same group or cohort as the subject being analysed. For example, if the subjects being analysed are patients with a specific medical condition, the independent subjects would be patients without the medical condition who are part of a different group or cohort, or vice-versa. It is to be noted that all subjects may get their respective I-RCV as long as said subject meets the criteria, which is at least 3 TP in a healthy state. The next step in the computer-implemented non-parametric method involves applying two I-RCV models on the longitudinal data set to estimate the upper and lower bounds of the I-RCV for the subject being analyzed. The two models are designed to have a symmetry property between the upper and lower bounds, meaning that the upper and lower bounds of the I-RCV are estimated to be equidistant from the null point of the test values. To estimate the upper and lower bounds of the I-RCV, the two I-RCV models use a quantile function that takes into account the time difference or time lag between consecutive measurements for each subject. The quantile function is used to obtain the lower and upper bounds of the I-RCV for each subject, with the probabilities τ_1 and τ_2 denoting the probability of the lower and upper I-RCV bounds, respectively. The two I-RCV models also include subject-specific parameters that are shared between the two models, which are used to adjust for any individual differences in the test results or response to treatment that may be present between subjects. These subject-specific parameters are determined using an iterative penalized estimation procedure that uses two penalty terms to estimate the parameters. The approach also takes into account the time differences or time lags between measurements. An iterative penalized estimation approach is used to estimate the I-RCV, which does not require information of coefficient variations from external databases. Instead, the method utilizes the between-subjects information sharing property to estimate I-RCV even with a small number of test results per subject. As will be demonstrated below the method performs well, especially when the sample size and the number of repeated measurements are increased. The method is also robust in estimating I-RCVs, providing reliable coverages in realistic situations, even with a minimum of 20 subjects and only three repeated measurements. The practical application of I-RCVs estimated using the newly developed method to real-life serum creatinine data illustrates the potential clinical utility of the method. The application reveals situations in which a new clinical test result is deemed clinically important, which would have gone unnoticed if medical professionals relied solely on individual reference intervals. Additionally, the method could be extended to incorporate baseline covariates such as sex, allowing for a more precise analysis. A person of skill in the art would readily recognize that steps of various above-described method can be performed by programmed computers. Herein, some embodiments are also intended to cover program storage devices, e.g., digital data storage media, which are machine or computer readable and encode machine-executable or computer-executable programs of instructions, wherein said instructions perform some or all of the steps of said above-described methods. ^e program storage devices may be, e.g., digital memories, magnetic storage media such as a magnetic disks and magnetic tapes, hard drives, or optically readable digital data storage media. ^e program storage devices may be resident program storage devices or may be removable program storage devices, such as smart cards. ^e embodiments are also intended to cover computers programmed to perform said steps of the above-described methods. ^e description and drawings merely illustrate the principles of the present invention. It will thus be appreciated that those skilled in the art will be able to devise various arrangements that, although not explicitly described or shown herein, embody the principles of the present invention and are included within its scope. Furthermore, all examples recited herein are principally intended expressly to be only for pedagogical purposes to aid the reader in understanding the principles of the present invention and the concepts contributed by the inventor(s) to furthering the art, and are to be construed as being without limitation to such specifically recited examples and conditions. Moreover, all statements herein reciting principles, aspects, and embodiments of the present invention, as well as specific examples thereof, are intended to encompass equivalents thereof. ^e functions of the various elements shown in thefigures, including any functional blocks labelled as “processors”, may be provided through the use of dedicated hardware as well as hardware capable of executing software in association with appropriate software. When provided by a processor, the functions may be provided by a single dedicated processor, by a single shared processor, or by a plurality of individual processors, some of which may be shared. Moreover, explicit use of the term “processor” or “controller” should not be construed to refer exclusively to hardware capable of executing software, and may implicitly include, without limitation, digital signal processor (DSP) hardware, network processor, application specific integrated circuit (ASIC), field programmable gate array (FPGA), read only memory (ROM) for storing software, random access memory (RAM), and non-volatile storage. Other hardware, conventional and / or custom, may also be included. Similarly, any switches shown in thefigures are conceptual only. ^eir function may be carried out through the operation of program logic, through dedicated logic, through the interaction of program control and dedicated logic, or even manually, the particular technique being selectable by the implementer as more specifically understood from the context. It should be appreciated by those skilled in the art that any block diagrams herein represent conceptual views of illustrative circuitry embodying the principles of the present invention. Similarly, it will be appreciated that any flowcharts, flow diagrams, state transition diagrams, pseudo code, and the like represent various processes which may be substantially represented in computer readable medium and so executed by a computer. It should be noted that the above-mentioned embodiments illustrate rather than limit the present invention and that those skilled in the art will be able to design alternative embodiments without departing from the scope of the appended claims. In the claims, any reference signs placed between parentheses shall not be construed as limiting the claim. ^e word “comprising” does not exclude the presence of elements or steps not listed in a claim. ^e word “a” or “an” preceding an element does not exclude the presence of a plurality of such elements. ^e present invention can be implemented by means of hardware comprising several distinct elements and by means of a suitably programmed computer. In claims enumerating several means, several of these means can be embodied by one and the same item of hardware. ^e usage of the words “first”, “second”, “third”, etc. does not indicate any ordering or priority. ^ese words are to be interpreted as names used for convenience. In the present invention, expressions such as “comprise”, “include”, “have”, “may comprise”, “may include”, or “may have” indicate existence of corresponding features but do not exclude existence of additional features. Data description The real-life IAM Frontier longitudinal data was utilised to provide empirical evidence and a comparative analysis that highlights the strengths and potential benefits of the new I-RCV approach in a real-world setting. This dataset comprises monthly clinical test results of 30 healthy individuals without any self- reported chronic diseases, collected from the pilot IAM Frontier study that ran for 12 months (13 data points)

[0012] . The purposes of incorporating this data is to show that the I-RCV model performance in ten clinical biochemistry tests frequently measured in clinical laboratories and to showcase the practical application of the newly introduced I-RCV concept, specifically in the context of the serum creatinine test. Below, a comparison between the serum creatinine I-RCV estimated using the I-RCV model with the conventional RCV estimated using established methods found in the literature [6, 13], and the corresponding IRI estimates as what would have been done in real clinical practice. I-RCV model formulation The I-RCV model is formulated as an extension of the method used for estimating the IRIs[9]. Quantile regression models are used for obtaining the lower and upper bounds of the I-RCVs, for every subject at all different time lags. In what follows, Yiis the change value of subject i, i.e. the difference between two measurements on the same subject i, at a time lag δ apart from one another. Qi(τ;δ) is representative for the quantile function. For a pair of probabilities τ1and τ2> τ1, and for a given time lag δ, the interval [Qi(τ1;δ),Qi(τ2;δ)] has coverage probability τ2− τ1and is referred to as the I-RCV. For a given dataset with longitudinal data, is the time difference or time lag (in day units) of subject i between the j-th and the k-th measurement i.e. δijk = tik −tij, i = k = j,...,ni and j̸= k. The I-RCV lower and upper bound models for subject i then becomes Qi(τ1;δ) = −β0 − ui + viβ1δijk (2) Qi(τ2;δ) = β0 + ui + viβ2δijk, (3) where β0 denotes the fixed intercept and the subject-specific effects ui and vi are shared among the two models. The lower and upper quantiles in (2) and (3) are modelled as functions of time lags δijk, with a symmetry property between the two models: the I-RCV location (i.e. the bounds for the limiting case of δ = 0) for subject i is given by β0 + ui for the upper bound, and −(β0 + ui) for the lower bound. Hence, the models allow for the I-RCV locations to vary across subjects. Serial correlations between measurements within the same subject are frequently observed, suggesting that as the time gap between two measurements increases, the similarity of the measurements decreases. Because of this reason, the additional assumption that the I-RCV range of subject i becomes wider as the time lag increases can be made. This assumption is attained by including the observed time lags δijk as a covariate in the models, allowing the width of the interval to increase with time lag δ. To also make the width of the range individualized to each subject, the non-negative individual scaling factors vis (vi ≥ 0) are added with fixed slopes specific to the lower and upper bounds, β1 and β2. Parameter estimation The β-parameters and the subject-specific effects uiand viare estimated by minimizing the following function, where yijk= yik− yij. The first two terms define the objective functions that are typically used for estimating parameters in linear quantile regression models, one for the lower and one for the upper bound. The parameter estimation problem is approached as in a setting of predictive modelling, because the aim is to obtain the correct probabilistic interpretation when the I-RCVs are applied to new measurements. A penalised estimation procedure with ℓ2penalty terms is used, these are the last two terms in (4). The initial set of penalty parameters λuand λvare user-specified, λu,λv≥ 0. Next, an iterative procedure to minimise the objective function for a given λuand λv. is performed. The optimal λuand λvare selected based on the procedure explained in Section 2.4. First the estimation procedure with fixed penalty parameters λu and λv is described. The initial estimates of β0, and the uis are computed but before entering the iterative procedure. Initial estimations • Initial estimation of uiand viIn the first iteration, all ui= 0 and vi= 1 are set. • Initial estimation of β0, β1 and β2 auxiliary parameters β1and β2and the initial parameters β1and β2from the ordinary quantile regression models are estimated. β1δijk Q(τ2;δ) = β2 + β2δijk. The initial estimate of β0 The next steps are repeated iteratively until convergence. Iterative procedure Let the I-RCV length B =Qi(τ2;δ)) − Qi(τ1;δ) = 2β0+ 2ui+ viδijk(β1− β1). The iterative procedure reach convergence when log < 0.001, where!"^is the I-RCV length from the previous iteration, or when a maximum of 20 iterations are reached. • Estimation of ui The uis are estimated by direct minimisation of the following objective function: The estimates uis are centered so that ^,^← ^,^− average^^,^^ and set ^+^ ← ^+^ + average^^,^^.• Estimation of vi Consider the objective function (note that the penalty term for uiis dropped because it does not affect the estimation of the zis) The vis are estimated, one by one, by direct minimization of this objective function. This sequential procedure does not necessarily minimize the objective function simultaneously for all vis, particularly because of the penalty term. As a consequence, the resulting estimates of the vis are often not well centered about 1 (which is expected because of the form of the penalty term). To remediate this problem, a rescaling step may be added. In particular, the rescaled estimates to 9^,^, are set with 9=1so that ^,^← 9^,^, and ^^++;; ←9, < = 1,2.• Estimation of β1 and β2 Let *>^^ First note that there is no penalization acting on the βg-parameters. The objective function can be written as Each of the two terms is exactly the objective function of a quantile regression model with *>^^and *>^^as the outcomes and ^,^^^^^as the regressor. Thus, the estimates of β1and β2can be obtained from the estimated slopes by fitting this quantile regression model (without intercept). Selection of the Optimal Penalty Parameters (λu, λv) The selection of the optimal penalty parameters proceeds by splitting the data into the training and the test data. First, the parameter estimation procedure using the training data is conducted, and next the test data is used for evaluating the obtained interval. The evaluation makes use of two criteria: the results of fitting a binary logistics regression model and the empirical coverage of I- RCVs when existing subjects in the data have new measurements. The complete steps are explained as follow. Consider two sets of possible values for λu and λv, say Lu and Lv. For each λu ∈ Lu and each λv ∈ Lv, the following steps are performed for each subject i = 1. Split the dataset into two sets: (1) the test dataset Dl, l = nii.e. last measurement for subject i; this dataset contains the measurement changes between the last and the second last clinical test result from all subjects, yini−yi(ni−1)or furthered refer to it as yijl, and (2) the training dataset; all measurement changes except yijl. In practical scenarios, the training data reflects situations where the subjects already included in the study receive new measurements (or new clinical tests results). The split is illustrated in the matrix below (the grey area in the matrix is the training data, the last line is the test data i.e. yijl). 2. Use the training data for estimating all model parameters and examine if the measurements of the test data are within or outside the I-RCV limits. Define a binary indicator Oijl, defined as one if yijl is contained in the I-RCV interval for subject i and time lag δijl. Otherwise Oijl = 0. 3. Fit a binary logistic regression model for the indicator Oijl, as a function of time lag δijl logit(P(Oijl = 1)) = α0 + α1δijl. An ideal I-RCV interval must have the nominal coverage of α = τ2−τ1for all time lags δ. This corresponds to α1= 0 and α0= logit(α).Therefore, the optimal (λu,λv) is selected from the smallest Euclidean distance between (∆O, |αˆ1|) and the origin (0, 0); ∆O refers to the smallest absolute differences of ˆα0 and the true probability (e.g. logit(0.95) for τ1 = 0.025 and τ2 = 0.975). In an ideal scenario, the time differences between the training and the test data is aimed to give no effect to the probability of whether yijl is contained in the I-RCV limits, hence ˆα1 = 0 and αˆ0 = logit(0.95). 4. Select ten candidates (λu,λv) with the smallest Euclidean distance, and between them, select one final (λu,λv) with the largest Time Empirical Coverage (TEC). The TEC is the empirical coverage calculated by comparing the measurement changes in the test data, yijl, with the estimated I-RCVs for all subjects; the relative frequency of yijl in Dl that are contained within the I-RCV limits of the corresponding subjects. The selected optimal (λu,λv) are then used to obtain the final estimates of all parameters in the original data. Simulation Study The simulated data was used in the simulation study aimed for evaluating the proposed I-RCV estimation method. The data were generated through a similar procedure in the linear mixed model (LMM) framework. Furthermore, monthly sample collection dates for each individual were generated, randomly sampled between the 1stand the 15thday of the month. With this scenario, the nearest possible time lag between two consecutive measurements is 15 days and the farthest is 45 days. In many cases of longitudinal data, a correlation is also commonly present between two consecutive measurements where the coefficient decreases as the time lag between these measurements increases. The concept of the RCV mainly focuses on the differences between these consecutive test results and therefore, to capture the interdependencies among these tests and to ensure a realistic representation, the dataset also incorporates the serial correlations. The serial correlations were generated from a multivariate normal distribution with a covariance matrix that follows the first order auto-regressive structure (AR1). As εij∼ N(0,θi2), is set when a correlation between a time point t (in day unit) and t + 1 is present, denoted by γ, the covariance of εi(t) and εi(t + δijk) can be written as follows, where δijk is the time lag of subject i between the j-th and the k-th measurement. ρ = γδ12is defined as the correlation between two measurements that ±1 month apart (monthly correlation), and ρ is set to different values to demonstrate different scenarios of serial correlation present in the simulated longitudinal data. It is assumed that the first order time lags are the same for all pairs of measurements from the same subject e.g. δi23 = δi34 = ..., so that (5) can be written as The detailed description of all simulation scenarios are presented in Appendix Table A1. A simulation study to evaluate the I-RCV method as described in the above sections. In the simulation study, 100 Monte Carlo simulation runs were performed for each scenario presented in Table A1 in Appendix. The same model performance evaluation setting as in the IRI study was used: for each scenario, data for N + 1 subjects with n + 1 repeated measurements was simulated. The training dataset that consist of the first N subjects and the first n repeated measurements were used for estimating the model parameters. The remaining data i.e. the test dataset of the N +1th subject and for the n+1th repeated measurements were then used for computing the empirical coverages: the time Empirical Coverage (TEC) and the Subject Empirical Coverage (SEC). As explained above, the TEC is the empirical coverage probability of the I-RCV for new measurement changes of existing subjects in the training data (i.e. based on the n+1th measurements of the N subjects in the training dataset). The SEC, on the other hand, is the empirical coverage probability of the I-RCV for measurements of a new subject (i.e. based on the N+1th subject). The training and the test data for computing SEC is illustrated in the matrix below The grey area in this matrix is the training data, and the last column illustrates the measurements of the new N +1th subject. The training data was used for estimating all parameters. Moreover, by using the first n repeated measurements available from this subject, his / her I-RCV was computed. The SEC was then obtained by calculating the relative frequency when the last measurement change of this subject, y(N+1)(n+1)n, is contained within the estimated I-RCV limits across 100 Monte Carlo runs. The generation of data for an additional subject and for additional time points agrees with two possible settings: 1) when existing subjects have new measurements, and 2) when there is a new subject that was not included in the data used for the parameter estimation. The ideal I-RCV estimation should produce TEC and SEC that are close to the nominal coverage level i.e.95% for τ1= 0.025 and τ2= 0.975. The simulation results of I-RCV at the 95% nominal coverage are shown in Figure 2. They show that in general the TEC is smaller than the nominal 95%, but it increases with increasing numbers of repeated measurements. With 30 subjects and no serial correlation (ρjk = 0), the TEC can reach up to 90% with only three repeated measurements (n = 3). These coverages are slightly lower in data with serial correlations, although they become similar as N and n become larger, for example at n = 10. The TEC also reaches up to 95% at n = 10 when N = 50 and when serial correlations are present. The other simulation results, with different serial correlation coefficients can be consulted in Appendix. With respect to the random effects distributions, in terms of the TEC, the method performs best with data simulated from normal distributions with subject-specific variances. This finding is favorable, because in real-life settings it is likely that the variances of clinical tests are subject-specific, it is likely to have serial correlation, i.e. ρjk̸= 0. No strong effects of choice of the random effects distributions on the SEC were observed, although the SECs are often higher and closer to the nominal coverage in data with larger n. The simulation study was also extended to investigate the I-RCV method performance in a realistic real-life situation, i.e. when samples from a large number of subjects, each with only a few repeated measurements are collected. The median coverage (median of TEC and SEC) with data generated with numbers of subjects varying from N = 3 up to N = 200, but with only n = 3 and n = 4 were calculated. The serial correlation is fixed to 0.7 and the normal distribution with subject- specific variances was used for simulating the data. Figure 3 shows the results in terms of the median coverages. The simulation study demonstrates that the I-RCV method performs very well with short time series, as small as with three repeated measurements (n = 3), when at least samples from N = 20 individuals are used for the estimation. When five repeated measurements are present, the number of individuals needed to achieve the optimal I-RCV can be reduced to only 10. I-RCV method’s performance in IAM Frontier data In addition to assessing the method performance of the proposed I-RCV model using simulated data, it was also examined how well this method performs in various monthly clinical tests from the IAM Frontier dataset. This is feasible since all data comes from healthy subjects and a sufficient number of repeated measurements (n) is available. The empirical coverages (TEC and SEC) for each clinical test when n varies from 3 to 10 were computed. The procedure described in the section relating to the selection of the optimal penalty parameters was used for computing the TEC. For computing the SEC, the leave-one-out cross validation scheme (LOOCV) was used to cross validate, as shown in figure 9. In particular, for each test, N − 1 subjects are included for the I-RCV estimation, and a binary indicator is defined for indicating whether or not the test result change of the left-out subject is contained within the IRCV limits. This step was repeated N times, leaving out one subject as the test data in every iteration, and the SEC as the average of this indicator over all subjects was computed. Table 1 presents the TEC and SEC computed for ten IAM Frontier clinical tests. Overall, when n ≥ 8, at least four clinical tests where both the TEC and SEC are close to 95% were observed. However, with 30 subjects included in the estimation (or 29 to compute the SEC), this result are not as good as for the simulation study mentioned above. It is hard to exactly pinpoint the reason, but a possible explanation may be that the distributional conditions of these real data are very different from the conditions in the simulation study. The simulations, however, indicated that the SEC and TEC become better as the number of subjects increases, even with only few numbers of repeated measurements. Hence, maybe if more subjects were included in the study, better coverages would be obtained. Table 1: Benchmarking. SEC and TEC for 95% I-RCVs, applied to the VITO IAM Frontier clinical biochemistry data. Different numbers of repeated measurements (n) are used for fitting the model. The values between 95% ± 2.5% are printed in bold face. n=3 n=5 TEC SEC TEC SEC Albumin 0.9231 0.9615 0.9333 0.9000 Apolipoprotein A1 0.7308 0.6154 0.9667 0.9000 Apolipoprotein B 0.6538 0.6538 0.9333 0.8667 LDL cholesterol 0.9615 0.9231 0.7333 0.8333 Creatinine 0.9231 0.9231 0.9000 0.9000 Glucose 0.5769 0.7692 0.9000 0.8000 HDL cholesterol 0.7308 0.6923 0.9000 0.8667 non-HDL 0.9615 0.9231 0.8000 0.8667 cholesterol Total cholesterol 0.9615 0.9231 0.9333 0.8333 Triglyceride 0.8846 0.9231 0.9000 0.9667 n=8 n=10 TEC SEC TEC SEC Albumin 0.9310 0.9655 1.0000 0.9667 Apolipoprotein A1 0.4138 0.4828 0.6000 0.6667 Apolipoprotein B 0.2069 0.3793 0.5000 0.5667 LDL cholesterol 0.9655 0.9310 0.9333 0.9333 Creatinine 0.9655 0.9655 0.9333 0.9667 Glucose 0.8966 0.7931 0.7667 0.7667 HDL cholesterol 0.3793 0.5517 0.6000 0.7000 non-HDL 0.8966 0.8966 0.9667 0.9333 cholesterol Total cholesterol 0.8621 0.9310 0.9667 0.9333 Triglyceride 0.9310 0.8966 0.9333 0.9333 Analysis of serum creatinine in IAM Frontier data The I-RCV application in a real-life cohort study data of IAM Frontier

[0012] has been illustrated. In this study, Figure 4 presents the I-RCV estimates for blood serum creatinine computed using the IAM Frontier clinical biochemistry data. The first seven monthly test results of 30 subjects to obtain the I-RCV estimates were used. However, in this figure, only the application for the 15 male participants is illustrated. The remaining I-RCV estimates for female participants can be consulted in Figure 7. The changes between the 8thtest and the first seven test results in each subject were also computed and plotted them together with the I-RCV estimates. The estimated I-RCVs can then be used for interpreting these between-test changes, for every subject. The first-order change (dark grey dots) indicate the differences or changes between the 8thand the 7thtest results; for this the I- RCV range is expected to be the smallest as the time difference is the shortest. This area is also where the medical professional would mostly be interested in and where the current RCV is utilised; for interpreting whether there is a sudden change between two successive clinical tests. For this reason, the published population RCV for serum creatinine (%RCV=12.7%) in the same measurement unit

[0013] is shown, calculated relatively to the 7thtest result (±%RCV yi7). Therefore, the interpretation of the first-order changes can be compared, as shown in dark grey dots, both towards the population RCV and the I-RCV. At the first sight, I-RCV detects a sudden decrease of Toefiel’s 8th creatinine level, but it is still at the borderline if the published population RCV is used. From this result it can be seen that I-RCV provides a narrower interval, indicating the potential in providing a more precise interpretation of an important change between test results. Figure 4 also shows that the population RCV estimates are different between subjects; it is because the %RCV were compared with subjects’ 7th test results. The %RCV, however, is the same for all subjects hence provide less individualised interpretation. It also does not take into account the time intervals between tests, i.e. if a large time span is observed between two clinical tests, the %RCV remains the same. Here the I-RCV estimates offers a different approach is shown. As an example, while the serum creatinine levels in the IAM Frontier data were measured in a relatively uniform time lags, the changes between the 8thtest results with the other test results data were also plotted, as shown as the larger grey dots in Figure 4. This situation illustrates the real-life setting where the time spans between clinical tests could be large and therefore, the changes would fall more at the right side of the x axis. The I-RCV handles this situation very well as the time intervals between tests in the model (see (2) and (3)) were incorporated. An extrapolation of the I-RCV estimates could possibly be done to accommodate changes beyond the plotted time range, such as in the last test change of Alfred, but it is currently not within the scope of the study. The RCV interpretation is commonly proceeded by the reading of the test result together with the reference intervals, and therefore also the Individual Reference Intervals (IRIs) of serum creatinine was shown. In Figure 4, the focus is on the first-order differences, Jozef and Mauritius have been detected with a sudden increase between his creatinine laboratory results at month-7 and month-8. Interestingly, when their results by using IRIs in Figure 5 are examined, Jozef’s creatinine test at month-8 is still within his IRI bounds. From the same figure it can also be seen that his 7thcreatinine level suddenly decreased from the 6th, and then increased again at the 8thtime point. This sudden increase (or the previous decrease) of Jozef’s serum creatinine level would probably not being detected if his GPs or clinicians only use the IRIs. Similarly, a sudden decrease is also seen in Toefiel’s 8thcreatinine test, and his IRI would not be able to detect it. The remaining IRI estimates for female participants are presented in Figure 8. From Figure 5, Bernard’s 8thcreatinine measurement is outside the lower limit of his IRI, and conversely, his first-order difference is still within the I-RCV range. This shows an example that the I-RCV should also not be used as a sole instrument for the laboratory results interpretation; it should be accompanied by the IRIs. In all Jozef, Mauritius, Teofiel, and Bernard’s cases, a further examination is advised following the I-RCV and the IRI readings of their 8thcreatinine test.

[0002]  References [1] Harris EK, Brown SS. Temporal changes in the concentrations of serum constituents in healthy men. Annals of Clinical Biochemistry: International Journal of Laboratory Medicine 1979;16:169–76. doi:10.1177 / 000456327901600142. [2] Harris EK, Yasaka T. On the calculation of a ”reference change” for comparing two consecutive measurements. Clinical Chemistry 1983;29:25–30. doi:10.1093 / clinchem / 29.1.25. [3]Jones GRD. Critical difference calculations revised: inclusion of variation in standard deviation with analyte concentration. Annals of Clinical Biochemistry: International Journal of Laboratory Medicine 2009;46:517–9. doi:10.1258 / acb.2009.009083. [4]Regis M, Postma T, van den Heuvel E. A note on the calculation of reference change values for two consecutive normally distributed laboratory results. Chemometrics and Intelligent Laboratory Systems 2017;171:102– 11. doi:10.1016 / j.chemolab.2017.10.008. [5] Fraser CG. Reference change values: the way forward in monitoring. Annals of Clinical Biochemistry: International Journal of Laboratory Medicine 2009;46:264–5. doi:10.1258 / acb.2009.009006. [6] Fraser CG. Reference change values. Clinical Chemistry and Laboratory Medicine 2012;50. doi:10.1515 / cclm.2011.733. [7] Carobene A, Aarsand AK, Bartlett WA, Coskun A, Diaz-Garzon J, Fernandez-Calle P, et al. The european biological variation study (eubivas): a summary report. Clinical Chemistry and Laboratory Medicine (CCLM) 2022;60:505–17. doi:10.1515 / cclm-2021-0370. [8] Pusparum M, Ertaylan G, Thas O. From population to subject-specific reference intervals; vol.12140 LNCS.2020. ISBN 9783030504229. doi:10.1007 / 978-3-030-50423-6_35. [9] Pusparum M, Ertaylan G, Thas O. Individual reference intervals for personalised interpretation of clinical and metabolomics measurements. Journal of Biomedical Informatics 2022;131. doi:10.1016 / j.jbi.2022.104111.

[0010] Lund F, Petersen PH, Fraser CG. A dynamic reference change value model applied to ongoing assessment of the steady state of a biomarker using more than two serial results. Annals of Clinical Biochemistry: International Journal of Laboratory Medicine 2019;56:283– 94. doi:10.1177 / 0004563219826168.

[0011] McCormack JP, Holmes DT. Your results may vary: the imprecision of medical measurements. BMJ 2020;:m149doi:10.1136 / bmj.m149.

[0012] I AM Frontier study - VITO, Belgium. https: / / iammyhealth.eu / en / i-am-frontier; ???? 10 August 2023, date last accessed.

[0013] Carobene A, Marino I, Co¸skun A, Serteser M, Unsal I, Guerra E, et al. The EuBIVAS Project: Within- and Between-Subject Biological Variation Data for Serum Creatinine Using Enzymatic and Alkaline Picrate Methods and Implications for Monitoring. Clinical Chemistry 2017;63(9):1527–36. URL: https: / / doi.org / 10.1373 / clinchem.2017.275115. doi:10.1373 / clinchem.2017.275115.

Claims

CLAIMS 1. A computer-implemented non-parametric method for estimating the upper and lower bounds of an Individual Reference Change Value, I-RCV, for a measured test value of a subject, said method using a longitudinal data set of corresponding test values for said subject and at least three different independent subjects, and applying two I-RCV models on said longitudinal data to estimate said upper and lower bounds with a symmetry property between said upper and lower bounds, characterized in that the two I-RCV models include the observed time lags between consecutive measurements in the longitudinal data as a covariate in the model to determine a difference between the two consecutive measurements on the same subject.

2. The computer-implemented method of claim 1, wherein the two I-RCV models include two subject-specific parameters shared amongst the two I-RCV models.

3. The computer-implemented method of claim 2, wherein the subject-specific parameters are estimated using an iterative penalised estimation procedure using two penalty terms.

4. The computer-implemented method of claim 3, wherein the selection of the penalty terms are determined by splitting the longitudinal data set into test data and training data, wherein the test data contains the measurement changes between the last test value and the previous corresponding test values of all subjects in the longitudinal data set; and wherein the training data are all measurement changes, but the measurement changes between the last test value and the previous corresponding test values of all subjects in the longitudinal data set.

5. The computer-implemented method of claim 4, wherein the optimal penalty terms are selected by computing the Euclidean distance between the origins 0,0 and, the slope and intercept estimates of a fitted binary logistic regression model; the model use the observed time lags on the test data as covariate and the probability of having the changes in the test data to be within the I-RCV bounds as response, and computing the Time Empirical Coverage, TEC, described as the proportion or the frequency of the changes in the test data to be within the I-RCV bounds, and wherein the penalty terms with the largest TEC and the smallest Euclidean distance are selected.

6. The computer-implemented method of claim 1, wherein the two I-RCV models use quantile function for obtaining respectively the lower Q_i (τ_1;δ) bound and upper Q_i (τ_2;δ) bound for subject i corresponds to^^^^^; ^^ = ^^+ ^^+ ^^^^^^^^(2)where τ_1 and τ_2 denote the probability of the lower and the upper I-RCV bounds, respectively, and τ_2-τ_1 denote the true coverage probability of the estimated I-RCV, δijk denotes the time difference or time lag (in day units) of subject i between the j-th and the k-th measurement i.e. δijk = tik −tij, β0 denotes the fixed intercept, β1 denotes the fixed slope specific to the lower bound, β2 denotes the fixed slope specific to the upper bound, ui and vi denote the subject-specific parameters that are shared among the two models.

7. The computer-implemented method of claims 5 and 6, wherein the optimal and selected penalty terms are used to estimate the β-parameters and the subject-specific parameters ui and vi of the two I-RCV models.

8. Use of anyone of the aforementioned models in determining whether a measured change of a test value is within or outside of the I-RCV of said subject.

9. Use according to claim 8 wherein a measured change of a test value outside of the subject’s I- RCV is indicative of an important change.

10. Use according to claim 8 wherein a measured change of a test value inside of the subject’s I- RCV is indicative of a healthy change of the test value over time.

11. Use according to claims 8 or 9, wherein the subject is a human or non-human animal and the test value is a (clinical) biochemical test value, such as frequently measured in clinical laboratories.

12. A computer program product comprising a computer-executable program of instructions for performing, when executed on a computer, the steps of the method of any one of claims 1-7

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