Joint Longitudinal Biomarker Modeling for Cumulative Change and Survival Risk
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Solution Overview
Problem
Existing statistical models fail to systematically describe the longitudinal index cumulative change rate and its influence on survival data models, leading to inaccurate risk predictions, particularly in fields like cardiovascular disease, financial technology, and industrial manufacturing.
Innovation Solution
A joint modeling method is developed that includes determining expressions for longitudinal index mean and cumulative change rate functions, constructing sub-models for longitudinal and survival data, and calculating maximum likelihood estimations using an EM algorithm to quantify and compare the influence of these factors on survival risk.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If sample standard deviation or coefficient of variation of longitudinal data is used as independent variable in survival data model, then the operation is simple and easy, but the description of change rate is not sufficient and stable, causing serious deviation in parameter estimation
Solution Approach 1:
The patent transforms the longitudinal index process into a parametric form by introducing a cumulative change rate function with specific parameters. Instead of using simple sample statistics, the patent defines a mathematical function with parameters that can be estimated through maximum likelihood, thereby improving measurement precision while maintaining operational feasibility through systematic estimation procedures.
Solution Approach 2:
The patent introduces a cumulative change rate function as an intermediary between the raw longitudinal data and the survival model. This intermediary function systematically captures the change rate information through its parameters, which then serve as independent variables in the survival analysis, bridging the gap between simple operations and precise measurement.
2Reliability
If the mean function or first derivative at current time point is used as independent variable, then the systematic influence of longitudinal index is considered, but the cumulative change rate until time t is not considered
Solution Approach 1:
The patent extends the analysis from instantaneous rates (first derivative at current time) to cumulative rates over time by introducing a time-integrated dimension. The cumulative change rate function accumulates information from time zero to time t, adding a temporal accumulation dimension that captures the history of changes, thereby preventing information loss while maintaining systematic influence consideration.
Solution Approach 2:
The patent performs preliminary integration of the longitudinal index process to obtain the cumulative change rate function before applying it to the survival model. This preliminary action of accumulating change information over time ensures that the cumulative effect is captured and incorporated into the survival analysis, avoiding the loss of historical change information.
3Measurement precision
If variance or logarithm of variance of random error is introduced as random effect in survival model, then measurement error is accounted for, but the cumulative change rate cannot be systematically described and lacks theoretical basis
Solution Approach 1:
The patent creates a multi-functional framework where the cumulative change rate function simultaneously serves multiple purposes: it systematically describes the change rate process, accounts for measurement errors through its parametric structure, and provides a theoretically grounded basis for survival analysis. This universal function replaces the need for separate error accounting mechanisms while maintaining theoretical rigor.
Solution Approach 2:
The patent combines elements of longitudinal data analysis, error modeling, and survival analysis into a composite statistical framework. The cumulative change rate function integrates information from multiple sources (longitudinal observations, error structures) into a unified representation that can be systematically applied to survival modeling, creating a composite approach that achieves both precision and systematic description.
4Measurement precision
If parametric and nonparametric algorithms are used to judge change points, then local change can be depicted, but the global dynamic change rate cannot be judged
Solution Approach 1:
The patent merges local change detection capabilities with global dynamic analysis by defining a cumulative change rate function that integrates information across the entire time period. The parametric structure of this function allows simultaneous estimation of local characteristics (through its derivatives) and global behavior (through its cumulative nature), thereby combining the strengths of local and global analysis methods.
Solution Approach 2:
The patent ensures continuous capture of change rate information from time zero to the current time point through the cumulative change rate function. This continuous accumulation of change information maintains the useful action of tracking changes throughout the entire observation period, preventing loss of global dynamic information while preserving local change detection capabilities.
Data Source
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AI summary
Embodiments of the present invention disclose a joint modeling method, a method for judging the influence of an index on a model and a storage medium, wherein the joint modeling method comprises: determining an expression of a longitudinal index mean function and an expression of a longitudinal index cumulative change rate function; constructing a longitudinal data sub-model and a survival data sub-model; determining a covariance matrix structure of a random error in the longitudinal data sub-model based on a calculation model selection criterion, and calculating a maximum likelihood estimation value of parameters in the longitudinal data sub-model and the survival data sub-model by adopting an EM algorithm, and predicting a multidimensional random effect in the longitudinal index mean function to obtain the estimation of a smooth function in the longitudinal index mean function.