Exponential Survival Curve Modeling for Cancer Risk Group Separation

The patent divides the survival curve model into multiple exponential functions, each representing different patient subgroups with distinct risk profiles. This segmentation allows the model to capture heterogeneous progression patterns (rapid progressors vs. slow progressors) that a single exponential function cannot represent, thereby improving patient group separation accuracy while maintaining reasonable model complexity through structured decomposition.

The patent introduces multiple parameters (α1, α2, β1, β2) to characterize different exponential functions, allowing flexible adjustment of progression rates and risk profiles for different patient subgroups. By changing these parameters, the model can accurately fit diverse survival patterns and separate patient groups based on their specific risk characteristics, resolving the limitation of fixed single-parameter models.

The patent segments the survival analysis into distinct components: early progression events and death events. By using multiple exponential functions with different parameters, the model separately captures these event types, preventing loss of early progression information that would occur in aggregated traditional models, while maintaining analytical tractability through structured decomposition.

The patent introduces intensity as an intermediary parameter derived from the ratio of exponential function components. This intensity metric serves as a mediator that quantifies the relative contribution of different progression patterns, enabling separate consideration of early progression and death while maintaining a unified analytical framework that preserves information without excessive complexity.

The patent moves beyond RMST by introducing multiple parameters (α1, α2, β1, β2) that characterize different exponential decay patterns. These parameters enable precise quantification of treatment effects on specific patient subgroups, improving measurement precision for treatment effectiveness evaluation while maintaining robustness through the flexible multi-parameter framework that adapts to different survival patterns.

The patent introduces dynamic intensity measures that vary over time and across patient groups, rather than relying on static RMST summaries. This dynamic approach allows the model to capture changing treatment effects and risk profiles over the survival trajectory, improving precision in evaluating treatment effectiveness while maintaining robustness through the underlying exponential function structure.