A measure of explained variation for event history data

Area of Science:

• Statistics
• Biostatistics
• Survival Analysis

Background:

• Existing measures for survival model prognostic value lack uniformity and broad applicability.
• Many current metrics fail to accommodate complex data structures like recurrent events or time-varying effects.
• There is a need for a universally accepted measure analogous to R-squared for regression.

Purpose of the Study:

• To present a novel measure for evaluating the prognostic value of general dynamic event history regression models.
• To develop a versatile metric applicable across diverse statistical modeling scenarios.
• To provide a unified measure that overcomes limitations of existing prognostic metrics.

Main Methods:

• Development of a new prognostic measure tailored for dynamic event history regression.
• Demonstration of applicability to discrete/continuous time, tied data, and time-varying covariates/effects.
• Extension to single/multiple event times, parametric/semiparametric models, and independent censoring.
• Reduction to the concordance index for simple survival data.

Main Results:

• The proposed measure is broadly applicable and interpretable across various complex survival data settings.
• It unifies existing concepts and extends prognostic assessment to dynamic event history models.
• Expressions for population value and estimator variance are provided, with R software available.

Conclusions:

• The new measure offers a robust and versatile tool for assessing survival model performance.
• It addresses critical limitations of existing prognostic metrics in statistical literature.
• This advancement facilitates more accurate and comprehensive evaluation of dynamic event history models.