An application of Harrell's C-index to PH frailty models

Area of Science:

• Biostatistics
• Survival Analysis
• Medical Statistics

Background:

• Frailty models are crucial in medical applications, but robust measures for their predictive ability are lacking.
• Existing research has not sufficiently addressed the quantification of predictive performance in these complex models.

Purpose of the Study:

• To introduce and define novel concordance probability measures for clustered data in frailty models: Overall Conditional C-index (C(O, C)) and Overall Marginal C-index (C(O, M)).
• To propose methods for estimating these indices, including 'Within C-index' (C(W)) and 'Between C-index' (C(B, C), C(B, M)), within both likelihood and Bayesian frameworks.
• To evaluate the performance of point estimates and confidence/credible intervals for these indices through simulation and real-data analysis.

Main Methods:

• Elaboration of concordance probability for clustered data, defining C(O, C), C(O, M), C(B, C), C(B, M), C(W, C), and C(W, M).
• Application of Harrell's C-index within likelihood and Bayesian contexts for estimating proposed indices.
• Extensive simulation study to compare the performance of point estimates and confidence/credible intervals.

Main Results:

• Point estimates for C(W) and C(B, M) demonstrated good performance in both likelihood and Bayesian approaches.
• The Bayesian approach exhibited reduced bias for C(B, C) point estimates compared to the likelihood approach.
• Confidence and credible intervals showed adequate coverage properties, aligning with the performance of the point estimates.

Conclusions:

• The proposed C-indices offer valuable tools for quantifying the predictive performance of frailty models with clustered data.
• The Bayesian estimation approach shows advantages for specific components like C(B, C), suggesting its utility in frailty model assessment.
• The study provides a comprehensive evaluation of these novel statistical measures, validated through simulations and real-world data.