Quantifying discrimination of Framingham risk functions with different survival C statistics

Area of Science:

• Biostatistics
• Epidemiology
• Cardiovascular Research

Background:

• Cardiovascular risk prediction models are vital clinical tools, often built using survival regression.
• Evaluating the performance of these models requires intuitive and interpretable metrics.
• Discrimination, a key concept in logistic regression, has been extended to survival analysis, but extensions vary.

Purpose of the Study:

• To define and evaluate discrimination in survival analysis consistently with logistic regression.
• To examine four proposed C statistics for assessing survival model performance.
• To identify the most appropriate C statistic for measuring a model's ability to differentiate survival times.

Main Methods:

• Defined discrimination in survival analysis as the model's capacity to separate individuals with longer versus shorter event-free survival within a specific time frame.
• Employed practical examples, conceptual illustrations, and numerical simulations.
• Analyzed four distinct C statistics from existing literature.

Main Results:

• The four examined C statistics yield different numerical values and capture varied aspects of discrimination.
• The C statistic proposed by Harrell demonstrated the greatest alignment with the defined concept of discrimination.
• Significant differences exist in how various C statistics quantify model performance.

Conclusions:

• Harrell's C statistic is recommended for evaluating discrimination in survival models based on the defined criteria.
• Researchers should clearly report the specific C statistic used and justify its selection.
• Comparing discrimination metrics across studies may lack validity due to inherent differences in C statistics.