Prognostic R² in Survival Models Is Design-Dependent: The Role of Censoring and Follow-Up

Thomas M. Menino Convention & Exhibition Center 

Measures of explained variation, such as prognostic R², are widely used to evaluate survival models and to inform key design decisions, including sample size planning and external validation. In time-to-event settings, explained variation is not solely determined by the prognostic signal, but also by the amount of event information observed. We show that prognostic R² measures are inherently design-dependent and require explicit conditioning on censoring and recruitment mechanisms. Using controlled simulations with fixed hazard ratios, we investigate the behavior of common R² statistics under varying administrative censoring and follow-up. Likelihood-based measures show substantial downward bias as censoring increases, even when prognostic separation is unchanged, whereas separation-based measures remain stable. These results indicate that differences in explained variation may primarily reflect study design rather than model performance. We discuss implications for comparative modeling, external validation, and planning of prognostic studies, emphasizing that explained variation depends on both prognostic signal and information accrual.

Survival analysis

Study design

Censoring

Prognostic R²

Prognostic models

Risk prediction 

Biometrics Section