Focused Information Criterion for Restricted Mean Survival Times: Non-Parametric or Parametric Estimators

Abstract

Restricted Mean Survival Time (RMST), the average time without an event of interest until a specific time point, is a model-free, easy to interpret statistic. The heavy reliance on non-parametric or semi-parametric methods in the survival analysis has drawn criticism, due to the loss of efficacy compared to parametric methods. This assumes that the parametric family used is the true one, otherwise the gain in efficacy might be lost to interpretability problems due to bias. The Focused Information Criterion (FIC) considers the trade-off between bias and variance and offers an objective framework for the selection of the optimal non-parametric or parametric estimator for scalar statistics. Herein, we present the FIC framework for the selection of the RMST estimator with the best bias-variance trade-off. The aim is not to identify the true underling distribution that generated the data, but to identify families of distributions that best approximate this process. Through simulation studies and theoretical reasoning, we highlight the effect of censoring on the performance of FIC. Applicability is illustrated with a real life example. Censoring has a non-linear effect on FICs performance that can be traced back to the asymptotic relative efficiency of the estimators. FICs performance is sample size dependent; however, with censoring percentages common in practical applications FIC selects the true model at a nominal probability (0.843) even with small or moderate sample sizes.

Asymptotic Relative Efficiency of Parametric and Nonparametric Survival Estimators

“…From the perspective of correlation, we can look at ARE as the amount of (linear) information that the Kaplan-Meier estimate contains about the form of the parametric model. Near zero ARE or correlation at the beginning of the follow-up likely suggests that the Kaplan-Meier estimate confers limited knowledge about possible parametric estimators, which might complicate the data driven choice of parametric estimators [8,25,26]. While theoretically this is a problem at follow-up times where the survival probability approaches zero, in practice, at that time, survival estimates are rarely meaningful from an interpretation point of view [27].…”