Asymptotic Relative Efficiency of Parametric and Nonparametric Survival Estimators

The dominance of non- and semi-parametric methods in survival analysis is not without criticism. Several studies have highlighted the decrease in efficiency compared to parametric methods. We revisit the problem of Asymptotic Relative Efficiency (ARE) of the Kaplan-Meier survival estimator compared to parametric survival estimators. We begin by generalizing Miller's approach and presenting a formula that enables the estimation (numerical or exact) of ARE for various survival distributions and types of censoring. We examine the effect of follow-up time and censoring on ARE. The article concludes with a discussion about the reasons behind the lower and time-dependent ARE of the Kaplan-Meier survival estimator.