Evaluation of Methods for Survival Analysis in the Presence of Extremely Few Events Per Variable

Abstract

A general rule of thumb for survival analysis is to have at least 15 events per variable in order to produce reliable inference in terms of accuracy and precision of regression coefficient estimates. Sometimes, even well designed studies may not meet this condition. Data may contain few events per variable due to the event of interest being rare, adjusting for an unavoidably large number of confounders, or interest in subgroup analysis. Propensity score methods and penalized regression are two approaches to handle similar problems with logistic regression, but further research is necessary to evaluate how these methods perform with the Cox proportional hazards model in the presence of extremely few events per variable. Exploring this problem, we conducted simulations based on a drug repurposing study in which significant findings were made for association of treatment with some common cancer types, but not for rare cancer types that did not have enough events despite a large sample of electronic records. Simulation results lead us to conclude that cox regression directly adjusting for the propensity score with an additional heterogeneity adjustment, or penalized cox regression that penalizes all but the coefficient for the exposure of interest perform the best out of the methods considered.