A Comparison of Different Methods to Adjust Survival Curves for Confounders

TL;DR

This study compares various statistical methods for adjusting survival curves for confounders in observational studies, evaluating their bias and fit through simulations and real data, highlighting the advantages of doubly-robust estimators.

Contribution

It provides a comprehensive comparison of multiple confounder adjustment methods for survival analysis, including their performance in different scenarios and sample sizes.

Findings

All methods showed no bias in medium to large samples when used properly.

Cox regression methods exhibited bias in small samples.

Doubly-robust estimators were unbiased when either model was correct and had good fit.

Abstract

Treatment specific survival curves are an important tool to illustrate the treatment effect in studies with time-to-event outcomes. In non-randomized studies, unadjusted estimates can lead to biased depictions due to confounding. Multiple methods to adjust survival curves for confounders exist. However, it is currently unclear which method is the most appropriate in which situation. Our goal is to compare forms of Inverse Probability of Treatment Weighting, the G-Formula, Propensity Score Matching, Empirical Likelihood Estimation and augmented estimators as well as their pseudo-values based counterparts in different scenarios with a focus on their bias and goodness-of-fit. We provide a short review of all methods and illustrate their usage by contrasting the survival of smokers and non-smokers, using data from the German Epidemiological Trial on Ankle-Brachial-Index. Subsequently, we compare the methods using a Monte-Carlo simulation. We consider scenarios in which correctly or incorrectly specified models for describing the treatment assignment and the time-to-event outcome are used with varying sample sizes. The bias and goodness-of-fit is determined by taking the entire survival curve into account. When used properly, all methods showed no systematic bias in medium to large samples. Cox regression based methods, however, showed systematic bias in small samples. The goodness-of-fit varied greatly between different methods and scenarios. Methods utilizing an outcome model were more efficient than other techniques, while augmented estimators using an additional treatment assignment model were unbiased when either model was correct with a goodness-of-fit comparable to other methods. These doubly-robust methods have important advantages in every considered scenario.