A Comparison of Different Methods to Adjust Survival Curves for Confounders
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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 these methods 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 covariate sets 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 summary statistics which take into account the entire survival curve. 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. Pseudo-Value based methods, coupled with isotonic regression to correct for non-monotonicity, are viable alternatives to traditional methods.
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