Doubly-robust methods for differences in restricted mean lifetimes using pseudo-observations

Abstract

In clinical studies or trials comparing survival times between two treatment groups, the restricted mean lifetime (RML), defined as the expectation of the survival from time 0 to a prespecified time-point, is often the quantity of interest that is readily interpretable to clinicians without any modeling restrictions. It is well known that if the treatments are not randomized (as in observational studies), covariate adjustment is necessary to account for treatment imbalances due to confounding factors. In this article, we propose a simple doubly-robust pseudo-value approach to effectively estimate the difference in the RML between two groups (akin to a metric for estimating average causal effects), while accounting for confounders. The proposed method combines two general approaches: (a) group-specific regression models for the time-to-event and covariate information, and (b) inverse probability of treatment assignment weights, where the RMLs are replaced by the corresponding pseudo-observations for survival outcomes, thereby mitigating the estimation complexities in presence of censoring. The proposed estimator is double-robust, in the sense that it is consistent if at least one of the two working models remains correct. In addition, we explore the potential of available machine learning algorithms in causal inference to reduce possible bias of the causal estimates in presence of a complex association between the survival outcome and covariates. We conduct extensive simulation studies to assess the finite-sample performance of the pseudo-value causal effect estimators. Furthermore, we illustrate our methodology via application to a dataset from a breast cancer cohort study. The proposed method is implementable using the R package drRML, available in GitHub.