Doubly robust estimators of the restricted mean time in favor estimands in individual- and cluster-randomized trials

TL;DR

This paper introduces doubly robust estimators for the restricted mean time in favor of treatment in multi-state survival trials, applicable to individual and cluster-randomized designs, improving efficiency and interpretability without restrictive assumptions.

Contribution

It develops a novel class of doubly robust estimators for RMT-IF that handle right censoring and cluster effects, extending existing methods to more complex trial settings.

Findings

Estimators are consistent if either outcome or censoring model is correct.

Simulation studies show improved finite-sample performance.

Application to real trials demonstrates practical utility.

Abstract

Progressive multi-state survival outcomes are common in trials with recurrent or sequential events and require treatment effect estimands that remain interpretable without proportional intensity or Markov assumptions. The restricted mean time in favor of treatment (RMT-IF) extends the restricted mean survival time to ordered multi-state processes and provides such an interpretable estimand. However, existing RMT-IF methods are nonparametric, assume covariate-independent censoring for independent observations, and do not accommodate cluster-randomized trials (CRTs), limiting both efficiency and applicability. We develop a class of doubly robust estimators for RMT-IF under right censoring using an augmented inverse-probability weighting framework that combines stage-specific outcome regression with arm-specific censoring models, yielding consistency when either nuisance model is correctly specified. We further extend the framework to CRTs by formalizing both cluster-level and individual-level average RMT-IF estimands to address informative cluster size and by constructing corresponding doubly robust estimators that account for within-cluster correlation. For inference, we employ model-agnostic jackknife variance estimators in both individually randomized and cluster-randomized settings. Extensive simulation studies demonstrate finite-sample performance, and the methods are illustrated using two randomized trial examples.