Clustered restricted mean survival time regression

Abstract

For multicenter randomized trials or multilevel observational studies, the Cox regression model has long been the primary approach to study the effects of covariates on time‐to‐event outcomes. A critical assumption of the Cox model is the proportionality of the hazard functions for modeled covariates, violations of which can result in ambiguous interpretations of the hazard ratio estimates. To address this issue, the restricted mean survival time (RMST), defined as the mean survival time up to a fixed time in a target population, has been recommended as a model‐free target parameter. In this article, we generalize the RMST regression model to clustered data by directly modeling the RMST as a continuous function of restriction times with covariates while properly accounting for within‐cluster correlations to achieve valid inference. The proposed method estimates regression coefficients via weighted generalized estimating equations, coupled with a cluster‐robust sandwich variance estimator to achieve asymptotically valid inference with a sufficient number of clusters. In small‐sample scenarios where a limited number of clusters are available, however, the proposed sandwich variance estimator can exhibit negative bias in capturing the variability of regression coefficient estimates. To overcome this limitation, we further propose and examine bias‐corrected sandwich variance estimators to reduce the negative bias of the cluster‐robust sandwich variance estimator. We study the finite‐sample operating characteristics of proposed methods through simulations and reanalyze two multicenter randomized trials.

Restricted mean survival time to estimate an intervention effect in a cluster randomized trial

“…Chen et al. 28 recently proposed an extended method for estimating normalΔ R M S T false( t * false) for clustered data based on a different approach directly modeling the RMST as a continuous function of the horizon time t * and accounting for covariate-dependent censoring with inverse probability of censoring weights. Our method is suitable when there is a clear time horizon, but the Chen et al.…”

“…25–27 Recently, Chen et al. 28 adapted to clustered data a method initially proposed by Zhong and Schaubel 27 for independent data that estimates the RMST as a continuous function of the horizon time t * allowing for covariate-dependent censoring. To our knowledge, no other RMST estimation approach has been extended to clustered data.…”

“…Several methods have been developed to estimate a difference in RMST for independent data such as the direct integration of the Kaplan-Meier survival curves, 21 Andersen's pseudo-values regression method, [22][23][24] Royston and Parmar's flexible parametric survival model 15,20 as well as methods based on the inverse probability of censoring weighting accounting for covariate-dependent censoring. [25][26][27] Recently, Chen et al 28 adapted to clustered data a method initially proposed by Zhong and Schaubel 27 for independent data that estimates the RMST as a continuous function of the horizon time t* allowing for covariate-dependent censoring. To our knowledge, no other RMST estimation approach has been extended to clustered data.…”

Improving sandwich variance estimation for marginal Cox analysis of cluster randomized trials

“…More recently, Chen et al. (2022) studied the bias‐corrected variance estimators for clustered restricted mean survival time regression models, Blaha et al. (2022) considered the bias‐corrected variance estimators for CRTs with time‐to‐event outcomes under the additive hazards mixed model, and Chen and Li (2022) compared different bias‐corrected variance estimators for the marginal Fine–Gray regression model in CRTs with competing risks, but none of them studied the bias‐corrected variance estimators for the Cox model analysis of CRTs.…”