Estimating the difference in restricted mean survival time accounting for trial effect in individual patient data meta-analyses

Abstract

Introduction The difference in restricted mean survival times (RMSTs) between two treatment groups is a useful tool to provide information on the average causal treatment effect in a randomised clinical trial. This method is particularly appealing since it does not require a proportional hazards assumption, unlike the hazard ratio based on the Cox model. The RMST can be obtained by integrating under the survival curve up to a predetermined horizon. A particular concern in individual patient data meta-analyses (IPD-MA) is to properly account for the trial effect in the estimation of the difference in RMSTs. Objective Our objective is to estimate the difference in RMSTs in an IPD-MA using various propositions where the RMST is adjusted on covariates and includes a random trial effect. Methods In our first proposition, we use the Breslow estimator as proposed by Zucker (JASA, 1998) to have an estimation of the baseline hazard adjusted on the trials and on other covariates, and calculate the area under the curve. A variance estimator is obtained with an added term in the expression (Chen and Tsiatis, Biometrics, 2001) to remove the conditioning on the trial. The second proposition is based on a general linear mixed model that includes a random trial effect. The Poisson regression allows the estimation of the survival baseline hazard. We use a variance based on the Delta method. Finally, the third proposition is based on a Breslow estimator, which takes into account the random trial effect (Gorfine et al., Biometrika, 2006). An IPD-MA from the Global Advanced/Adjuvant Stomach Tumor Research International Collaboration (GASTRIC, JAMA, 2010) is used for illustration. Results A simulation study has been set up generating Weibull data with random trial and treatment-by-trial effects. A true “RMST” is calculated through a double integration of the parametric survival function; and the bias and variance of our estimation methods is evaluated with respect to this value. The IPD-MA included 3288 patients with resectable gastric cancer from 14 randomised trials of adjuvant chemotherapy versus surgery alone. At the 10 y [20 y] horizon, the estimated difference in RMSTs is 141 [354] days (SE 45 [104] days; P = 0.002 [P Conclusions We proposed estimation methods for the difference of RMSTs between two treatment groups in the IPD meta-analyses context.