Estimating the Treatment Effect in a Clinical Trial Using Difference in Restricted Mean Survival Time

Abstract

The causal effect of a new medical treatment compared with a standard regimen is best assessed in a randomized controlled trial setting. When the main outcome is time to some event of interest, such as death, studies often use the hazard ratio to describe the treatment effect. Typically, proportional hazards are assumed. Here I discuss several significant disadvantages of using the hazard ratio, including its vulnerability to the proportionality assumption, its relative nature, and its lack of relationship with time-to-event or survival probabilities. I describe the use of restricted mean survival time as an alternative outcome measure in time-to-event trials. With this method, the treatment effect is defined as the difference in restricted mean between the trial arms. I suggest the use of Royston and Parmar's (2002, Statistics in Medicine 21: 2175–2197) class of flexible parametric models, implemented through the command stpm2 (Lambert and Royston [2009, Stata Journal 9: 265–290] and Andersson and Lambert [2012, Stata Journal 12: 623–638]), to estimate the required quantities. With this approach, proportional hazards are not assumed. I describe a new command, strmst, for implementing these calculations. This method supports “direct” adjustment for covariates by using marginalization over their observed distribution, and it supports estimation of treatment effects conditional on fixed values of covariates. I illustrate the methodology using data from a trial in primary biliary cirrhosis. I provide an example that demonstrates the importance of understanding the relationship between the treatment effect, the prognosis of the disease outcome, and the often-neglected time domain.