The Use of Restricted Mean Survival Time (RMST) Method When Proportional Hazards Assumption is in Doubt

In a recent article from AJRCCM (American Journal of Respiratory and Critical Care Medicine), Harhay et al discussed "An Alternative Approach for the Analysis of Time-to-Event and Survival Outcomes in Pulmonary Medicine'. The alternative approach discussed in the paper is called 'restricted mean survival time' or RMST in short.

In analyzing the time to event data, the most common approach is to draw Kaplan-Meier plots and then use non-parametric method (log-rank test or Wilcoxon test) to compare two different survival curve or use semi-parametric method (proportional hazard model) to perform the regression-type analyses to estimate the magnitude of the treatment difference. A key assumption is that the proportional hazards as the name of the method suggest. What it essentially means is that the ratio of the hazards for any two individuals or for any two groups is constant over time. However, in a lot of situations, the proportional hazard assumption may not hold - we call it non-proportional hazards. If we look at the Kaplan-Meier plots and see two curves crossover, it is likely there exist non-proportional hazards.

In a presentation by FDA statisticians (John Lawrence, Junshan Qiu, Steven Bai, and Jim Hung) "Comparison of Hazard Ratio and Restricted Mean Survival Analysis for Cardiorenal Drug Trials", several examples of the survival data with non-proportional hazards were presented. In the situation of the non-proportional hazards, the common approach such as the Cox proportional hazard model will give a biased estimate.

There are various methods to test the proportional hazard assumption. Please see the link below for details "testing the proportional hazard assumption in Cox models"

In the situation that the proportional hazard assumption is violated, the alternative approach should be explored. One approach coming in handy is the Restricted Mean Survival Time (RMST) method.

The RMST represents the area under the survival curve from time 0 to a specific follow-up time point; it is called restricted mean survival time because given X as the time until any event, the expectation of X (mean survival time) will be the area under the survival function (from 0 to infinity). RMST can be interpreted as the average time until an event occurs during a defined time period ranging from time 0 to a specific follow-up time point.

In the FDA's presentation above, there were final remarks about the RMST method: 

• RMST which is directly related to patient’s survival/event-free time, is viable for quantifying treatment effect. • RMST can give better clinical interpretation of treatment effect.
• The results came from a R function. Yesterday, I found that someone in Lily actually developed SAS macro for RMST.

In the article by Harhay et al, there were also the final comments:

"As shown in these examples, the RMST offers several inferential advantages over other
time-to-event statistics. Though we examined survival, any time-to-event endpoint can be assessed using the RMST approach. Statistical inference (i.e., estimation and hypothesis testing) using the RMST, including p-values, confidence intervals, and covariate-adjustment, can be performed in most popular statistical software packages, such as R and STATA. Study group comparisons using the RMST estimate also confer comparable statistical power to the log-rank test and test for the HR in many situations, thereby providing an alternative and clinically meaningful measure of time gained or lost to inform research and patient care."

Programs have been developed to calculate the RMST.

There is an R package developed by Uno H:

• https://cran.r-project.org/web/packages/survRM2/vignettes/survRM2-vignette3-2.html

In SAS, there was a SAS macro available:

• https://pdfs.semanticscholar.org/5411/7b8fb137211bcab04534017abf12cc581eb6.pdf
• http://bcb.dfci.harvard.edu/~huno/computer-program/rmst2_ver003.sas
• Calculating Restricted Mean Survival Time

Other References:

• An application of restricted mean survival time in a competing risks setting: comparing time to ART initiation by injection drug use
• Comparison of the restricted mean survival time with the hazard ratio in superiority trials with a time-to-event end point: Comparison of the RMST with the HR
• FDA NDA Medical Review for 207997Orig1s000 and 207997Orig2s000
• Tai-Tsang Chen "Alternative Survival Endpoints" from Immuno-Oncology Drug Development Workshop
• Royston P, Parmar M. The use of restricted mean survival time to estimate the treatment effect in randomized clinical trials when the proportional hazards assumption is in doubt. Stat Med. 2011;30:2409-2421.