Short Courses4
Short Course 4: On RMST in survival analysis
May 18, 2025, 8:30am - 5:00pm,PDT
Stanford Campus, LKSC 130
Instructor: Lu Tian, Stanford University
Lu Tian is Professor of the Department of Biomedical Data Science at Stanford University. He received his Doctor of Science degree in Biostatistics from Harvard University. Dr. Tian has rich experience in statistical methodological research, and study design for randomized clinical trials. He has published more than 300 research papers in both statistical and clinical journals. He is an elected Fellow of American Statistical Association. His current research interest is in developing statistical methods in precision medicine, meta-analysis, randomized clinical trial, and survival analysis.
Abstract
Since Professor Sir David Cox proposed the hazard ratio (HR) and its inference procedure in 1972, the HR has been routinely used for quantifying the treatment effect on time to event endpoint. The Cox regression model has also been commonly used for the association and prediction analysis. While an ideal summary measure for the treatment effect should be model-free to avoid the model misspecification at the analysis, the HR is not such a measure. Indeed, there are very few model-free measures for time to event endpoint. The most popular one is either based on the median failure time or the event rate at a specific time point. Both measures are “local” and cannot catch the short- or long-term survival profile.
In the past few years, issues of utilizing HR have been extensively discussed. The validity of the HR estimate depends on a strong model assumption; that is, the ratio of two hazard functions is constant over time. When the proportion hazards assumption is not met, the HR estimate is difficult, if not impossible to interpret. In fact, the parameter for which the empirical HR estimates is not a simple weighted average of the HR over time and it generally depends on the censoring distributions. This is highly undesirable. Moreover, even when the proportional hazards assumption is plausible, the physical/clinical interpretation of a single ratio such as the HR estimate between two groups can not be easily translated into the clinical utility of a new treatment in the absence of a reference hazard level.
In this short course, I will illustrate issues of the HR and present an alternative, that is, the t-year mean survival time (restricted mean survival time, RMST). It is the mean event-free time up to a specific time point, say, t-year. The RMST was introduced in the statistical literature in 1949, but had not got much attention until recently. Here is the list of the topics we will discuss in this short course.
Issues of Hazard Ratio (HR)
Restricted mean survival time (RMST)
Power comparison between RMST-based test and HR-based tests
Empirical choice of a truncation time for RMST
Study design based on RMST
RMST for stratified analysis of survival data.
RMST to non-inferiority trials
RMST to quantify long-term survival benefit
RMST to assess duration of response
RMST in the presence of competing risks
RMST for recurrent event time data
Average hazard as an extension of RMST.