On the Restricted Mean Survival Time Curve in Survival Analysis

Abstract

Summary For a study with an event time as the endpoint, its survival function contains all the information regarding the temporal , stochastic profile of this outcome variable. The survival probability at a specific time point, say t, however, does not transparently capture the temporal profile of this endpoint up to t. An alternative is to use the restricted mean survival time (RMST) at time t to summarize the profile. The RMST is the mean survival time of all subjects in the study population followed up to t, and is simply the area under the survival curve up to t. The advantages of using such a quantification over the survival rate have been discussed in the setting of a fixed-time analysis. In this article, we generalize this approach by considering a curve based on the RMST over time as an alternative summary to the survival function. Inference, for instance, based on simultaneous confidence bands for a single RMST curve and also the difference between two RMST curves are proposed. The latter is informative for evaluating two groups under an equivalence or non-inferiority setting, and quantifies the difference of two groups in a time scale. The proposal is illustrated with the data from two clinical trials, one from oncology and the other from cardiology.

Inotuzumab Ozogamicin versus Standard Therapy for Acute Lymphoblastic Leukemia

“…The primary objective to demonstrate significantly improved final overall survival with inotuzumab ozogamicin vs standard care was not met at prespecified boundary of P =0.0208. However, overall survival data appeared to depart from the proportional hazards assumption; therefore, an exploratory posthoc restricted mean survival time analysis was applied 32 (truncation time, 37.7 months) to more precisely define the clinical benefit of inotuzumab ozogamicin. This analysis demonstrated a longer mean overall survival with inotuzumab ozogamicin vs standard care (mean [SE] 13.9 [1.10] vs 9.9 [0.85] months; P =0.005).…”

“…2C). Given this, an exploratory posthoc restricted mean survival time analysis was performed, 32 which demonstrated prolonged mean overall survival with inotuzumab ozogamicin versus standard care ( P =0.005). Based on the apparent separation of the overall survival curves after ~14 months, it may be speculated that the survival benefit occurs at later time points.…”

Prognostic Value of Braden Activity Subscale for Mobility Status in Hospitalized Older Adults

“…As an alternative, logistic regression was used to model the probability of impairment/recovery outcomes. In addition, a survival time estimate that is robust to the proportionality assumption was derived according to Royston and Parmar 14,15 and Zhao et al 16 This approach reports the difference between 2 survival curves using the restricted mean—a measure of average survival using the area under the survival curve from time point zero to last observed follow-up time. All models were adjusted for age, sex, race, and hospital length of stay.…”

Visualizing the quantile survival time difference curve

“…The SAS macro %kmdiff provides an easy‐to‐use computational tool to visually assess the estimated quantile survival time difference curve and its sample variability. The curve is intended as useful complement but not as replacement of the survival probability difference curve and all the refined approaches based thereon …”

“…The quantile survival time difference curve is not to be confused with the survival probability difference curve and approaches related to it . Besides that, the term “quantile difference” itself is not unambiguously defined.…”