Lifetime Data Analysis

, Volume 25, Issue 3, pp 439–468 | Cite as

Improved precision in the analysis of randomized trials with survival outcomes, without assuming proportional hazards

  • Iván DíazEmail author
  • Elizabeth Colantuoni
  • Daniel F. Hanley
  • Michael Rosenblum


We present a new estimator of the restricted mean survival time in randomized trials where there is right censoring that may depend on treatment and baseline variables. The proposed estimator leverages prognostic baseline variables to obtain equal or better asymptotic precision compared to traditional estimators. Under regularity conditions and random censoring within strata of treatment and baseline variables, the proposed estimator has the following features: (i) it is interpretable under violations of the proportional hazards assumption; (ii) it is consistent and at least as precise as the Kaplan–Meier and inverse probability weighted estimators, under identifiability conditions; (iii) it remains consistent under violations of independent censoring (unlike the Kaplan–Meier estimator) when either the censoring or survival distributions, conditional on covariates, are estimated consistently; and (iv) it achieves the nonparametric efficiency bound when both of these distributions are consistently estimated. We illustrate the performance of our method using simulations based on resampling data from a completed, phase 3 randomized clinical trial of a new surgical treatment for stroke; the proposed estimator achieves a 12% gain in relative efficiency compared to the Kaplan–Meier estimator. The proposed estimator has potential advantages over existing approaches for randomized trials with time-to-event outcomes, since existing methods either rely on model assumptions that are untenable in many applications, or lack some of the efficiency and consistency properties (i)–(iv). We focus on estimation of the restricted mean survival time, but our methods may be adapted to estimate any treatment effect measure defined as a smooth contrast between the survival curves for each study arm. We provide R code to implement the estimator.


Covariate adjustment Efficiency Targeted minimum loss based estimation Random censoring 



Funding was provided by Patient-Centered Outcomes Research Institute (Grant No. ME-1306-03198), U.S. Food and Drug Administration (US) (Grant No. HHSF223201400113C) and National Institute of Neurological Disorders and Stroke (US) (Grant No. U01NS062851).

Supplementary material

10985_2018_9428_MOESM1_ESM.pdf (163 kb)
Proofs for the main results in the paper.
10985_2018_9428_MOESM2_ESM.r (13 kb)
R functions to compute the proposed estimator.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Iván Díaz
    • 1
    Email author
  • Elizabeth Colantuoni
    • 2
  • Daniel F. Hanley
    • 3
  • Michael Rosenblum
    • 2
  1. 1.Division of Biostatistics and EpidemiologyWeill Cornell MedicineNew YorkUSA
  2. 2.Department of BiostatisticsJohns Hopkins Bloomberg School of Public HealthBaltimoreUSA
  3. 3.Division of Brain Injury OutcomesJohns Hopkins Medical InstitutionsBaltimoreUSA

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