TY - JOUR
T1 - Improved precision in the analysis of randomized trials with survival outcomes, without assuming proportional hazards
AU - Díaz, Iván
AU - Colantuoni, Elizabeth
AU - Hanley, Daniel F.
AU - Rosenblum, Michael
N1 - Funding Information:
Acknowledgements 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).
Funding Information:
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).
Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2019/7/15
Y1 - 2019/7/15
N2 - 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.
AB - 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.
KW - Covariate adjustment
KW - Efficiency
KW - Random censoring
KW - Targeted minimum loss based estimation
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U2 - 10.1007/s10985-018-9428-5
DO - 10.1007/s10985-018-9428-5
M3 - Article
C2 - 29492746
AN - SCOPUS:85042608023
SN - 1380-7870
VL - 25
SP - 439
EP - 468
JO - Lifetime Data Analysis
JF - Lifetime Data Analysis
IS - 3
ER -