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

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1-30
Number of pages30
JournalLifetime Data Analysis
DOIs
StateAccepted/In press - Feb 28 2018

Fingerprint

Randomized Trial
Proportional Hazards
Hazards
Estimator
Kaplan-Meier Estimator
Baseline
Survival Time
Censoring
Random Censoring
Kaplan-Meier
Survival Distribution
Randomized Clinical Trial
Right Censoring
Relative Efficiency
Identifiability
Treatment Effects
Resampling
Regularity Conditions
Stroke
Leverage

Keywords

  • Covariate adjustment
  • Efficiency
  • Random censoring
  • Targeted minimum loss based estimation

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

@article{6d2499ed45db45888cb6a14e74e33075,
title = "Improved precision in the analysis of randomized trials with survival outcomes, without assuming proportional hazards",
abstract = "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.",
keywords = "Covariate adjustment, Efficiency, Random censoring, Targeted minimum loss based estimation",
author = "Iv{\'a}n D{\'i}az and Colantuoni, {Elizabeth Ann} and Hanley, {Daniel F} and Rosenblum, {Michael Aaron}",
year = "2018",
month = "2",
day = "28",
doi = "10.1007/s10985-018-9428-5",
language = "English (US)",
pages = "1--30",
journal = "Lifetime Data Analysis",
issn = "1380-7870",
publisher = "Springer Netherlands",

}

TY - JOUR

T1 - Improved precision in the analysis of randomized trials with survival outcomes, without assuming proportional hazards

AU - Díaz, Iván

AU - Colantuoni, Elizabeth Ann

AU - Hanley, Daniel F

AU - Rosenblum, Michael Aaron

PY - 2018/2/28

Y1 - 2018/2/28

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

UR - http://www.scopus.com/inward/record.url?scp=85042608023&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85042608023&partnerID=8YFLogxK

U2 - 10.1007/s10985-018-9428-5

DO - 10.1007/s10985-018-9428-5

M3 - Article

SP - 1

EP - 30

JO - Lifetime Data Analysis

JF - Lifetime Data Analysis

SN - 1380-7870

ER -