Confidence interval estimation for the changepoint of treatment stratification in the presence of a qualitative covariate-treatment interaction

Bernhard Haller, Ulrich Mansmann, Dennis Dobler, Kurt Ulm, Alexander Hapfelmeier

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

The goal in stratified medicine is to administer the “best” treatment to a patient. Not all patients might benefit from the same treatment; the choice of best treatment can depend on certain patient characteristics. In this article, it is assumed that a time-to-event outcome is considered as a patient-relevant outcome and a qualitative interaction between a continuous covariate and treatment exists, ie, that patients with different values of one specific covariate should be treated differently. We suggest and investigate different methods for confidence interval estimation for the covariate value, where the treatment recommendation should be changed based on data collected in a randomized clinical trial. An adaptation of Fieller's theorem, the delta method, and different bootstrap approaches (normal, percentile-based, wild bootstrap) are investigated and compared in a simulation study. Extensions to multivariable problems are presented and evaluated. We observed appropriate confidence interval coverage following Fieller's theorem irrespective of sample size but at the cost of very wide or even infinite confidence intervals. The delta method and the wild bootstrap approach provided the smallest intervals but inadequate coverage for small to moderate event numbers, also depending on the location of the true changepoint. For the percentile-based bootstrap, wide intervals were observed, and it was slightly conservative regarding coverage, whereas the normal bootstrap did not provide acceptable results for many scenarios. The described methods were also applied to data from a randomized clinical trial comparing two treatments for patients with symptomatic, severe carotid artery stenosis, considering patient's age as predictive marker.

Original languageEnglish
Pages (from-to)70-96
Number of pages27
JournalStatistics in Medicine
Volume39
Issue number1
Early online date7 Nov 2019
DOIs
Publication statusPublished - 15 Jan 2020

Fingerprint

Interval Estimation
Change Point
Stratification
Confidence interval
Covariates
Confidence Intervals
Fieller's Theorem
Interaction
Wild Bootstrap
Bootstrap
Delta Method
Randomized Clinical Trial
Coverage
Percentile
Therapeutics
Randomized Controlled Trials
Stenosis
Interval
Carotid Stenosis
Arteries

Keywords

  • changepoint
  • confidence intervals
  • covariate-treatment interaction
  • Cox regression
  • stratified medicine

Cite this

@article{36ec5d175ec545598cb6e4a813ea21d9,
title = "Confidence interval estimation for the changepoint of treatment stratification in the presence of a qualitative covariate-treatment interaction",
abstract = "The goal in stratified medicine is to administer the “best” treatment to a patient. Not all patients might benefit from the same treatment; the choice of best treatment can depend on certain patient characteristics. In this article, it is assumed that a time-to-event outcome is considered as a patient-relevant outcome and a qualitative interaction between a continuous covariate and treatment exists, ie, that patients with different values of one specific covariate should be treated differently. We suggest and investigate different methods for confidence interval estimation for the covariate value, where the treatment recommendation should be changed based on data collected in a randomized clinical trial. An adaptation of Fieller's theorem, the delta method, and different bootstrap approaches (normal, percentile-based, wild bootstrap) are investigated and compared in a simulation study. Extensions to multivariable problems are presented and evaluated. We observed appropriate confidence interval coverage following Fieller's theorem irrespective of sample size but at the cost of very wide or even infinite confidence intervals. The delta method and the wild bootstrap approach provided the smallest intervals but inadequate coverage for small to moderate event numbers, also depending on the location of the true changepoint. For the percentile-based bootstrap, wide intervals were observed, and it was slightly conservative regarding coverage, whereas the normal bootstrap did not provide acceptable results for many scenarios. The described methods were also applied to data from a randomized clinical trial comparing two treatments for patients with symptomatic, severe carotid artery stenosis, considering patient's age as predictive marker.",
keywords = "changepoint, confidence intervals, covariate-treatment interaction, Cox regression, stratified medicine",
author = "Bernhard Haller and Ulrich Mansmann and Dennis Dobler and Kurt Ulm and Alexander Hapfelmeier",
year = "2020",
month = "1",
day = "15",
doi = "10.1002/sim.8404",
language = "English",
volume = "39",
pages = "70--96",
journal = "Statistics in Medicine",
issn = "0277-6715",
publisher = "John Wiley and Sons Ltd",
number = "1",

}

Confidence interval estimation for the changepoint of treatment stratification in the presence of a qualitative covariate-treatment interaction. / Haller, Bernhard; Mansmann, Ulrich; Dobler, Dennis; Ulm, Kurt; Hapfelmeier, Alexander.

In: Statistics in Medicine, Vol. 39, No. 1, 15.01.2020, p. 70-96.

Research output: Contribution to JournalArticleAcademicpeer-review

TY - JOUR

T1 - Confidence interval estimation for the changepoint of treatment stratification in the presence of a qualitative covariate-treatment interaction

AU - Haller, Bernhard

AU - Mansmann, Ulrich

AU - Dobler, Dennis

AU - Ulm, Kurt

AU - Hapfelmeier, Alexander

PY - 2020/1/15

Y1 - 2020/1/15

N2 - The goal in stratified medicine is to administer the “best” treatment to a patient. Not all patients might benefit from the same treatment; the choice of best treatment can depend on certain patient characteristics. In this article, it is assumed that a time-to-event outcome is considered as a patient-relevant outcome and a qualitative interaction between a continuous covariate and treatment exists, ie, that patients with different values of one specific covariate should be treated differently. We suggest and investigate different methods for confidence interval estimation for the covariate value, where the treatment recommendation should be changed based on data collected in a randomized clinical trial. An adaptation of Fieller's theorem, the delta method, and different bootstrap approaches (normal, percentile-based, wild bootstrap) are investigated and compared in a simulation study. Extensions to multivariable problems are presented and evaluated. We observed appropriate confidence interval coverage following Fieller's theorem irrespective of sample size but at the cost of very wide or even infinite confidence intervals. The delta method and the wild bootstrap approach provided the smallest intervals but inadequate coverage for small to moderate event numbers, also depending on the location of the true changepoint. For the percentile-based bootstrap, wide intervals were observed, and it was slightly conservative regarding coverage, whereas the normal bootstrap did not provide acceptable results for many scenarios. The described methods were also applied to data from a randomized clinical trial comparing two treatments for patients with symptomatic, severe carotid artery stenosis, considering patient's age as predictive marker.

AB - The goal in stratified medicine is to administer the “best” treatment to a patient. Not all patients might benefit from the same treatment; the choice of best treatment can depend on certain patient characteristics. In this article, it is assumed that a time-to-event outcome is considered as a patient-relevant outcome and a qualitative interaction between a continuous covariate and treatment exists, ie, that patients with different values of one specific covariate should be treated differently. We suggest and investigate different methods for confidence interval estimation for the covariate value, where the treatment recommendation should be changed based on data collected in a randomized clinical trial. An adaptation of Fieller's theorem, the delta method, and different bootstrap approaches (normal, percentile-based, wild bootstrap) are investigated and compared in a simulation study. Extensions to multivariable problems are presented and evaluated. We observed appropriate confidence interval coverage following Fieller's theorem irrespective of sample size but at the cost of very wide or even infinite confidence intervals. The delta method and the wild bootstrap approach provided the smallest intervals but inadequate coverage for small to moderate event numbers, also depending on the location of the true changepoint. For the percentile-based bootstrap, wide intervals were observed, and it was slightly conservative regarding coverage, whereas the normal bootstrap did not provide acceptable results for many scenarios. The described methods were also applied to data from a randomized clinical trial comparing two treatments for patients with symptomatic, severe carotid artery stenosis, considering patient's age as predictive marker.

KW - changepoint

KW - confidence intervals

KW - covariate-treatment interaction

KW - Cox regression

KW - stratified medicine

UR - http://www.scopus.com/inward/record.url?scp=85074855518&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85074855518&partnerID=8YFLogxK

U2 - 10.1002/sim.8404

DO - 10.1002/sim.8404

M3 - Article

VL - 39

SP - 70

EP - 96

JO - Statistics in Medicine

JF - Statistics in Medicine

SN - 0277-6715

IS - 1

ER -