Confidence intervals for the selected population in randomized trials that adapt the population enrolled

Research output: Contribution to journalArticle

Abstract

It is a challenge to design randomized trials when it is suspected that a treatment may benefit only certain subsets of the target population. In such situations, trial designs have been proposed that modify the population enrolled based on an interim analysis, in a preplanned manner. For example, if there is early evidence during the trial that the treatment only benefits a certain subset of the population, enrollment may then be restricted to this subset. At the end of such a trial, it is desirable to draw inferences about the selected population. We focus on constructing confidence intervals for the average treatment effect in the selected population. Confidence interval methods that fail to account for the adaptive nature of the design may fail to have the desired coverage probability. We provide a new procedure for constructing confidence intervals having at least 95% coverage probability, uniformly over a large class Q of possible data generating distributions. Our method involves computing the minimum factor c by which a standard confidence interval must be expanded in order to have, asymptotically, at least 95% coverage probability, uniformly over Q. Computing the expansion factor c is not trivial, since it is not a priori clear, for a given decision rule, for which data generating distribution leads to the worst-case coverage probability. We give an algorithm that computes c, and then prove an optimality property for the resulting confidence interval procedure.

Original languageEnglish (US)
Pages (from-to)322-340
Number of pages19
JournalBiometrical Journal
Volume55
Issue number3
DOIs
StatePublished - May 2013

Fingerprint

Randomized Trial
Coverage Probability
Confidence interval
Confidence Intervals
Population
Subset
Average Treatment Effect
Interim Analysis
Interval Methods
Computing Methods
Health Services Needs and Demand
Decision Rules
Optimality
Trivial
Randomized trial
Target
Computing
Design

Keywords

  • Adaptive enrichment design
  • Interval estimation
  • Uniform asymptotics

ASJC Scopus subject areas

  • Statistics and Probability
  • Medicine(all)
  • Statistics, Probability and Uncertainty

Cite this

Confidence intervals for the selected population in randomized trials that adapt the population enrolled. / Rosenblum, Michael Aaron.

In: Biometrical Journal, Vol. 55, No. 3, 05.2013, p. 322-340.

Research output: Contribution to journalArticle

@article{bdc55b8fc86f44d0b385c64e491f3ebc,
title = "Confidence intervals for the selected population in randomized trials that adapt the population enrolled",
abstract = "It is a challenge to design randomized trials when it is suspected that a treatment may benefit only certain subsets of the target population. In such situations, trial designs have been proposed that modify the population enrolled based on an interim analysis, in a preplanned manner. For example, if there is early evidence during the trial that the treatment only benefits a certain subset of the population, enrollment may then be restricted to this subset. At the end of such a trial, it is desirable to draw inferences about the selected population. We focus on constructing confidence intervals for the average treatment effect in the selected population. Confidence interval methods that fail to account for the adaptive nature of the design may fail to have the desired coverage probability. We provide a new procedure for constructing confidence intervals having at least 95{\%} coverage probability, uniformly over a large class Q of possible data generating distributions. Our method involves computing the minimum factor c by which a standard confidence interval must be expanded in order to have, asymptotically, at least 95{\%} coverage probability, uniformly over Q. Computing the expansion factor c is not trivial, since it is not a priori clear, for a given decision rule, for which data generating distribution leads to the worst-case coverage probability. We give an algorithm that computes c, and then prove an optimality property for the resulting confidence interval procedure.",
keywords = "Adaptive enrichment design, Interval estimation, Uniform asymptotics",
author = "Rosenblum, {Michael Aaron}",
year = "2013",
month = "5",
doi = "10.1002/bimj.201200080",
language = "English (US)",
volume = "55",
pages = "322--340",
journal = "Biometrical Journal",
issn = "0323-3847",
publisher = "Wiley-VCH Verlag",
number = "3",

}

TY - JOUR

T1 - Confidence intervals for the selected population in randomized trials that adapt the population enrolled

AU - Rosenblum, Michael Aaron

PY - 2013/5

Y1 - 2013/5

N2 - It is a challenge to design randomized trials when it is suspected that a treatment may benefit only certain subsets of the target population. In such situations, trial designs have been proposed that modify the population enrolled based on an interim analysis, in a preplanned manner. For example, if there is early evidence during the trial that the treatment only benefits a certain subset of the population, enrollment may then be restricted to this subset. At the end of such a trial, it is desirable to draw inferences about the selected population. We focus on constructing confidence intervals for the average treatment effect in the selected population. Confidence interval methods that fail to account for the adaptive nature of the design may fail to have the desired coverage probability. We provide a new procedure for constructing confidence intervals having at least 95% coverage probability, uniformly over a large class Q of possible data generating distributions. Our method involves computing the minimum factor c by which a standard confidence interval must be expanded in order to have, asymptotically, at least 95% coverage probability, uniformly over Q. Computing the expansion factor c is not trivial, since it is not a priori clear, for a given decision rule, for which data generating distribution leads to the worst-case coverage probability. We give an algorithm that computes c, and then prove an optimality property for the resulting confidence interval procedure.

AB - It is a challenge to design randomized trials when it is suspected that a treatment may benefit only certain subsets of the target population. In such situations, trial designs have been proposed that modify the population enrolled based on an interim analysis, in a preplanned manner. For example, if there is early evidence during the trial that the treatment only benefits a certain subset of the population, enrollment may then be restricted to this subset. At the end of such a trial, it is desirable to draw inferences about the selected population. We focus on constructing confidence intervals for the average treatment effect in the selected population. Confidence interval methods that fail to account for the adaptive nature of the design may fail to have the desired coverage probability. We provide a new procedure for constructing confidence intervals having at least 95% coverage probability, uniformly over a large class Q of possible data generating distributions. Our method involves computing the minimum factor c by which a standard confidence interval must be expanded in order to have, asymptotically, at least 95% coverage probability, uniformly over Q. Computing the expansion factor c is not trivial, since it is not a priori clear, for a given decision rule, for which data generating distribution leads to the worst-case coverage probability. We give an algorithm that computes c, and then prove an optimality property for the resulting confidence interval procedure.

KW - Adaptive enrichment design

KW - Interval estimation

KW - Uniform asymptotics

UR - http://www.scopus.com/inward/record.url?scp=84876968631&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84876968631&partnerID=8YFLogxK

U2 - 10.1002/bimj.201200080

DO - 10.1002/bimj.201200080

M3 - Article

C2 - 23553577

AN - SCOPUS:84876968631

VL - 55

SP - 322

EP - 340

JO - Biometrical Journal

JF - Biometrical Journal

SN - 0323-3847

IS - 3

ER -