### 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 language | English (US) |
---|---|

Pages (from-to) | 322-340 |

Number of pages | 19 |

Journal | Biometrical Journal |

Volume | 55 |

Issue number | 3 |

DOIs | |

State | Published - May 2013 |

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### 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.

Research output: Contribution to journal › Article

}

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 -