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.
authors.affiliation: Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD 21205, USA. mrosenbl@jhsph.edu
authors.forename: Michael
authors.initials: M
authors.lastname: Rosenblum
mesh_terms: D000465:Algorithms; D000928:Antidepressive Agents / Q000627:therapeutic use; D016001:Confidence Intervals; D003627:Data Interpretation, Statistical; D003863:Depression / Q000188:drug therapy; D006801:Humans; D016032:Randomized Controlled Trials as Topic / Q000379:methods*; D012107:Research Design; D016896:Treatment Outcome
chemical_list: D000928:Antidepressive Agents
references.citation: Pharm Stat. 2007 Jul-Sep;6(3):227-44
references.pmid: 17688238
references.citation: Biometrics. 1999 Dec;55(4):1286-90
references.pmid: 11315085
references.citation: Stat Med. 2005 Dec 30;24(24):3697-714
references.pmid: 16320264
references.citation: Biometrika. 2011 Dec;98(4):845-860
references.pmid: 23049131
references.citation: Biom J. 2009 Apr;51(2):358-74
references.pmid: 19358222
references.citation: Stat Med. 2006 Oct 15;25(19):3366-81
references.pmid: 16220489
references.citation: Control Clin Trials. 1984 Mar;5(1):33-45
references.pmid: 6713906
references.citation: PLoS Med. 2008 Feb;5(2):e45
references.pmid: 18303940
references.citation: Stat Med. 1997 Feb 28;16(4):455-64
references.pmid: 9044532
references.citation: Biom J. 2005 Jun;47(3):257-68; discussion 269-81
references.pmid: 16053251
references.citation: J Biopharm Stat. 2007;17(6):1135-61
references.pmid: 18027222
references.citation: N Engl J Med. 2001 Mar 15;344(11):783-92
references.pmid: 11248153