title: Conditionally unbiased and near unbiased estimation of the selected treatment mean for multistage drop-the-losers trials.
abstract: The two-stage drop-the-loser design provides a framework for selecting the most promising of K experimental treatments in stage one, in order to test it against a control in a confirmatory analysis at stage two. The multistage drop-the-losers design is both a natural extension of the original two-stage design, and a special case of the more general framework of Stallard & Friede () (Stat. Med. 27, 6209-6227). It may be a useful strategy if deselecting all but the best performing treatment after one interim analysis is thought to pose an unacceptable risk of dropping the truly best treatment. However, estimation has yet to be considered for this design. Building on the work of Cohen & Sackrowitz () (Stat. Prob. Lett. 8, 273-278), we derive unbiased and near-unbiased estimates in the multistage setting. Complications caused by the multistage selection process are shown to hinder a simple identification of the multistage uniform minimum variance conditionally unbiased estimate (UMVCUE); two separate but related estimators are therefore proposed, each containing some of the UMVCUEs theoretical characteristics. For a specific example of a three-stage drop-the-losers trial, we compare their performance against several alternative estimators in terms of bias, mean squared error, confidence interval width and coverage.
authors.affiliation: MRC Biostatistics Unit, Cambridge, CB2 OSR, UK.
authors.forename: Jack
authors.initials: J
authors.lastname: Bowden
authors.forename: Ekkehard
authors.initials: E
authors.lastname: Glimm
mesh_terms: D015982:Bias; D001699:Biometry / Q000379:methods*; D002986:Clinical Trials as Topic / Q000379:methods*; D006801:Humans; D016013:Likelihood Functions; D017211:Treatment Failure
keywords: Bias-adjusted estimation; Drop-the-losers design; Treatment selection; UMVCUE