title: Precision of maximum likelihood estimation in adaptive designs.
abstract: There has been increasing interest in trials that allow for design adaptations like sample size reassessment or treatment selection at an interim analysis. Ignoring the adaptive and multiplicity issues in such designs leads to an inflation of the type 1 error rate, and treatment effect estimates based on the maximum likelihood principle become biased. Whereas the methodological issues concerning hypothesis testing are well understood, it is not clear how to deal with parameter estimation in designs were adaptation rules are not fixed in advanced so that, in practice, the maximum likelihood estimate (MLE) is used. It is therefore important to understand the behavior of the MLE in such designs. The investigation of Bias and mean squared error (MSE) is complicated by the fact that the adaptation rules need not be fully specified in advance and, hence, are usually unknown. To investigate Bias and MSE under such circumstances, we search for the sample size reassessment and selection rules that lead to the maximum Bias or maximum MSE. Generally, this leads to an overestimation of Bias and MSE, which can be reduced by imposing realistic constraints on the rules like, for example, a maximum sample size. We consider designs that start with k treatment groups and a common control and where selection of a single treatment and control is performed at the interim analysis with the possibility to reassess each of the sample sizes. We consider the case of unlimited sample size reassessments as well as several realistically restricted sample size reassessment rules.
authors.affiliation: Medical University of Vienna, Center for Medical Statistics, Informatics and Intelligent Systems, Spitalgasse 23, 1090, Vienna, Austria.
authors.forename: Alexandra Christine
authors.initials: AC
authors.lastname: Graf
authors.affiliation: University of Bremen, Competence Center for Clinical Trials, Linzer Strasse 4, 28359, Bremen, Germany.
authors.forename: Georg
authors.initials: G
authors.lastname: Gutjahr
authors.affiliation: University of Bremen, Competence Center for Clinical Trials, Linzer Strasse 4, 28359, Bremen, Germany.
authors.forename: Werner
authors.initials: W
authors.lastname: Brannath
mesh_terms: D015982:Bias; D002986:Clinical Trials as Topic / Q000379:methods / Q000706:statistics & numerical data*; D006801:Humans; D016013:Likelihood Functions; D015233:Models, Statistical; D012107:Research Design; D018401:Sample Size
keywords: adaptive designs; maximum likelihood estimation; sample size reassessment; treatment selection