Two stage conditionally unbiased estimators of the selected mean

Unbiased Estimation of Selected Treatment Means in Two‐Stage Trials

“…By conditioning on the stage 1 treatment estimates, Cohen and Sackrowitz (1989) proposed an unbiased estimator for m ð1Þ , which we will callm m ð1Þ . Assuming that X 1 ; .…”

“…Our focus in this paper is point estimation, and for that reason we concentrate on the work of Cohen and Sackrowitz (1989), who proposed an unbiased estimate for the mean of the best performing treatment. In Section 2 we describe in more detail the two-stage design under consideration, define three estimators for the selected treatment and decide on a common criteria for rating each estimator.…”

“…Nevertheless, designs of this sort are seen as a practical and efficient way to fast track the most promising compounds in drug development. In this paper we extend the method of Cohen and Sackrowitz (1989) who proposed a two-stage unbiased estimate for the best performing treatment at interim. This enables their estimate to work for unequal stage one and two sample sizes, and also when the quantity of interest is the best, second best, or j-th best treatment out of k. The implications of this new flexibility are explored via simulation.…”

Challenges in Implementing Adaptive Designs: Comments on the Viewpoints Expressed by Regulatory Statisticians

“…Also, in contrast to the non-adaptive multiple comparison situation, minimum variance mean unbiased estimates and exact confidence intervals exist for adaptive designs if the selection procedure at interim is fully specified (Cohen and Sackrowitz (1989), Sampson and Sill (2005)). Hence, concerns about estimation in adaptive designs should be viewed relative to other conventional standards, to the magnitudes of biases (and the existence of conservative approaches), and to other advantages that the adaptive design may offer.…”

A note on unbiased estimation following selection

“…It is known that the unbiased estimator for θ I of the selected normal population does not exist. For example, Cohen and Sackrowitz [7] quote unpublished technical report by Putter and Rubinstein [6]. For the sake of completeness, we give below a proof which brings out also certain additional features of the problem.…”