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Abstract
Two-stage trial designs provide the flexibility to stop early for efficacy or futility and are popular because they have a smaller sample size on average than a traditional trial has with the same type I and II error rates. This makes them financially attractive but also has the ethical benefit of reducing, in the long run, the number of patients who are given ineffective treatments. Designs that minimise the expected sample size are often referred to as ‘optimal’. However, two-stage designs can impart a substantial bias into the parameter estimate at the end of the trial. In this paper, we argue that the expected performance of one's chosen estimation method should also be considered when deciding on a two-stage trial design. We review the properties of standard and bias-adjusted maximum likelihood estimators as well as mean and median unbiased estimators. We then identify optimal two-stage design and analysis procedures that balance projected sample size considerations with those of estimator performance. We make available software to implement this new methodology. Copyright © 2012 John Wiley & Sons, Ltd.
Highlights
When investigating new and potentially promising treatments in the early stages of drug development, it is common to conduct a small-scale single-arm trial
The uniform minimum variance unbiased estimate (UMVUE) is generally chosen when more of the weight is on the bias of the design, whereas the bias-corrected maximum likelihood estimate (MLE) is generally chosen when more of the weight is on the mean squared error (MSE)
A noteworthy observation is that the traditional method of carrying out two-stage cancer trials, that is, the null-optimal design coupled with the MLE, is one of the admissible pairings
Summary
When investigating new and potentially promising treatments in the early stages of drug development, it is common to conduct a small-scale single-arm trial. Two-stage designs that allow the possibility to stop early for efficacy or futility are a popular choice for such trials because they have a smaller sample size on average compared with a traditional trial with the same type I and II error rates. This makes them financially and ethically attractive. We review and evaluate several methods for estimating the response probability in a two-stage trial, concentrating on their bias and mean squared error (MSE) This comparison is greatly aided by applying the sample space ‘T -mapping’ approach proposed by Jovic and Whitehead [1].
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