A Cost-Benefit Approach to the Amount of Experimentation in Clinical Trials
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S TAT 1ST I (S
Hamid Pezeshk, DPhii
Associate Professor of Statistics, Centre of Excellence in Biomathematics, School of Mathematics, University College of Science, University of Tehran, Iran
John Gittins, DSc
Professor of Statistics, Department of Statistics, University of Oxford, Oxford, UK
Key Words
Sample size determination; Clinical trial; Bayesian approach; Expected net benefit
Correspondence Address
Hamid Pezeshk, DPhil, School of Mathematics, University College of Science, University of Tehran, Tehran 14155-6455, Iran (e-mail: [email protected]).
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A Cost-Benefit Approach to the Amount of Experimentation in Clinical Trials
INTRODUCTION An important question in the planning of clinical trials for new drugs or treatments is how large to make the trial. The problem, in its statistical formulation, is to determine the optimal size of a trial. There have been a number of articles, from both the frequentist and Bayesian points of view, on this subject (listed, eg, by Adcock (in Ref. 1 J). Bayesian methods, which use a prior distribution for the unknown parameter(s), may be divided into two groups: methods that are inferential and employ, for example, moments of the posterior distribution for the unknown pararneter(s) to make inferences (see, eg, 2-4) Bayesian methods, which are based on a loss or utility function (see, eg, 5-7). Pezeshk (8) reviewed the Bayesian rules. In this work, we consider a fully Bayesian approach to sample size determination in which the number of subsequent users of the therapy under investigation and hence also the total benefit resulting from the trial depend on the strength of the evidence provided by the trial. Moreover we model the subsequent usage by plausible assumptions for actual behavior rather than assuming that this represents decisions that are in some sense optimal. This work extends the Pezeshk-Gittins methodology for sample size determination in clinical trials
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The aim of this paper is to discuss a behavioral Bayes approach to the question of the size of a clinical trial. The optimal size is obtained by maximizing the expected net benefit function, which is the expected benefit from subsequent use of the new treatment minus the cost of the trial. A plausible model for thenumber of subsequent users of thenew treatment is introduced.
(2000) to the case of normally distributed data by making more natural assumptions for the number of subsequent users of the new treatment. In the next section, we give a brief background of the problem and introduce our notation. The third section is on the number of subsequent users of the new treatment. Two types of benefit functions are introduced. Then, the methodology is applied to an actual trial to obtain the optimal size. We give a brief discussion of strengths and weaknesses of the methodology presented.
BACKGROUND Suppose that X/s are the clinical outcomes on some appropriate scale for patients using the new treatment, and the Y/s are those for patients using another (current) treatment. Suppose that Zj=Xi - Y
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