Optimal sample size determinations from an industry perspective based on the expected value of information

Andrew R Willan
Clinical Trials: Journal of the Society for Clinical Trials 2008, 5 (6): 587-94

BACKGROUND: Traditional sample size calculations for randomized clinical trials depend on somewhat arbitrarily chosen factors, such as type I and II errors. As an alternative, taking a societal perspective, and using the expected value of information based on Bayesian decision theory, a number of authors have recently shown how to determine the sample size that maximizes the expected net gain, i.e., the difference between the cost of the trial and the value of the information gained from the results. Other authors have proposed Bayesian methods to determine sample sizes from an industry perspective.

PURPOSE: The purpose of this article is to propose a Bayesian approach to sample size calculations from an industry perspective that attempts to determine the sample size that maximizes expected profit.

METHODS: A model is proposed for expected total profit that includes consideration of per-patient profit, disease incidence, time horizon, trial duration, market share, discount rate, and the relationship between the results and the probability of regulatory approval. The expected value of information provided by trial data is related to the increase in expected profit from increasing the probability of regulatory approval. The methods are applied to an example, including an examination of robustness. The model is extended to consider market share as a function of observed treatment effect.

RESULTS: The use of methods based on the expected value of information can provide, from an industry perspective, robust sample size solutions that maximize the difference between the expected cost of the trial and the expected value of information gained from the results.

LIMITATIONS: The method is only as good as the model for expected total profit. Although the model probably has all the right elements, it assumes that market share, per-patient profit, and incidence are insensitive to trial results. The method relies on the central limit theorem which assumes that the sample sizes involved ensure that the relevant test statistics are normally distributed.

CONCLUSIONS: Industry officials should consider the use of expected value of information methods for determining sample sizes for proposed trials. The method also can be used to select, from a number of proposed trials, those which maximize return from a fixed research budget.

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