Bayesian decision-theoretic group sequential clinical trial design based on a quadratic loss function: a frequentist evaluation

Roger J Lewis, Ari M Lipsky, Donald A Berry
Clinical Trials: Journal of the Society for Clinical Trials 2007, 4 (1): 5-14
The decision to terminate a controlled clinical trial at the time of an interim analysis is perhaps best made by weighing the value of the likely additional information to be gained if further subjects are enrolled against the various costs of that further enrollment. The most commonly used statistical plans for interim analysis (eg, O'Brien-Fleming), however, are based on a frequentist approach that makes no such comparison. A two-armed Bayesian decision-theoretic clinical trial design is developed for a disease with two possible outcomes, incorporating a quadratic decision loss function and using backward induction to quantify the cost of future enrollment. Monte Carlo simulation is used to compare frequentist error rates and mean required sample sizes for these Bayesian designs with the two-tailed frequentist group-sequential designs of, O'Brien-Fleming and Pocock. When the terminal decision loss function is chosen to yield typical frequentist error rates, the mean sample sizes required by the Bayesian designs are smaller than those of the corresponding O'Brien-Fleming frequentist designs, largely due to the more frequent interim analyses typically used with the Bayesian designs and the ability of the Bayesian designs to terminate early and conclude equivalence. Adding stochastic curtailment to the frequentist designs and using the same number of interim analyses results in largely equivalent trials. An example of a Bayesian design for the data safety monitoring of a clinical trial is given. Our design assumes independence of the probabilities of success in the two trial arms. Additionally, we have chosen non-informative priors and selected loss functions to produce trials with appealing frequentist error rates, rather than choosing priors that reflect realistic prior information and loss functions that reflect true costs. Our Bayesian designs allow interpretation of the final results along either Bayesian or frequentist lines. For the Bayesian, they minimize the total cost and allow the direct calculation of the probability density function for the difference in efficacy. For the frequentist, they have well-characterized type I and II error rates and in some cases lead to a reduction in the mean sample size.

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