One-Sided Sequential Stopping Boundaries for Clinical Trials: A Decision- Theoretic Approach

Abstract

We address one-sided stopping rules for clinical trials, or more generally, drug development programs, from a decision-theoretic point of view. If efficacy results are sufficiently negative then the trial will be stopped. But regardless of how positive the efficacy results are, the trial will continue in order to demonstrate safety. We show how sequential decisions should be made by a pharmaceutical company attempting to maximize its expected profits.

A Sample-Size Optimal Bayesian Procedure for Sequential Pharmaceutical Trials

“…The gain function g for a sequential pharmaceutical trial is a function of the value of 6 and which of H 0 (i.e., At = 0) or H 1 (i.e., At = 1) is specified at time t. Potentially, the function itself could also vary with t. In what is to follow, we use Berry and Ho's (1988) specification:…”

“…First, we shall describe the B-procedure, generalized slightly here to handle any prespecified sample-size rule n. Berry and Ho (1988) show it to be Bayes using backward induction (e.g., DeGroot. 1970, Section 12.4).…”

“…We deliberately chose one example to be that considered by Berry and Ho (1988), in order to validate our results. In this example, their choice of nt = 30 (t = 0, 1, 2 -T) turns out to be close to optimal.…”

“…The efficacy of the new drug under consideration has a prior distribution obtained from the underlying biological process, animal experiments, clinical experience, and so forth. In an important paper, Berry and Ho (1988) show how these components are used to establish an optimal (Bayes) sequential procedure, assuming a known constant sample size at each decision point. We show in this article how it is also possible to optimize with respect to the sample-size rule.…”

“…In Section 3, the optimal (Bayes) sequential procedure cf Berry and Ho (1988) is re-established and then improved by further optimizing over sample sizes. Two illustrative examples are given in Section 4: in one, the benefits of sample-size optimization are seen to be substantial.…”