SUMMARY /Consider a pharmaceutical trial where the consequences of different decisions are expressed on a financial scale. 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. This last component of the design, which is missing from most sequential procedures, has the potential to yield considerably larger expected net gains.

SUMMARY /Consider a pharmaceutical trial where the consequences of different decisions are expressed on a financial scale. 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. This last component of the design, which is missing from most sequential procedures, has the potential to yield considerably larger expected net gains.

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3.2.2 Gain structure Ill 3.3 Some Technical Results 112 3.3.1 The posterior parameters of the distribution of the efficacy S. 112 3.3.2 The predictive distribution of the sample mean differ ence seen at time t-f 1 115 3.3.3 The gain functions for the hypotheses HQ and 116 3.3.4 The expected gain function of stopping at time t, conditional on and Tf 117 iv 3.3.5 Properties of hf{pi,T^), the gain function for choosing at time t 120 3.3.6 ^0'"o] ' the expected gain from sampling; r = 123 3.3.7 Properties of $~^('), the inverse of the gaussian distribution function 133 3.4 Theoretical Results 135 3.4.1 gtiPti'^t)i the gain function at time t minus the expected gain net of costs at time t+1 135 3.5 Formal Definition of the B-Procedures 139 3.5.1 The B2 and procedures 139