Optimal Bayesian two-phase designs

In this paper we present a Bayesian decision theoretic approach to the two-phase design problem. The solution of such sequential decision problems is usually difficult to obtain because of their reliance on preposterior analysis. In overcoming this problem, we adopt the Monte-Carlo-based approach of Muller and Parmigiani (1995) and develop optimal Bayesian designs for two-phase screening tests. A rather attractive feature of the Monte-Carlo approach is that it facilitates the preposterior analysis by replacing it with a sequence of scatter plot smoothing/regression techniques and optimization of the corresponding fitted surfaces. The method is illustrated for depression in adolescents using data from past studies. (C) 1998 Elsevier Science B.V.