In this study, we discuss a decision theoretic or fully Bayesian approach to the sample size question in clinical trials with binary responses. Data are assumed to come from two binomial distributions. A Dirichlet distribution is assumed to describe prior knowledge of the two success probabilities p1 and p2. The parameter of interest is p = p1 - p2. The optimal size of the trial is obtained by maximising the expected net benefit function. The methodology presented in this article extends previous work by the assumption of dependent prior distributions for p1 and p2.

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Judgment post-stratification is used to supplement observations taken from finite mixture models with additional easy to obtain rank information and incorporate it in the estimation of model parameters. To do this, sampled units are post-stratified on ranks by randomly selecting comparison sets for each unit from the underlying population and assigning ranks to them using available auxiliary information or judgment ranking. This results in a set of independent order statistics from the underlying model, where the number of units in each rank class is random. We consider cases where one or more rankers with different ranking abilities are used to provide judgment ranks. The judgment ranks are then combined to produce a strength of agreement measure for each observation. This strength measure is implemented in the maximum likelihood estimation of model parameters via a suitable expectation maximization algorithm. Simulation studies are conducted to evaluate the performance of the estimators with or without the extra rank information. Results are applied to bone mineral density data from the third National Health and Nutrition Examination Survey to estimate the prevalence of osteoporosis in adult women aged 50 and over.

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