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The Safari Cat Data , Performance Indicators and Possibly Monotonic Population Proportions

Two applications are described of a hierarchical model that can express uncertainty regarding a pre-specified monotonicity hypothesis for binomial probabilities. The results relate to time series with possibly monotonic success rates, isotonic regression, and the evaluation of performance indicators. The model can alternatively be interpreted as a random effects over-dispersion formulation for beta-binomial observations, within which the population proportions definitely satisfy a monotonicity specification. Practical ways of choosing the prior parameters for a Bayesian analysis are recommended. The primary application relates to a study of early hematopoiesis, and revisits a time series of proportions of masked progenitor cells from the bone marrow of a hybrid safari cat. The data for this cat are shown to be reasonably consistent with an assumption of strictly decreasing population proportions. The experimental outcomes for the other cats in the study are reviewed. An introductory application results from a Veterans' Administration hospital quality monitor, and concerns the failure to return rates for psychiatric patients attending substance abuse clinics. While smoothed performance indicators are devised, estimated standard errors of the corresponding sample proportions, which measure their extra-binomial sampling variation, are also calculated .