Speaker
Description
A common goal in medical research is to estimate a difference between treatment groups and quantify its uncertainty, or to infer a population-level difference. The most commonly used nonparametric group difference measure is the Mann-Whitney (MW) effect. It applies to a broad range of outcomes, including skewed, heteroskedastic and ordinal distributions, since it does not assume a parametric form of the data. This is especially useful in situations where sample sizes are too small to do empirical checks of parametric assumptions. In addition, the MW effect appears in diagnostic trials as the popular target parameter Area under the Receiver Operating Characteristic Curve (AUC).
Despite decades of research on the inference of MW effects, few Bayesian methods have been developed. Advantages of Bayesian estimation include (a) full uncertainty quantification via the posterior distribution, (b) improved numerical stability, and (c) the capability to include prior knowledge. Modeling external knowledge as a prior distribution can raise study power to a sufficient level in small-sample settings. This permits inference, for example, in rare diseases where recruitment rates are low, and enables more precise AUC estimates in the most interesting parameter ranges near its upper boundary.
We investigate whether Bayesian methods can improve inference for the MW effect in the unpaired, paired, and longitudinal two-group designs. For the unpaired design, an existing algorithm is extended to improve performance for small samples and parameter values near the boundary. For the paired and longitudinal designs novel approaches are developed. Empirical Likelihood is a nonparametric data model that has been widely used for Bayesian estimation over the last 20 years.
Extensive simulation studies demonstrate that credible interval coverage is approximately 95% across a broad range of data distributions. The influence of prior specification on coverage and precision (interval length) will be investigated. Additionally, the type-I error and power of Bayesian credible intervals when used as a statistical testing criterion will be evaluated and compared with those of frequentist methods.
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