Random effects models are used in many applications in medical statistics, including meta-analysis, cluster randomized trials and comparisons of health care providers. This paper provides a tutorial on the practical implementation of a flexible random effects model based on methodology developed in Bayesian non-parametrics literature, and implemented in freely available software. The approach is applied to the problem of hospital comparisons using routine performance data, and among other benefits provides a diagnostic to detect clusters of providers with unusual results, thus avoiding problems caused by masking in traditional parametric approaches. By providing code for Winbugs we hope that the model can be used by applied statisticians working in a wide variety of applications.
In light of recent interest by health authorities into the use of subgroup analysis in the context of drug development, it appears that Bayesian approaches involving shrinkage techniques could play an important role in this area. Hopefully, the developments outlined here provide useful methodology for tackling such a problem, in-turn leading to better informed decisions regarding subgroups.
A wide variety of statistical methods have been proposed for detecting unusual performance in cross-sectional data on health care providers. We attempt to create a unified framework for comparing these methods, focusing on a clear distinction between estimation and hypothesis testing approaches, with the corresponding distinction between detecting 'extreme' and 'divergent' performance. When assuming a random-effects model the random-effects distribution forms the null hypothesis, and there appears little point in testing whether individual effects are greater or less than average. The hypothesis testing approach uses "p"-values as summaries and brings with it the standard problems of multiple testing, whether Bayesian or classical inference is adopted. A null random-effects formulation allows us to answer appropriate questions of the type: 'is a particular provider worse than we would expect the true worst provider (but still part of the null distribution) to be'? We outline a broad three-stage strategy of exploratory detection of unusual providers, detailed modelling robust to potential outliers and confirmation of unusual performance, illustrated by using two detailed examples. The concepts are most easily handled within a Bayesian analytic framework using Markov chain Monte Carlo methods, but the basic ideas should be generally applicable. Copyright 2007 Royal Statistical Society.
Bayesian approaches to the monitoring of group sequential designs have two main advantages compared with classical group sequential designs: first, they facilitate implementation of interim success and futility criteria that are tailored to the subsequent decision making, and second, they allow inclusion of prior information on the treatment difference and on the control group. A general class of Bayesian group sequential designs is presented, where multiple criteria based on the posterior distribution can be defined to reflect clinically meaningful decision criteria on whether to stop or continue the trial at the interim analyses. To evaluate the frequentist operating characteristics of these designs, both simulation methods and numerical integration methods are proposed, as implemented in the corresponding R package gsbDesign. Normal approximations are used to allow fast calculation of these characteristics for various endpoints. The practical implementation of the approach is illustrated with several clinical trial examples from different phases of drug development, with various endpoints, and informative priors.
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