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Bayesian Profile Regression With An Application To The National Survey Of Children's Health

John Molitor, Michail Papathomas, Michael Jerrett, Sylvia Richardson

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Abstract Standard regression analyses are often plagued with problems encountered when one tries to make inference going beyond main effects using data sets that contain dozens of variables that are potentially correlated. This situation arises, for example, in epidemiology where surveys or study questionnaires consisting of a large number of questions yield a potentially unwieldy set of interrelated data from which teasing out the effect of multiple covariates is difficult. We propose a method that addresses these problems for categorical covariates by using, as its basic unit of inference, a profile formed from a sequence of covariate values. These covariate profiles are clustered into groups and associated via a regression model to a relevant outcome. The Bayesian clustering aspect of the proposed modeling framework has a number of advantages over traditional clustering approaches in that it allows the number of groups to vary, uncovers subgroups and examines their association with an outcome of interest, and fits the model as a unit, allowing an individual's outcome potentially to influence cluster membership. The method is demonstrated with an analysis of survey data obtained from the National Survey of Children's Health. The approach has been implemented using the standard Bayesian modeling software, WinBUGS, with code provided in the supplementary material available at Biostatistics online. Further, interpretation of partitions of the data is helped by a number of postprocessing tools that we have developed.