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.

is a recently developed R package for Bayesian clustering using a Dirichlet process mixture model. This model is an alternative to regression models, non-parametrically linking a response vector to covariate data through cluster membership (Molitor, Papathomas, Jerrett, and Richardson 2010). The package allows binary, categorical, count and continuous response, as well as continuous and discrete covariates. Additionally, predictions may be made for the response, and missing values for the covariates are handled. Several samplers and label switching moves are implemented along with diagnostic tools to assess convergence. A number of R functions for post-processing of the output are also provided. In addition to fitting mixtures, it may additionally be of interest to determine which covariates actively drive the mixture components. This is implemented in the package as variable selection.

We construct data exploration tools for recognizing important covariate patterns associated with a phenotype, with particular focus on searching for association with gene-gene patterns. To this end, we propose a new variable selection procedure that employs latent selection weights and compare it to an alternative formulation. The selection procedures are implemented in tandem with a Dirichlet process mixture model for the flexible clustering of genetic and epidemiological profiles. We illustrate our approach with the aid of simulated data and the analysis of a real data set from a genome-wide association study.

BackgroundProfile regression is a Bayesian statistical approach designed for investigating the joint effect of multiple risk factors. It reduces dimensionality by using as its main unit of inference the exposure profiles of the subjects that is, the sequence of covariate values that correspond to each subject.ObjectivesWe applied profile regression to a case–control study of lung cancer in nonsmokers, nested within the European Prospective Investigation into Cancer and Nutrition (EPIC) cohort, to estimate the combined effect of environmental carcinogens and to explore possible gene–environment interactions.MethodsWe tailored and extended the profile regression approach to the analysis of case–control studies, allowing for the analysis of ordinal data and the computation of posterior odds ratios. We compared and contrasted our results with those obtained using standard logistic regression and classification tree methods, including multifactor dimensionality reduction.ResultsProfile regression strengthened previous observations in other study populations on the role of air pollutants, particularly particulate matter ≤ 10 μm in aerodynamic diameter (PM10), in lung cancer for nonsmokers. Covariates including living on a main road, exposure to PM10 and nitrogen dioxide, and carrying out manual work characterized high-risk subject profiles. Such combinations of risk factors were consistent with a priori expectations. In contrast, other methods gave less interpretable results.ConclusionsWe conclude that profile regression is a powerful tool for identifying risk profiles that express the joint effect of etiologically relevant variables in multifactorial diseases.