Bayesian Inference for Bivariate Skew-Normal/Independent Linear Mixed Models with application to Periodontal Disease

Abstract:  Bivariate clustered data, often encountered in epidemiological and clinical research, are routinely analyzed under the linear mixed models framework with underlying normality assumptions of the random effects and within-subject errors. However, such normality assumptions might be questionable if the dataset particularly exhibit skewness and heavy tails. Under a Bayesian paradigm, we introduce a new class of skew-normal/independent distribution as a tool for robust modeling of bivariate clustered data under a linear mixed model setup. We assume that the random effects follow multivariate skew-normal/independent distributions and the random errors follow symmetric normal/independent distribution, which provides substantial robustness over the symmetric normal process in a linear mixed model framework. The methodology is illustrated through simulation studies and an application to a real data which records the periodontal health status of an interesting population using periodontal pocket depth and clinical attachment loss.

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