Linear Mixed Models for Skew-Normal Independent bivariate responses with an application to Periodontal Disease

摘要

Bivariate clustered (correlated) data often encountered in epidemiological and clinical research are routinely analyzed under a linear mixed model framework with underlying normality assumptions of the random effects and within-subject errors. However, such normality assumptions might be questionable if the data-set particularly exhibit skewness and heavy tails. Using a Bayesian paradigm, we use the skew-normal/independent (SNI) distribution as a tool for modeling clustered data with bivariate non-normal responses in a linear mixed model framework. The SNI distribution is an attractive class of asymmetric thick-tailed parametric structure which includes the skew-normal distribution as a special case. We assume that the random effects follows multivariate skew-normal/independent distributions and the random errors follow symmetric normal/independent distributions which provides substantial robustness over the symmetric normal process in a linear mixed model framework. Specific distributions obtained as special cases, viz. the skew-t, the skew-slash and the skew-contaminated normal distributions are compared, along with the default skew-normal density. The methodology is illustrated through an application to a real data which records the periodontal health status of an interesting population using periodontal pocket depth (PPD) and clinical attachment level (CAL).