Goodness-of-fit Tests for Correlated Bilateral Data from Multiple Groups

Correlated bilateral data often arise in ophthalmological and otolaryngological studies, where responses of paired body parts of each subject are measured. A number of statistical methods have been proposed to tackle this intra-class correlation problem, and in practice it is important to choose the most suitable one which fits the observed data well. Tang et al. (Stat Methods Med Res 21(4):331-345, 2012, [16]) compared different goodness-of-fit statistics for correlated data including only two groups. In this article, we investigate the general situation for g ≥ 2 groups. Our simulation results show that the performance of the goodness-of-fit test methods, as measured by the power and the type I error rate, is model depending. The observed performance difference is more significant in scenario with small sample size and/or highly dependent data structure. Examples from ophthalmologic studies are used to illustrate the application of these goodness-of-fit test methods.