Goodness-of-fit Tests for Combined Unilateral and Bilateral Data

Clinical trials involving paired organs often yield a mixture of unilateral and bilateral data, where each subject may contribute either one or two responses under certain circumstances. While unilateral responses from different individuals can be treated as independent, bilateral responses from the same individual are likely correlated. Various statistical methods have been developed to account for this intra-subject correlation in the bilateral data, and in practice it is crucial to select an appropriate model for accurate inference. Tang et. al. (2012) discussed model selection issues using a variety of goodness-of-fit test statistics for correlated bilateral data for two groups, and Liu and Ma (2020) extended these methods to settings with $g\ge2$ groups. In this work, we investigate the goodness-of-fit statistics for the combined unilateral and bilateral data under different statistical models that address the intra-subject correlation, including the Clayton copula model, in addition to those considered in prior studies. Simulation results indicate that the performance of the goodness-of-fit tests is model-dependent, especially when the sample size is small and/or the intra-subject correlation is high, which is consistent with the findings by Liu and Ma (2020) for purely bilateral data. Applications to real data from otolaryngologic and ophthalmologic studies are included.