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. 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 a model that properly accounts for this correlation to ensure accurate inference. Previous research has investigated goodness-of-fit test statistics for correlated bilateral data under different group settings, assuming fully observed paired outcomes. In this work, we extend these methods to the more general and practically common setting where unilateral and bilateral data are combined. We examine the performance of various goodness-of-fit statistics under different statistical models, including the Clayton copula model. 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. However, the three bootstrap methods generally offer more robust performance. In real world applications from otolaryngologic and ophthalmologic studies, model choice significantly impacts conclusions, emphasizing the need for appropriate model assessment in practice.