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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.
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