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

2025-06-27

AI Summary

In clinical trials, mixed univariate and bivariate data (e.g., bilateral eyes or ears) are common; however, conventional goodness-of-fit tests fail to simultaneously accommodate model adequacy and within-subject dependence—since univariate observations are independent, whereas paired measurements from the same subject exhibit intra-individual correlation. To address this, we propose an extended goodness-of-fit testing framework for multigroup mixed data based on the Clayton copula, explicitly modeling the within-subject dependence structure and incorporating a robust model selection strategy. Through theoretical derivation, Monte Carlo simulations, and analyses of real otolaryngological and ophthalmological datasets, we demonstrate that the proposed method significantly outperforms conventional approaches—particularly in small-sample and high-correlation settings—yielding more stable statistical power and up to 15–28% improvement in test efficacy. This work provides a generalizable statistical inference tool for medical research involving paired organs or anatomically symmetric structures.

Technology Category

• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Multi-instance/Multi-view Learning

Application Category

• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

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 $gge2$ 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.

Problem

• Evaluating goodness-of-fit tests for mixed unilateral and bilateral data
• Assessing model performance under intra-subject correlation conditions
• Testing statistical models for correlated organ response data

Innovation

• Goodness-of-fit tests for combined data models
• Using Clayton copula for intra-subject correlation
• Model-dependent performance evaluation via simulation