Joint modeling of clustered binary data with crossed random effects via the Gaussian copula mixed model
Date
2019-07-11
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Abstract
Models with crossed random effects are common in reader-based diagnostic studies, where the same group of readers evaluate patients for certain diseases; an example is diabetic retinopathy study in Alberta, Canada. Although generalized linear mixed models (GLMMs) are well developed for non-Gaussian responses (e.g., binary outcomes) with crossed random effects, evaluation of the marginal likelihood is still technically and computationally demanding and can become prohibitive in applications, since the data cannot be grouped into independent blocks. The available estimation methods are also not free from problems. A recent approach involves application of data cloning (DC) to obtain maximum likelihood (ML) estimates using a Bayesian framework. Their approach is proved to be superior over the other two alternatives they considered in terms of providing relatively unbiased and efficient parameter estimates. However, this approach is based on a multivariate latent Gaussian description of the multiple correlated binary outcomes. In this thesis, we relax this assumption by allowing for disparate non-Gaussian latent variables for the binary responses, and propose a joint modeling via the Gaussian copula mixed model (GCMM). We applied maximum pairwise likelihood (PL) estimation instead of doing full ML analysis to reduce computational complexities. We conducted simulation studies with a setting analogous to the diabetic retinopathy data to see the performance of PL estimators for GCMM with crossed random effects. Simulation results suggest that although the estimation of regression coefficients and correlation parameter exhibit no problem, a much bigger sample size is required for the other scale parameters to provide reasonably accurate approximate results. We also analyzed the retinopathy data with the proposed approach considering three different conditional margins.
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Keywords
retinopathy, gaussian copula, crossed random effects
Citation
Jaman, A. (2019). Joint modeling of clustered binary data with crossed random effects via the Gaussian copula mixed model (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.