The first part of this thesis involves the development of models and associated methodologies for the analysis of multi-disease reader-based correlated binary diagnostic data from binocular or paired (e.g., fellow eyes) organs. These entail the construction of joint models that can flexibly represent the complex dependence structure characterizing the nature of the relationships between measurements on the same and/or different subjects. A hierarchical generalized linear mixed model (GLMM) is proposed to estimate disease-specific sensitivities and specificities for the correlated binocular binary data, assuming readers are nested within patients, with patients assumed to be independent. Reader-, disease-, and organ-specific random effects are incorporated to capture the variability between readers, between diseases, and within-patient (i.e., between paired organs), respectively.
However, in many reader-based diagnostic studies, the same readers assess all of the patients, and hence, patients and readers are crossed rather than nested. We thus relax the assumption that measurements from different patients are independent, and develop a methodology based on GLMMs with crossed and nested random effects using the data cloning approach.
In the second part, a new copula-based approach to joint modeling of clustered non-Gaussian outcomes with disparate non-Gaussian distributions is developed. Specifically, the Gaussian copula is used to glue separate linear mixed models (LMMs) and/or GLMMs for multiple outcomes and to model the dependence between the outcomes; the resulting joint model is referred as a Gaussian copula mixed model (GCMM). Unlike in conventional shared-parameter LMM/GLMM methodology, the approach does not assume conditional independence of outcomes; hence, the GCMM generalizes and provides greater modeling flexibility than conventional LMMs and GLMMs. The GCMM approach is able to capture the different associations in the data, including the correlations between the same and/or different outcomes for the same and/or different subjects within a cluster, as well as the direct correlation between the outcomes for the same subject. Implementation of the methodology is readily carried out using standard statistical software and packages such as SAS's PROC NLMIXED. The GCMM approach is illustrated using data from a comet assay study and a study on pain among children, as well as the diabetic retinopathy data in first part.