Statistical methodology is to be extended to accommodate unique statistical problems that arise in several different biomedical studies involving the estimation of within-cluster effects. Examples of such effects include differences in response to chemical toxicity among groups of litters within blocks, within-subject differences in treatment response among tumors in different organs across time, within-subject differences in risk of periodontal diseases among different regions of the dentition across time, and within-subject treatment effects in a cross-over study of bioequivalence. These examples arise in four areas of application: 1) a developmental toxicity study of the synergistic effect of combinations of possible carcinogens ; 2) a comparison of treatment responses of metastatic tumors in different organs that originated from renal cell carcinoma; 3) an observational study of temporal changes in the spatial distribution of periodontal disease ina the dentition; and 4) an investigation of the bioequivalence of different formulations of a drug with respect to a discrete response. These areas of research present a number of unresolved issues regarding mixed effects discrete response models that are the focus of this proposal. First, mixed effects models that accommodate multiple endpoints are addressed. Three cases are to be examined: 1) multiple discrete endpoints; 2) discrete and continuous endpoints; and 3) multiple discrete endpoints with a discrete time failure response. For case 1), a hybrid of random effects and marginal models is proposed. For case 2), an extension of measurement error mixed effects models is considered. And for case 3), a mixed effect ordinal response model conditional on a discrete time failure response is discussed. Additional issues include adapting mixed effects discrete response models to accommodate random cluster sizes (e.g., litter sizes and numbers of tumors for a given subject) and negative intracluster correlations (e.g., strong litter mates benefiting at the expense of weak litter mates). Finally, the analysis of bioequivalence discrete response data has demonstrated differences in confidence-interval- based inference between population-averaged and mixed effects logistic regression models. It is proposed that other link functions be investigated that lead to consistent confidence interval-based inference for bioequivalence in this context.
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