On some procedures for analyzing clustered exchangeable data.

摘要

Many biomedical studies often result in clustered data. For such data, ignoring the dependence between measurements within cluster usually leads to misleading inference. The primary focus of this thesis is the analysis of exchangeably clustered multinomial data and the hierarchical modeling of such clustered data when jointly distributed with continuous components. We propose three procedures which address modeling and computational issues in the analysis of clustered data.;First, using a representation of clustered multinomial data by George et al. (2010), we develop estimating equations for analyzing teratology data with clustered trinomial endpoints and showed that the use of the representation of George et al. facilitates the computation of maximum likelihood estimates of higher moments for use in generalized estimating equations. This leads to more efficient estimates of parameters than what is obtained using existing procedures such as the quasilikelihood and Dirichlet-trinomial methods. We demonstrate these properties with a developmental toxicity data set from the National Toxicology Program.;Second, we extend the results of Szabo and George (2010) to develop a test for trend with clustered multinomial exchangeable variables. This test is more robust than existing methods in many respects: (1) It provides a more flexible approach because the use of stochastic ordering allows for all forms of monotonic increase in trend. (2) By assuming interpretability, it allows the augmentation for sparse data. A likelihood ratio test is constructed and probabilities are estimated using EM (expectation-maximization) on compact sets of discrete probability measures.;The third part of the thesis deals with exchangeable bivariate discrete and continuous clustered data. Examples of such data include those resulting in weight loss and the indicator of malformation in teratology. Since such responses are related to each other, it is desirable to model them together. However, the analysis of such data presents challenges due to their complex dependence structure. We approach this problem with a hierarchical Bayes method in which conditional independence is replaced by conditional exchangeability, thus generalizing the work of Albert and Chib (1993). An application of our procedure to developmental toxicology studies is described.