Composite Conditional Likelihood Open Access

Wang, Lijia (2016)

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Sparse clustered data often arise in genetic and epidemiologic studies, such as studies of complex diseases that tend to aggregate within households. Fine stratification is needed to adjust for the population heterogeneity that is commonly encountered in such studies. In this dissertation, we consider a finely stratified study, and we aim to find a robust and flexible method to measure the pairwise associations between individual outcomes within clusters. We propose a composite conditional likelihood approach that allows the investigator to specify only marginal densities and intracluster pairwise densities, and is insensitive to the stratum-specific nuisance parameters. We investigate the asymptotic properties of our composite conditional likelihood method under both the standard situation and the sparse data situation. We also develop and apply general odds ratio models, which accommodate either discrete or continuous observations, for use in composite conditional likelihood. We propose a specific odds ratio model for use in household aggregation studies, which not only rewards pairwise departure from the references points but also penalizes lack of agreement. We demonstrate via simulation studies that the proposed method provides a valid and flexible way to obtain robust inference in studies of pairwise association with sparse clustered data. We apply the method to a study of drinking water quality within households, finely stratified by small geographic area. We finally conduct an exploratory study regarding the selection of weights for each cluster in the proposed composite conditional likelihood to improve efficiency of estimation. We investigate the optimal choice of cluster-specific weights under both the standard situation and the sparse data situation. We demonstrate via simulation studies that the efficiency of estimation is improved. We reanalyze the water quality data after incorporating the proposed weights and compare the results analyzed under equal and unequal weights.

Table of Contents

1 Introduction. 1

1.1 Motivation. 3

1.2 Background. 7

1.2.1 Composite likelihood methods. 7

1.2.2 Composite conditional likelihood for sparse clustered binary data. 8

1.2.3 General odds ratio function. 10

1.3 Outline. 13

2 Develop A General Composite Conditional Likelihood and Investigate Its Properties. 15

2.1 A General Composite Conditional Likelihood. 17

2.2 Asymptotic Results. 20

2.2.1 Standard asymptotic results. 21

2.2.2 Results under sparse data situation. 22

2.3 Appendix. 24

3 Develop and Apply General Odds Ratio Models for Use in Composite Conditional Likelihood. 31

3.1 General Odds Ratio Models. 33

3.1.1 Model intracluster pairwise association via odds ratio function under the composite conditional likelihood approach. 33

3.1.2 Develop a odds ratio model for use in composite conditional likelihood. 35

3.2 Simulation Studies. 38

3.3 Water Quality Study. 41

3.4 Appendix. 44

4 Investigate Optimal Choices of Cluster-specific Weights. 47

4.1 Introduction. 49

4.2 Optimal Choices of Cluster-specific Weights for Proposed Composite Conditional Likelihood Under Standard Situation. 53

4.3 Optimal Choices of Cluster-specific Weights for Proposed Composite Conditional Likelihood Under Sparse Data Situation. 63

4.4 Water Quality Study Reanalysis. 67

4.5 Appendix. 72

5 Summary and Future Direction of Study. 77

5.1 Summary. 79

5.2 Future Direction of Study. 80

Bibliography. 81

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