GLM, GLMM, GEE for Correlated Discrete Data with Over-dispersion, Zero-inflation, Measurement Error and Misspecification

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The main area of my research is methodological development of statistical procedures in the general area of biostatistics where longitudinal or clustered correlated data arise in the form of counts, proportions or survival times. Longitudinal data arise, for example, in medical studies, where patients are observed over time for survival after a medical procedure. Clustered data arise in many situations as groups of responses. For example, in family studies, family members (mother and her children or siblings in the same family) will have similar medical problems. So, the responses of members of the same family will be correlated. One aim in such studies is to establish the relationship between a response variable (disease status) and covariates or regression variables (age, ethnicity, presence of other disease of the patient). However, data that arise in practice often have a lot of complications. For example, count data or data in the form of proportions often show over-dispersion (variance is greater than the mean), zero-inflation (more zeros than what can be predicted by a simple model for the analysis of the data). Further, measurement error in explanatory (regression) variables and missing values in both response and explanatory variables are prevalent in many scientific fields. Data of these types arise in fields as diverse as biology, epidemiology, social science and engineering.