Statistical methods for complex clinical and survey data

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The proposed research has the goal of developing innovative methods for analyzing complex clinical and survey data. In clinical studies, we often observe longitudinal and time-to-event data with complex dependence structures featuring many important issues including frailties, measurements with the limit of detection (LOD), time-dependent covariates, and outliers in follow-up measurements. Joint models for longitudinal and survival data are typically used when the focus is on the survival times and one wishes to investigate the effect of an endogenous time-dependent covariate on the survival of patients. I will develop and explore efficient methods by addressing the aforementioned complex issues of survival analysis. Specifically, I will investigate robust methods that can bound the influence of outliers when jointly analyzing the longitudinal and time-to-event data.I will also investigate efficient and computationally feasible methods for incomplete longitudinal data commonly encountered in clinical studies. The modeling of longitudinal data is often complicated by the fact that the response variable is not always observed at all assessment times. Often the missingness process is considered nonignorable, i.e., the missingness depends on the unobserved value of the outcome at that time. To define a full likelihood for nonignorable missing responses over time, one needs to specify a joint distribution for the repeated outcomes as well as a model for the missing data mechanism. I will develop and study a semi-parametric approach to analyzing longitudinal data with non-ignorable missing responses, where the mean response may be described as a function of the covariates by an unknown smooth function.In survey sampling, data are often clustered correlated and the focus is on the estimation of area means or proportions (e.g., proportions of subjects who are cognitively impaired in different socio-demographic groups) based on predictors of random area effects. I will investigate novel methods for small area estimation when the outcome variable of interest is discrete or categorical. Specifically, I will develop a robust method in the framework of generalized linear mixed models for clustered correlated data. Unlike ordinary linear unbiased estimators, the proposed robust estimators will not be influenced by outliers in the data.The developments will enable researchers in the health sciences to engage in reliable estimation and assessment of their hypothesized models for analyzing longitudinal as well as clustered correlated data in the presence of missing observations and/or outliers, and hence will greatly benefit clinical practitioners working with complex data.