Modeling and analysis of correlated data is a recurring challenge in health sciences research. These data arise routinely in clinical trials and epidemiological studies of cancer and other diseases, where correlation may be due to the longitudinal nature of data collection on each subject, clustering of observations from the same center or family, or geographical orientation. Much statistical research has been devoted to mixed effects models, which take account of correlation through incorporation of random effects. A prevailing concern is that standard assumptions may be unrealistic or too restrictive to represent the data, which may lead to unreliable inferences on scientific questions of interest and to important features of the data to be obscured. Recent interest has focused on relaxing these assumptions by either (i) allowing more flexible functional dependence of response variables on covariates or (ii) allowing more flexible representation of the distribution of the random effects than provided by the usual normal distribution. The objective of the research in this proposal is to develop flexible mixed effects models that address (i) and (ii), providing the data analyst tools for correlated data for which standard assumptions do not apply. We will develop semiparametric generalized linear models, which allow more flexible representation of the random effects; semiparametric generalized additive models, which further allow flexible covariate dependence; semiparametric frailty models, which allow flexible models for multivariate time-to-event data; and flexible joint models for longitudinal data and primary outcomes, where the goal is to explore the association between a longitudinal measure, e.g. prostate specific antigen, and a response of interest, e.g. cancer risk. Maximum likelihood inference will be developed, and the utility of the methods will be evaluated by simulation study and application to several data sets in cancer and other disease research. A key goal is to provide public-domain, documented general software and examples to the research community.
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