Statistical Methods for Modeling and Design of Life History Studies

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Life history studies are conducted by following study subjects over some period of time and collecting information about the occurrence of events and other outcomes. Such studies have been widely used in medicine, engineering, social sciences and economics. This research program addresses challenges associated with modeling and designs for life history studies. The specific research problems include: 1) methods for joint analysis of multiple recurrent episodes; 2) modelling spatially correlated life history data; and 3) adaptive designs for two-stage longitudinal trials.   Complex types of association structure arise in life history studies when several processes are involved or underlying cluster structures exists among observations. Examples include paired or related organ systems, multiple types of diseases, community or school based intervention studies. One of the main objectives of this proposal is to develop statistical methods to deal with association and heterogeneity in life history processes. For multiple recurrent episodes, dependence model can be formulated by introducing shared random effects in transition intensities or via Copula's. When interest lies in covariate effects on marginal properties of recurrent event processes, marginal models are more appealing and associations among processes can be formulated using cupula functions. Spatially correlated data arise in life history studies when spatial clustering is evident both in the placement of population mixtures corresponding to different sub-groups and in their evolution over time. In the context of mixture models, copula functions are adopted for the multivariate distribution of failure times in susceptible population, marginal models are specified for the latent susceptibility indicators where the spatial associations are characterized via pairwise odds ratios. Intensity based multistate models have been increasingly used for modelling transitions in life history processes. Spatial random effects can be incorporated in the transition intensities to account for the correlation in disease progression due to environmental risk factors. The challenges associated with these models include complex association structures between dynamic processes and methods for parameter estimation.  Adaptive designs allow characteristics of the study itself, for example sample size or probability of treatment assignment, to change during the trail in response to data being collected. Such designs have drew a lot of attention but most of the exiting work consider the simple situation with a continuous or binary response that is immediately observable. Modern adaptive designs for life history studies with survival or multistate data will be developed in this research program. In particular, sample size adjustment and response adaptive randomization in a two-stage design for longitudinal trials will be investigated.