AbstractsMathematics

Many studies in biomedical, psychosocial and related services research involve mixtures of populations. For example, when evaluating the effect of an HIV prevention intervention for a population of adolescent girls, it is not only of significant importance to study whether the intervention has an effect on those who are sexually active (the at-risk subgroup), but also on abstinent girls (the non-risk sub-group), since the intervention is likely to have differential effects between the two different populations. Since the sub-groups are generally unobservable, it is not possible to compare intervention effects across such sub-populations using existing methods. In this thesis, we propose a novel approach to tackle the analytic problems. We employ a Zero-inflated Poisson (ZIP) like model to help identify the two latent subgroups and integrate this sub-model into the context of a primary model of interest to enable estimation of parameters of interest such as the intervention effect in the HIV prevention study. We develop this proposed system of models by utilizing a new class of functional response models (FRM). To provide inference for longitudinal data analysis, we integrate the inverse probability weighted (IPW) estimate within the context of FRM and develop distribution-free inference about the parameters of the system of models. As we have demonstrated in our prior research on investigating the differences in modeling longitudinal data between the dueling parametric generalized linear mixed-effects model (GLMM) and distribution-free generalized estimating equations (GEE) paradigms, the proposed distribution-free approach seems to offer the only sensible solution to this type of modeling problem involving population mixtures.