Statistical Models for Scalar Response with Longitudinal Covariates

Open Access
Graduate Program:
Doctor of Philosophy
Document Type:
Date of Defense:
October 07, 2014
Committee Members:
  • Runze Li, Dissertation Advisor
  • Runze Li, Committee Chair
  • Naomi S Altman, Committee Member
  • Zhibiao Zhao, Committee Member
  • Stephanie Trea Lanza, Committee Member
  • longitudinal study
  • functional data
  • nonparametric regression
  • measurement error
  • generalized linear model
  • zero-inflated count
Motivated by several health behavior studies, this dissertation is concerned with modeling distal outcome with longitudinal covariates. Specifically, the covariates for each subject are repeatedly observed at a sequence of time points, while the response is measured at one single time point, typically, at the end of the study. Such data are different from those in standard longitudinal models, where both response and covariates are repeatedly collected for each of many subjects. We first develop models for scalar response with discrete longitudinal covariates, when the covariates can be characterized by a distribution from an exponential family. Recognizing that the observed longitudinal covariates are often subject to measurement errors while the true subject-specific profiles are unobservable, we propose a two-stage calibration regression procedure to estimate the effect function using the natural cubic smoothing spline technique. The performance of the proposed estimation procedure is compared under various circumstances via a set of simulation studies. The consistency and asymptotic normality of the estimated population profile function in the longitudinal covariate model are established, while allowing the number of observation time points to diverge as the sample size increases. A slight extension of the model is further proposed to accommodate an extra clustered random effect, then adopted in a study of alcoholic couples. In many drug and alcohol studies, the longitudinal covariates are counted values with excess of zeros. Thus, special techniques for handling the zero inflation are considered. Specifically, we propose estimating the longitudinal covariate processes through a hurdle model with zero-truncated Poisson distribution. Simulation experiments are conducted to evaluate the performance and feasibility of this particular estimation procedure. The method is then applied to data from an alcohol study for further illustration.