Joint modeling of longitudinal biomarkers and panel count data

In cancer chemoprevention clinical trials, the primary objective is to assess the efficacy of the chemopreventive agent. With the clinical endpoint being cancer incidence, which requires large sample size and long time period and thus high cost, biomarkers have been under investigation for their potential as surrogate endpoints. Biomarkers are generally collected intermittently and measured with error. Using them directly as covariates for modeling cancer incidence will lead to bias. Therefore, joint models of biomarkers and cancer incidence become necessary.;The Skin Cancer Chemoprevention Trial was carried out to evaluate the effect of alpha-difluoromethylornithine (DFMO) in preventing the recurrence of skin cancers. The primary endpoint was the number of new tumors developed between successive visits. Four biomarkers were collected on a subset of the subjects.;In this thesis work, a latent class joint model is proposed for the Skin Cancer Chemo-prevention Trial data, which consists of three sub-models: a generalized logit model for the latent class membership, a linear mixed-effects model for the longitudinal biomarkers, and a Poisson regression model for the tumor count or a mixed Poisson model for the panel count. The biomarker data and tumor count data are considered conditionally independent given the class membership and marginally correlated through the class membership. Sub-population structures for both biomarkers and the event process can be identified. The latent class joint model is very flexible with non time-to-event clinical outcome. It can include multiple hiomarkers in the linear model and incorporate frailty in the mixed Poisson model.;A generalized EM algorithm is developed to compute the maximum likelihood estimators of the joint model. At the E-step, the expectation of the complete data log likelihood given the observed data and current parameter estimates is calculated. At the M-step, the parameters are updated by maximizing the conditional expectation. For parameters without closed form maximizers, one step of the Newton-Raphson method is used within the M-step. The E-step and M-step iterate until the preset convergence criteria are met. Fitting the latent class joint model requires complex computation. Therefore improving the efficiency of the GEM algorithm is an important task.