Integrated Analysis of Longitudinal Tumor Burden Data

Abstract

The first part of this thesis introduces a new statistical method to estimate parameter values in a mixed population consisting of both single- and bi- phasic longitudinal trajectories. This pro- posed model is capable of categorizing patients according to their longitudinal relationships and estimating the associated parameters of interest, while accounting for between-patient variability. We applied this method to a large phase III randomized trial and found significant differences in patients between different treatment cohorts and within the same treatment cohort, in terms of their longitudinal relationships, with the majority of patients displaying complex bi-phasic trends. In the second part of this thesis, we designed a dynamical system model to explain the observed bi-phasic longitudinal trends and their implications for the underlying cancer biology. We found that a hybrid model encompassing both hierarchical cellular model and clonal expansion model is needed to explain the observed bi-phasic patterns. The third part of this thesis explores the effects of proliferative patterns in colon crypt on crypt stability and rates of somatic evolution.