Parameter estimation in mathematical models of lung cancer

摘要

The goal of this thesis is to improve upon existing mathematical models of lung cancer that inform policy decisions related to lung cancer screening. Construction of stochastic, population-based models of lung cancer relies upon careful statistical estimation of biological parameters from diverse data sources. In this thesis, we focus specifically on two distinct aspects of parameter estimation. First, we propose a model-based framework to estimate lung cancer risk due to repeated low-dose radiation exposures using the two-stage clonal expansion (TSCE) model. We incorporate the TSCE model into a Bayesian framework and formulate a likelihood function for randomized screening data. The likelihood function depends on model-based risk correlates and effectively penalizes parameter values that correspond to model-based contradictions. The net result is that both the sensitivity and specificity of parameter estimation relating to excess lung cancer risk is increased. This methodology is applied to data from the Mayo Lung Project and estimates of 10-year excess lung cancer risk as a function of age at enrollment and number of screens are derived. Second, we describe a new statistical approach aimed at improving our understanding of the natural course of lung cancer. Specifically, we are interested in evaluating the evidence for, or against, the hi-modal hypothesis which proposes that lung cancers are of two categories, either slow-growing and non-invasive cancers (tending to over-diagnosis) or rapidly-growing and highly aggressive. We represent the growth trajectory of lung tumors using the evolutionary parameters of cancer stern cell branching fraction (f) and cell mutation rate (mu). While concern over widespread implementation of lung cancer screening has focused primarily on the extent of over-diagnosis, these results are consistent with the presence of a high percentage of rapidly-growing, aggressive cancers.