Stochastic and State Space Models of Carcinogenesis Under Complex Situation

With more and more biological mechanisms of cancer development being discovered, in order to improve cancer control and prevention, it becomes necessary to develop effective and efficient mathematical and statistical models and methods to incorporate the biological information, and to identify critical events in the process of carcinogenesis. In this dissertation, the complex nature of carcinogenesis has been represented by stochastic system model; combining this model with information from observations and prior knowledge, we have developed state space models to evaluate cancer gene mutations and cell proliferation at different cancer development stages. Also, we have proposed a generalized Bayesian method via multi-level Gibbs sampling procedure to predict state (stage) variables of the models. In this dissertation, stochastic models have been proposed for initiation, promotion and complete carcinomas experiments; these experiments are most commonly performed in cancer risk assessment of environmental agents. These stochastic models are simple multi-pathway models which are constructed based on biological mechanisms. The estimates we obtained from the models have provided quantitative evaluation of dose related mutation rates of major genes and cells proliferation rates; these results could be used to assess the risk of developing malignant tumor in the environment we live. More complicated stochastic and state space models have been developed for sporadic human colon cancer and for hereditary and non-hereditary human liver cancer. We have utilized the proposed models to fit to Surveillance Epidemiology and End Results (SEER) data. The results imply that our models have effectively incorporated biological information and observations; these models fitted the data very well and the inferences based on estimate were very consistent with biological findings. Furthermore, the models reflected the complex nature of carcinogenesis. We notice that many cancers are developed through multiple-stage multiple-pathway. Our analyses of colon cancer and liver cancer have showed that some pathways are more devastated than others. This suggests thus it would be more efficient to intervene or treat the critical events in the more devastated pathways

The population incidence of cancer

In this thesis stochastic techniques are used in attempts to understand cancer risk, its relationship to patient age and genotype, as well as its distribution in human populations. The starting point for the thesis is the general observation that cancer incidence grows in approximate proportion to an integer power of age. Quasi-mechanistic mathematical models of cancer incidence have suggested that the integer power in a given case is related to the number of crucial cellular events that must occur for a malignant tumour to evolve from a healthy tissue. This idea and its limitations are explored. Further applications of cancer incidence models are then evaluated and developed. Specifically, a critical examination is presented of the notion that increases in risk associated with a particular predisposing germline gene mutation, can provide information about the disease-associated activity of that gene. Finally, there is a discussion of heterogeneity in liability to cancer. Methods for quantifying this heterogeneity and its effect on incidence patterns are investigated

Design Issues for Generalized Linear Models: A Review

Generalized linear models (GLMs) have been used quite effectively in the modeling of a mean response under nonstandard conditions, where discrete as well as continuous data distributions can be accommodated. The choice of design for a GLM is a very important task in the development and building of an adequate model. However, one major problem that handicaps the construction of a GLM design is its dependence on the unknown parameters of the fitted model. Several approaches have been proposed in the past 25 years to solve this problem. These approaches, however, have provided only partial solutions that apply in only some special cases, and the problem, in general, remains largely unresolved. The purpose of this article is to focus attention on the aforementioned dependence problem. We provide a survey of various existing techniques dealing with the dependence problem. This survey includes discussions concerning locally optimal designs, sequential designs, Bayesian designs and the quantile dispersion graph approach for comparing designs for GLMs.Comment: Published at http://dx.doi.org/10.1214/088342306000000105 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Heterogeneity in multistage carcinogenesis and mixture modeling

Carcinogenesis is commonly described as a multistage process. In a first step, a stem cell is transformed via a series of mutations into an intermediate cell having a growth advantage. Under favorable conditions, such a cell will give rise to a clone of initiated cells. Eventually, further alterations may transform a cell out of this clone into a malignant tumor cell. A mechanistic model of this process is given by the widely used two-stage clonal expansion model (TSCE). In this thesis, we take up a generalization of the TSCE, and study, how to introduce the concept of population heterogeneity into the model. We use mixture modeling, which allows to describe frailty in a biologically meaningful way. In a first part, we focus on theoretical properties of the extended model. Especially identifiability is discussed extensively. In a second part, we fit the model to human cancer incidence data. We analyze a situation, in which maximum likelihood estimation fails, and describe alternatives for statistical inference. The applications show that good fits are achieved only when the mixing distribution separates the population clearly into a large, virtually immune group, and into a small, high risk group