Bayesian Space-time Analysis in Carcinogenesis Open Access

Abstract

Although the etiology of cancer remains under investigation, evidence has suggested that
multiple events occur during carcinogenesis, the process of the transformation of normal
cells into cancer cells. Statistical modeling of carcinogenesis has been used to study the
cancer formation and cancer risk assessment. In this dissertation, I present three studies
involving carcinogenesis models in estimating cancer mortality rates.
First, I develop a Bayesian Armitage-Doll multistage carcinogenesis model. This research is the first effort to use an alternative Bayesian approach in the Armitage-Doll multistage model. Different likelihoods and prior settings are discussed and sensitivity analysis and model assessment show that the Bayesian Armitage-Doll model fits the cancer mortality data well.
Second, I develop a Bayesian extended APC model where non-specific age
effects are replaced by the hazard functions derived from multi-stage carcinogenesis models. The Bayesian extended APC model is applied to study colon cancer mortality rates in the US achieving high consistency between the estimated rates and observed rates for older age groups (≥ 45). In addition, model comparisons show that the Bayesian extended APC model can be used to replace the conventional APC model without increasing the deviance information criterion (DIC) values while providing a more sound biological meaning to the model.
Third, I further apply the Bayesian extended APC model to study the spatio-temporal
variation in cancer mortality rates. The county level lung and colon cancer mortality data in Iowa are used as examples. The study shows the Bayesian extended AAPC model with area-cohort interaction and Armitage-Doll age effects achieved the lowest DIC values and good convergency among all models. The Bayesian extended AAPC model can be used to study spatial-temporal patterns of cancer mortality with strong biological prior beliefs in the age effects.

In summary, my dissertation focuses on developing carcinogenesis analytic approaches using Bayesian methods. The three studies show that carcinogenesis model can be used to study the relationship between cancer mortality rate and spatial and temporal effects from the underlying disease process.

Table of Contents

1 Introduction 1

2 Literature Review 4

2.1 Mechanisms of Carcinogenesis . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2 Carcinogenesis Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2.1 Armitage-Doll Multistage Model . . . . . . . . . . . . . . . . . . . . 5

2.2.2 Moolgavkar-Venzon-Knudson Two-stage Clonal Expansion (TSCE)

Carcinogenesis Model . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3 Age-Period-Cohort (APC) Model . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3.2 Identi ability Issue . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3.3 Area-APC Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3 Bayesian Armitage-Doll Multistage Carcinogenesis Model 14

3.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.2 Signi cance and Innovation . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.3 Build the Bayesian Armitage-Doll Multistage Carcinogenesis Model . . . . . 18

3.3.1 Normal Likelihood and Conjugate Prior . . . . . . . . . . . . . . . . 18

3.3.2 Poisson Likelihood and Noninformative Prior . . . . . . . . . . . . . 20

3.3.3 Binomial Likelihood and Noninformative Priors . . . . . . . . . . . . 22

3.3.4 Weibull Likelihood and Noninformative Priors . . . . . . . . . . . . 23

3.3.5 Results - NIG Priors . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.3.6 Results - Noninformative Priors . . . . . . . . . . . . . . . . . . . . . 25

3.4 Assess the Bayesian Armitage-Doll Multistage Carcinogenesis Model . . . . 27

3.4.1 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.4.2 Model Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.5 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4 Bayesian extended Age-Period-Cohort Model 34

4.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.2 Signi cance and Innovation . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.3 Apply Armitage-Doll Multistage Carcinogenesis Model into APC Model . . 37

4.4 Apply TSCE Carcinogenesis Model into APC Model . . . . . . . . . . . . . 41

4.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.5.1 Convergence Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.5.2 Model Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.5.3 Rate Estimation and Projection . . . . . . . . . . . . . . . . . . . . 47

5 Bayesian extended Area-Age-Period-Cohort (AAPC) Model 51

5.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5.2 Signi cance and Innovation . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

5.3 Bayesian AAPC Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

5.4 Bayesian extended AAPC Model - Introduction of Carcinogenesis Model into

AAPC Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5.5 Example 1 - Lung Cancer Mortality in Iowa . . . . . . . . . . . . . . . . . . 61

5.6 Example 2 - Colon Cancer Mortality in Iowa . . . . . . . . . . . . . . . . . 69

5.7 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

6 Conclusion 75

Appendices 83

A R2WINBUGS code 84

A.1 R code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

A.2 BUG code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

About this Dissertation

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School	Laney Graduate School
Department	Biostatistics
Degree	PhD
Submission	Dissertation
Language	English
Research Field	Mathematics Health Sciences, Oncology
Keyword	Carcinogenesis, Bayesian models, Age-period-cohort
Committee Chair / Thesis Advisor	Hertzberg, Vicki S, Emory University
Committee Members	Vidakovic, Brani , Emory University Waller, Lance, Emory University Yu, Tianwei, Emory University

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