Bayesian Space-time Analysis in Carcinogenesis Public
Xu, Roy (2011)
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.
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
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