| The purpose of this dissertation research is to compare the toxicity of the {dollar}alpha{dollar}-emitting, bone-seeking radionuclides {dollar}sp{lcub}239{rcub}{dollar}Pu and {dollar}sp{lcub}226{rcub}{dollar}Ra, develop a model for radiation induced osteosarcomas, and analyze the survival data of beagles exposed to these radionuclides. This research integrates the knowledge of radiation protection, survival theory and methods (competing risks, maximum likelihood estimation, and Bayesian techniques), numerical integration techniques (Monte Carlo, Lattice rule and Gauss-quadrature) and object-oriented programming in C++. The outline of this research is: (1) survival data preprocessing, (2) model identification and selection, (3) introduction of FGM model, the dependent competing risk model created by Farlie, Gumbel and Morgenstern, to the study of survival data with dependent competing risks: osteosarcomas and other diseases, development of the crude density of the FGM model and construction of the likelihood function for the FGM model, (4) Bayesian estimates of the posterior marginal density of the toxicity ratio in the FGM model using several numerical integration techniques (Monte Carlo, Lattice rule and Gaussian Quadrature), (5) construction of the likelihood function for the independent competing risk model, Bayesian estimate of the posterior marginal density of toxicity ratio in the model using Monte Carlo method, which is compared with the posterior marginal densities for the toxicity ratio obtained from the FGM model, (6) Bayesian estimates of all other parameters in the FGM model using Monte Carlo method, (7) Comparison of the cumulative hazard for {dollar}sp{lcub}239{rcub}{dollar}Pu calculated according to the model with Nelson's cumulative hazard plot under Bayesian point estimates of parameters and the mean activity in each injection level, (8) Comparison of the toxicity of plutonium in osteosarcoma with that of radium under Bayesian point estimates of parameters an d the selected activit of 0.85 {dollar}mu{dollar}C{dollar}sb{lcub}rm i{rcub},{dollar} (7) discuss Bayesian prediction of the cumulative failure distribution.; It is the first time for the FGM model and the independent competing risk model to compare the toxicity between {dollar}sp{lcub}239{rcub}{dollar}Pu and {dollar}sp{lcub}226{rcub}{dollar}Ra. Bayesian parameter estimates for these models are also the original contribution of this research. The approach is novel in the field of radiation risk assessment, particularly, for toxicity studies. |
