Title

Computational approach to Bayesian inference for risk assessment

Date of Completion

January 1998

Keywords

Biology, Biostatistics|Health Sciences, Toxicology|Statistics

Degree

Ph.D.

Abstract

Due to the concern for possible carcinogenic effects of potentially hazardous substances such as chemicals, drugs and food additives, many animal experiments have been conducted to investigate toxicity effects. We investigate three experiments, which have important applications in the risk assessment.^ Bayesian analysis using Gibbs sampling with data augmentation and Metropolis algorithm is used, which find posterior estimates of the model parameters and mortality rates and other several quantities of interest. Model selection based on conditional predictive ordinates from cross-validated data is also developed.^ In the analysis of tumorigenicity experiments with survival/sacrifice data, the times to tumor are often not directly observable. A multi-state model for tumor development and death in the presence of competing risk is useful to describe the passage of a subject. But, analytic and numerical results for the MLE are essentially intractable except in the simple exponential distribution case. Using sampling based approaches can circumvent this problem. We also incorporate the parametric regression to examine the effects of covariates on tumor onset and death rates.^ For the quantal response model, we explore the relationship between the survival probability and the concentration of the toxicity. Bayesian methods for estimating the dose response curves with the one-hit model, the gamma multi-hit model, and their modified versions with Abbott's correction are studied. We investigate the Bayes estimates of the potency curves. In addition, estimation of the "relative additional risk" and the "virtually safe dose" is studied.^ The third experiment presents the analysis of toxicological multivariate mortality data when the discrete mortality rate for a family of subjects at a given time depends on the time and the common toxic level experienced by the family. Our aim is to model and analyze the mortality data such as the fish tank data of O'Hara Hines and Lawless (1993) where the family sizes are substantially large compared to the size of each family. The model used is an extension of Efron's log-logistic model for discretized hazard (1988) with additional time-varying familial random effects. Recent tools in Bayesian model diagnostics have been incorporated to verify further modeling assumptions regarding effect of time and heterogeneity among the families on the mortality rate. ^