AdvisorPiegorsch, Walter W.
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PublisherThe University of Arizona.
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AbstractBenchmark analysis is a general risk estimation strategy for identifying the benchmark dose (BMD), past which the risk of exhibiting the adverse response exceeds a fixed value of benchmark response (BMR). The BMD has traditionally been applied in toxicological stimulus-response settings; the adverse outcomes have included cancer, birth defects, environmental toxicity, neurological damage, etc. For this context, risk is defined as the probability that a subject exhibits the adverse effect when exposed to a quantifiable dose level of the hazardous stimulus or agent. Such settings often involve binary or proportion responses—called quantal data—where the observations are taken as independent binomial variates at each exposure, input, or dose level. The estimation of BMD and its lower confident limit (BMDL) is well understood for the case of an adverse response to a single stimulus. However, in many situations one or more additional, secondary, qualitative factor(s) may collude to affect the risk, such that the risk changes with differential levels of the secondary factor. While the BMD is highly effective at integrating information over a single stimulus-response curve into the risk estimation problem, no dedicated methodology exists for modifying it to accommodate such secondary qualitative factors. Extending the translational capabilities of the BMD approach, this research is motivated by problems in childhood development, where early-age levels of some markers in blood, such as immunoglobulin E (IgE), may be useful in predicting future asthma diagnoses. A complicating factor here is that childhood obesity (a qualitative variable) often affects future asthma status, leading to differential asthma risk/response in children. In this framework, the goal of this research is to develop modern benchmark methods that can produce effective estimates of joint risk and from these, reliable inferences on BMD with mixed-factors and quantal-response data. Using as a dose-response function the logistic model, we derived the expressions for BMD and BMDL (ζ ̂(u) and ζ_L (u)). Four different approaches were used to derive the BMDL: i) Wald lower confidence limit (WALD), ii) Bivariate Normal lower confidence limit (BVN), iii) Wald lower limit on the log-transformation of the BMD (WALD-log), and iv) Bivariate Normal lower confidence limit on the log-transformation of the BMD (BVN-log). Using Monte Carlo simulations, we studied the performance of the four confidence limits described by examining their conditional coverage properties. We found that the conditional coverages were affected by the and ζ_L (u) construct, the ratio of individuals between the two levels of the qualitative variable, the level of the background response, and the underlying characteristics of the dose variable. In brief, WALD and BVN performed better than WALD-log and BVN-log. Moreover, the methodology worked better when the background response level was higher and when the ratio of individuals between the two levels of the qualitative variable was closer to one. Finally, skewness of the data also affected performance; higher coverages were obtained when the skewness was lower. The theory developed in this dissertation can be further extended to additional qualitative factors and/or to use other models as a risk function, such as the probit or quantal-linear model. Nevertheless, additional research is required to study whether our methods can translate effectively to other link functions for mixed-factor dose-response modeling.
Degree ProgramGraduate College