title: A Bayesian analysis of quantal bioassay experiments incorporating historical controls via Bayes factors.
abstract: This paper addresses model-based Bayesian inference in the analysis of data arising from bioassay experiments. In such experiments, increasing doses of a chemical substance are given to treatment groups (usually rats or mice) for a fixed period of time (usually 2 years). The goal of such an experiment is to determine whether an increased dosage of the chemical is associated with increased probability of an adverse effect (usually presence of adenoma or carcinoma). The data consists of dosage, survival time, and the occurrence of the adverse event for each unit in the study. To determine whether such relationship exists, this paper proposes using Bayes factors to compare two probit models, the model that assumes increasing dose effects and the model that assumes no dose effect. These models account for the survival time of each unit through a Poly-k type correction. In order to increase statistical power, the proposed approach allows the incorporation of information from control groups from previous studies. The proposed method is able to handle data with very few occurrences of the adverse event. The proposed method is compared with a variation of the Peddada test via simulation and is shown to have higher power. We demonstrate the method by applying it to the two bioassay experiment datasets previously analyzed by other authors. Copyright © 2017 John Wiley & Sons, Ltd.
authors.affiliation: Department of Biostatistics, The University of Texas Health Science Center at Houston-School of Public Health, 1200 Pressler St, RAS E805, Houston, 77030, TX, U.S.A.
authors.forename: Luis G
authors.initials: LG
authors.lastname: León Novelo
authors.affiliation: Department of Statistics, Indiana University, 309 N. Park Ave, Bloomington, 47408, IN, U.S.A.
authors.forename: Andrew
authors.initials: A
authors.lastname: Womack
authors.affiliation: Department of Statistics, Virginia Polytechnic Institute and State University Hutcheson Hall, RM 406-A, Virginia Tech 250 Drillfield Drive, Blacksburg, 24061, VA, U.S.A.
authors.forename: Hongxiao
authors.initials: H
authors.lastname: Zhu
authors.affiliation: Department of Statistics, Virginia Polytechnic Institute and State University Hutcheson Hall, RM 406-A, Virginia Tech 250 Drillfield Drive, Blacksburg, 24061, VA, U.S.A.
authors.forename: Xiaowei
authors.identifier: 0000-0001-9916-3624
authors.initials: X
authors.lastname: Wu
mesh_terms: D000818:Animals; D001499:Bayes Theorem; D001681:Biological Assay / Q000379:methods* / Q000592:standards / Q000706:statistics & numerical data; D003627:Data Interpretation, Statistical; D004305:Dose-Response Relationship, Drug; D064420:Drug-Related Side Effects and Adverse Reactions; D065386:Historically Controlled Study / Q000379:methods* / Q000592:standards / Q000706:statistics & numerical data; D010600:Pharmacology; D016019:Survival Analysis
keywords: peddada test; poly-k test; probit model; rodent; toxicity; tumor rate