Bootstrapping an empirical Bayes estimator of the distribution of historical controls in carcinogen bioassay

Abstract

Previous applications of tests for trend in tumor occurrence rates in laboratory studies of carcinogenicity have frequently employed a beta-binomial distribution for the historical control response rates. In this paper, we develop generalized score tests for trend based on a logistic does response model and an arbitrary distribution for the historical control tumor response probabilities. A closed-form expression for the score statistic is presented in the special case of a discrete uniform distribution with mass points corresponding to the observed historical control series. The asymptotic distribution of this statistic is shown to be a finite mixture of normal distributions. A discrete empirical Bayes shrinkage estimator of the historical control response rates is proposed, along with a bootstrap variance estimator for the corresponding score statistic which takes into account sampling variability in the historical data. The application of this test is illustrated using bioassay data taken from the literature.