Using historical controls to adjust for covariates in trend tests for binary data

Historical data often play an important role in helping interpret the results of a current study. This article is motivated primarily by one specific application: the analysis of data from rodent carcinogenicity studies. By proposing a suitable informative prior distribution on the relationship between control outcome data and covariates, we derive modified trend test statistics that incorporate historical control information to adjust for covariate effects. Frequentist and fully Bayesian methods are presented, and novel computational techniques are developed to compute the test statistics. Several attractive theoretical and computational properties of the proposed priors are derived. In addition, a semiautomatic elicitation scheme for the priors is developed. Our approach is used to modify a widely used prevalence test for carcinogenicity studies. The proposed methodology is applied to data from a National Toxicology Program carcinogenicity experiment and is shown to provide helpful insight on the results of the analysis.