Abstract: A score statistic for testing for trend in count data based on the joint likelihood of historical control and current experimental counts is proposed using the negative-binomial distribution to represent between-study extra-Poisson variation. The score statistic is also derived using a Poisson likelihood for the current experiment and a negative-binomial likelihood for the historical controls. Similar statistics are derived using generalized estimating equations based on the first two moments of the data. The type I and type II error rates of these tests are evaluated using computer simulation, and compared with those of the Cochran-Armitage test for trend that does not make use of historical controls. Test statistics proposed by Tarone (1982) and Kikuchi and Yanagawa (1988) for use with historical controls are also considered.
Key words and phrases: Poisson distribution, negative-binomial distribution, extra-Poisson variation, overdispersion, score test, maximum likelihood, estimating equations.