Power comparisons for tests of trend in dose-response studies

The Cochran-Armitage test for trend is a popular statistical procedure for detecting increasing or decreasing probabilities of response when a categorical exposure is ordered. Such associations may arise in a variety of biomedical research settings, particularly in dose-response designs such as carcinogenicity experiments. Previously, computing limitations mandated the use of the asymptotic trend test, but with the availability of new algorithms, increased computing power, and appropriate software the exact trend test is now a practical option. Nevertheless, the exact test is sometimes criticized on the grounds that it is conservative. In this paper we investigate the implications of this conservatism by comparing the true type I error and power of three alternative tests of trend - the asymptotic test, the exact test and an admissible exact test proposed by Cohen and Sackrowitz. The computations are performed by an extension to the network algorithm of Mehta et al. This allows us to make precise power comparisons between the tests under any given design without resorting to simulation. We show how this tool can guide investigators in choosing the most appropriate test by considering the design of two-year carcinogenicity studies carried out by the National Toxicology Program. We additionally compare the tests for various other combinations of sample sizes and number of groups or levels of exposure. We conclude that the asymptotic test, while more powerful where it is valid, generally does not preserve the type I error. This violation of the a priori testing level can be greatly affected by imbalance in the data or unequal spacing of dose levels.