Critical Values and Power for a Small Sample Test of Difference in Proportions in the Presence of Extra-Binomial Variation

10.6339/JDS.2006.04(3).275

John S. Lawson；Benjamin Ahlstrom

Beta-binomial distribution ； dual control groups ； extra-binomial variation ； Fisher's exact test, historical controls ； likelihood ratio test ； overdispersion ； rodent carcinogenicity bioassay ； significance level

Journal of Data Science

4卷3期（2006 / 07 / 01）

357 - 370

英文

We develop a likelihood ratio test statistic, based on the betabinomial distribution, for comparing a single treated group with dichotomous data to dual control groups. This statistic is useful in cases where there is overdispersion or extra-binomial variation. We apply the statistic to data from a two year rodent carcinogenicity study with dual control groups. The test statistic we developed is similar to others that have been developed for incorporation of historical control groups with rodent carcinogenicity experiments. However, for the small sample case we considered, large sample theory used by the other test statistics did not apply. We determined the critical values of this statistic by enumerating its distribution. A small Monte Carlo study shows the new test statistic controls the significance level much better than Fisher's exact test when there is overdispersion and that it has adequate power.