Trend Test for Overdispersed Proportions

Abstract

AbstractThe Cochran‐Armitage test has commonly been used for a trend test in binomial proportions. The quasi‐likelihood method provides a simple approach to model extra‐binomial proportions. Two versions of the score and Wald tests using different parameterizations for the extra‐binomial variance were investigated: one in terms of intercluster correlation, and another in terms of variance. The Monte Carlo simulation was used to evaluate the performance of the each version of the score test and the Wald test, and the Cochran‐Armitage test.The simulation shows that the Cochran‐Armitage test has the proper size only for the binomial sample data, and the test is no longer valid when applied to the extra‐binomial data. The Wald test is more likely to exceed the nominal level than the score test under either intercluster correlation model or variance model. Both score tests performed very well even with the binomial data; the tests control the type I error and in the meantime maintain the power of detecting the dose effects. Based on the design considered in this paper, the two scores test are comparable. The score test based on the intercluster correlations model seems better controlling the Type I error but appears less powerful than that based on the variance model. An example from a developmental toxicity experiment is given.