Large Sample Tests for Binary Outcomes in Fixed-Dose Combination Drug Studies

Several test statistics are developed for testing the hypothesis that the combination of two drugs at a fixed-dose regimen is more effective than both of the single drugs used alone with respect to a dichotomous response variable. The response probability, logit, and arcsine-root scales are considered. The power function and the significance level are derived for large samples. For the sample size per group of 20 or greater, the power and type I error rate can be accurately calculated using the large sample power function when the response probability ranges from 0.2 to 0.8. These tests have similar power behaviors. In small samples, the large sample power functions of two of the tests can severely underestimate the type I error rate while overestimation can occur with one other test. The utilities of these tests are extended to unbalanced sample size cases. Generally speaking, there is a loss of power with unequal sample size allocation, but the loss is not severe.