Efficacy evaluation for monotherapies in two-by-two factorial trials

For factorial clinical trials in which two monotherapy treatments under study can interact only in the presence of treatment effects for each treatment, the always-pooled test statistic using data from all four groups has a correct size in detecting the simple effect of an individual treatment used alone. However, this test statistic may have an unbounded bias in estimation of the simple effect. The never-pooled test statistic that uses only data from the treatment group not receiving the other treatment has poor precision for estimating the simple effect. Two alternative test statistics under consideration are the two-stage statistic involving a preliminary test of treatment interaction and the maximum test statistic taking the larger of the always-pooled and the never-pooled statistics. The power, bias, and mean square error of all four tests are compared. When negative interactions exist, the two-stage and maximum statistics are generally superior to the always-pooled statistic and compare reasonably well with the never-pooled statistic; the maximum statistic seems slightly more favorable than the two-stage statistic. The two-stage statistic is the best choice when a treatment interaction can be large.