Statistical methods for active extension trials

This paper develops methods of analysis for active extension clinical trials. Under this design, patients are randomized to treatment or placebo for a period of time (period 1), and then all patients receive treatment for an additional period of time (period 2). We assume a continuous outcome is measured at baseline and at the end of the two consecutive periods. If only period 1 data is available, classic estimators of the treatment effect include the change score, analysis of covariance, and maximum likelihood (ML). We show how to extend these estimators by incorporating period 2 data which we refer to as the period 2 estimators. Under the assumption that the mean responses for treatment and placebo arms are the same at the end of period 2, the new estimators are unbiased and more efficient than estimators that ignore period 2 data. If this assumption is not met, the period 2 tests may be more powerful than period 1 tests, but the estimators are biased downward (upward) if the treatment effect during period 2 is larger (smaller) in treatment arm than the placebo arm. In general, the proposed period 2 procedure can provide an efficient way to supplement but not supplant the usual period 1 analysis.