Interim analyses in 2 x 2 crossover trials.

A method is presented for performing interim analyses in long term 2 x 2 crossover trials with serial patient entry. The analyses are based on a linear statistic that combines data from individuals observed for one treatment period with data from individuals observed for both periods. The coefficients in this linear combination can be chosen quite arbitrarily, but we focus on variance-based weights to maximize power for tests regarding direct treatment effects. The type I error rate of this procedure is controlled by utilizing the joint distribution of the linear statistics over analysis stages. Methods for performing power and sample size calculations are indicated. A two-stage sequential design involving simultaneous patient entry and a single between-period interim analysis is considered in detail. The power and average number of measurements required for this design are compared to those of the usual crossover trial. The results indicate that, while there is minimal loss in power relative to the usual crossover design in the absence of differential carry-over effects, the proposed design can have substantially greater power when differential carry-over effects are present. The two-stage crossover design can also lead to more economical studies in terms of the expected number of measurements required, due to the potential for early stopping. Attention is directed toward normally distributed responses.