Drop-the-losers designs have been discussed extensively in the past decades, mostly focusing on two-stage models. The designs with more than two stages have recently received increasing attention due to their improved efficiency over the corresponding two-stage designs. In this paper, we consider the problem of estimating and testing the effect of selected treatment under the setting of three-stage drop-the-losers designs. A conservative interval estimator is proposed, which is proved to have at least the specified coverage probability using a stochastic ordering approach. The proposed interval estimator is also demonstrated numerically to have narrower interval width but higher coverage rate than the bootstrap method proposed by Bowden and Glimm (Biometrical Journal, vol. 56, pp. 332-349) in most cases. It is also a straightforward derivation from the stochastic ordering result that the family-wise error rate is strongly controlled with the maximum achieved at the global null hypothesis.
Keywords: Clinical trial; family-wise error rate; interval estimate; multi-arm multi-stage design; stochastic order.