Uniformly minimum variance conditionally unbiased estimation in multi-arm multi-stage clinical trials

Multi-arm multi-stage clinical trials compare several experimental treatments with a control treatment, with poorly performing treatments dropped at interim analyses. This leads to inferential challenges, including the construction of unbiased treatment effect estimators. A number of estimators which are unbiased conditional on treatment selection have been proposed, but are specific to certain selection rules, may ignore the comparison to the control and are not all minimum variance. We obtain estimators for treatment effects compared to the control that are uniformly minimum variance unbiased conditional on selection with any specified rule or stopping for futility.