Conditional Inference in Two-Stage Adaptive Experiments via the Bootstrap
We study two-stage adaptive designs in which data accumulated in the first stage are used to select the design for a second stage. Inference following such experiments is often conducted by ignoring the adaptive procedure and treating the design as fixed. Alternative inference procedures approximate the variance of the parameter estimates by approximating the inverse of expected Fisher information. Both of these inferential methods often rely on normal distribution assumptions in order to create confidence intervals. In an effort to improve inference, we develop bootstrap methods that condition on a non-ancillary statistic that defines the second stage design.