Synthetic estimators with moderating influence: the carry-over in cross-over trials revisited

A general approach to combining alternative estimators of a parameter is de scribed and applied to the analysis of 2 x 2 cross-over trials in which the treatment effect is of principal interest and carryover is a nuisance feat ure. The approach requires prior information about the carry-over. Although modest information is sufficient, more information is rewarded by greater efficiency. The combination, or synthetic, estimator exhibits a moderating influence: its mean squared error is a flat function of the carry-over effe ct in the range of its feasible values, and for the largest feasible carry- over effect it is superior to either of the originally considered estimator s. An extension of the approach is outlined and two other applications in m edical research discussed. Although the method can be regarded as Bayesian in spirit, we focus on its resampling (frequentist) properties. Copyright ( C) 2001 John Wiley & Sons, Ltd.