Contrasting principal stratum and hypothetical strategy estimands in multi-period crossover trials with incomplete data

Complete case analyses of complete crossover designs provide an opportunity to make comparisons based on patients who can tolerate all treatments. It is argued that this provides a means of estimating a principal stratum strategy estimand, something which is difficult to do in parallel group trials. While some trial users will consider this a relevant aim, others may be interested in hypothetical strategy estimands, that is, the effect that would be found if all patients completed the trial. Whether these estimands differ importantly is a question of interest to the different users of the trial results. This paper derives the difference between principal stratum strategy and hypothetical strategy estimands, where the former is estimated by a complete-case analysis of the crossover design, and a model for the dropout process is assumed. Complete crossover designs, that is, those where all treatments appear in all sequences, and which compare t treatments over p periods with respect to a continuous outcome are considered. Numerical results are presented for Williams designs with four and six periods. Results from a trial of obstructive sleep apnoea-hypopnoea (TOMADO) are also used for illustration. The results demonstrate that the percentage difference between the estimands is modest, exceeding 5% only when the trial has been severely affected by dropouts or if the within-subject correlation is low.