Power and sample size determination for group comparison of patient-reported outcomes using polytomous Rasch models

The analysis of patient-reported outcomes or other psychological traits can be realized using the Rasch measurement model. When the objective of a study is to compare groups of individuals, it is important, before the study, to define a sample size such that the group comparison test will attain a given power. The Raschpower procedure (RP) allows doing so with dichotomous items. The RP is extended to polytomous items. Several computational issues were identified, and adaptations have been proposed. The performance of this new version of RP is assessed using simulations. This adaptation of RP allows obtaining a good estimate of the expected power of a test to compare groups of patients in a large number of practical situations. A Stata module, as well as its implementation online, is proposed to perform the RP. Two versions of the RP for polytomous items are proposed (deterministic and stochastic versions). These two versions produce similar results in all of the tested cases. We recommend the use of the deterministic version, when the measure is obtained using small questionnaires or items with a few number of response categories, and the stochastic version elsewhere, so as to optimize computing time.