Power and sample size determination for the group comparison of patient-reported outcomes with Rasch family models

Patient-reported outcomes (PRO) that comprise all self-reported measures by the patient are important as endpoint in clinical trials and epidemiological studies. Models from the Item Response Theory (IRT) are increasingly used to analyze these particular outcomes that bring into play a latent variable as these outcomes cannot be directly observed. Preliminary developments have been proposed for sample size and power determination for the comparison of PRO in cross-sectional studies comparing two groups of patients when an IRT model is intended to be used for analysis. The objective of this work was to validate these developments in a large number of situations reflecting real-life studies.

The method to determine the power relies on the characteristics of the latent trait and of the questionnaire (distribution of the items), the difference between the latent variable mean in each group and the variance of this difference estimated using Cramer-Rao bound. Different scenarios were considered to evaluate the impact of the characteristics of the questionnaire and of the variance of the latent trait on performances of the Cramer-Rao method. The power obtained using Cramer-Rao method was compared to simulations.

Powers achieved with the Cramer-Rao method were close to powers obtained from simulations when the questionnaire was suitable for the studied population. Nevertheless, we have shown an underestimation of power with the Cramer-Rao method when the questionnaire was less suitable for the population. Besides, the Cramer-Rao method stays valid whatever the values of the variance of the latent trait.

The Cramer-Rao method is adequate to determine the power of a test of group effect at design stage for two-group comparison studies including patient-reported outcomes in health sciences. At the design stage, the questionnaire used to measure the intended PRO should be carefully chosen in relation to the studied population.