title: Power and sample size determination for the group comparison of patient-reported outcomes using the Rasch model: impact of a misspecification of the parameters.
abstract: BACKGROUND
  Patient-reported outcomes (PRO) are important as endpoints in clinical trials and epidemiological studies. Guidelines for the development of PRO instruments and analysis of PRO data have emphasized the need to report methods used for sample size planning. The Raschpower procedure has been proposed for sample size and power determination for the comparison of PROs in cross-sectional studies comparing two groups of patients when an item reponse model, the Rasch model, is intended to be used for analysis. The power determination of the test of the group effect using Raschpower requires several parameters to be fixed at the planning stage including the item parameters and the variance of the latent variable. Wrong choices regarding these parameters can impact the expected power and the planned sample size to a greater or lesser extent depending on the magnitude of the erroneous assumptions.
  
  
  METHODS
  The impact of a misspecification of the variance of the latent variable or of the item parameters on the determination of the power using the Raschpower procedure was investigated through the comparison of the estimations of the power in different situations.
  
  
  RESULTS
  The power of the test of the group effect estimated with Raschpower remains stable or shows a very little decrease whatever the values of the item parameters. For most of the cases, the estimated power decreases when the variance of the latent trait increases. As a consequence, an underestimation of this variance will lead to an overestimation of the power of the group effect.
  
  
  CONCLUSIONS
  A misspecification of the item difficulties regarding their overall pattern or their dispersion seems to have no or very little impact on the power of the test of the group effect. In contrast, a misspecification of the variance of the latent variable can have a strong impact as an underestimation of the variance will lead in some cases to an overestimation of the power at the design stage and may result in an underpowered study.
authors.affiliation: EA 4275, Biostatistics, Pharmacoepidemiology and Subjective Measures in Health Sciences, University of Nantes, 1 rue, Gaston Veil, 44000, Nantes, France. myriam.blanchin@univ-nantes.fr.
authors.forename: Myriam
authors.initials: M
authors.lastname: Blanchin
authors.affiliation: EA 4275, Biostatistics, Pharmacoepidemiology and Subjective Measures in Health Sciences, University of Nantes, 1 rue, Gaston Veil, 44000, Nantes, France. alice.guilleux@univ-nantes.fr.
authors.forename: Alice
authors.initials: A
authors.lastname: Guilleux
authors.affiliation: EA 4275, Biostatistics, Pharmacoepidemiology and Subjective Measures in Health Sciences, University of Nantes, 1 rue, Gaston Veil, 44000, Nantes, France. bastien.perrot@univ-nantes.fr.
authors.forename: Bastien
authors.initials: B
authors.lastname: Perrot
authors.affiliation: EA 4275, Biostatistics, Pharmacoepidemiology and Subjective Measures in Health Sciences, University of Nantes, 1 rue, Gaston Veil, 44000, Nantes, France. angelique.bonnaud@univ-nantes.fr.
authors.forename: Angélique
authors.initials: A
authors.lastname: Bonnaud-Antignac
authors.affiliation: EA 4275, Biostatistics, Pharmacoepidemiology and Subjective Measures in Health Sciences, University of Nantes, 1 rue, Gaston Veil, 44000, Nantes, France. jean-benoit.hardouin@univ-nantes.fr.
authors.forename: Jean-Benoit
authors.initials: JB
authors.lastname: Hardouin
authors.affiliation: EA 4275, Biostatistics, Pharmacoepidemiology and Subjective Measures in Health Sciences, University of Nantes, 1 rue, Gaston Veil, 44000, Nantes, France. veronique.sebille@univ-nantes.fr.
authors.forename: Véronique
authors.initials: V
authors.lastname: Sébille
mesh_terms: D000465:Algorithms; D003430:Cross-Sectional Studies; D006801:Humans; D015233:Models, Statistical; D017063:Outcome Assessment, Health Care / Q000379:methods* / Q000706:statistics & numerical data*; D015203:Reproducibility of Results; D018401:Sample Size; D057566:Self Report; D011795:Surveys and Questionnaires