Power and sample size determination in the Rasch model: evaluation of the robustness of a numerical method to non-normality of the latent trait

PLoS One. 2014 Jan 10;9(1):e83652. doi: 10.1371/journal.pone.0083652. eCollection 2014.

Abstract

Patient-reported outcomes (PRO) have gained importance in clinical and epidemiological research and aim at assessing quality of life, anxiety or fatigue for instance. Item Response Theory (IRT) models are increasingly used to validate and analyse PRO. Such models relate observed variables to a latent variable (unobservable variable) which is commonly assumed to be normally distributed. A priori sample size determination is important to obtain adequately powered studies to determine clinically important changes in PRO. In previous developments, the Raschpower method has been proposed for the determination of the power of the test of group effect for the comparison of PRO in cross-sectional studies with an IRT model, the Rasch model. The objective of this work was to evaluate the robustness of this method (which assumes a normal distribution for the latent variable) to violations of distributional assumption. The statistical power of the test of group effect was estimated by the empirical rejection rate in data sets simulated using a non-normally distributed latent variable. It was compared to the power obtained with the Raschpower method. In both cases, the data were analyzed using a latent regression Rasch model including a binary covariate for group effect. For all situations, both methods gave comparable results whatever the deviations from the model assumptions. Given the results, the Raschpower method seems to be robust to the non-normality of the latent trait for determining the power of the test of group effect.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Algorithms
  • Cross-Sectional Studies
  • Humans
  • Models, Statistical*
  • Outcome Assessment, Health Care*
  • Research Design
  • Sample Size*
  • Self Report

Grants and funding

This study was supported by the French National Research Agency, under reference N 2010 PRSP 008 01.(http://www.agence-nationale-recherche.fr/programmes-de-recherche/appel-detail/programme-de-recherche-en-sante-publique-prsp-2009/). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.