Biases and power for groups comparison on subjective health measurements

Subjective health measurements are increasingly used in clinical research, particularly for patient groups comparisons. Two main types of analytical strategies can be used for such data: so-called classical test theory (CTT), relying on observed scores and models coming from Item Response Theory (IRT) relying on a response model relating the items responses to a latent parameter, often called latent trait. Whether IRT or CTT would be the most appropriate method to compare two independent groups of patients on a patient reported outcomes measurement remains unknown and was investigated using simulations. For CTT-based analyses, groups comparison was performed using t-test on the scores. For IRT-based analyses, several methods were compared, according to whether the Rasch model was considered with random effects or with fixed effects, and the group effect was included as a covariate or not. Individual latent traits values were estimated using either a deterministic method or by stochastic approaches. Latent traits were then compared with a t-test. Finally, a two-steps method was performed to compare the latent trait distributions, and a Wald test was performed to test the group effect in the Rasch model including group covariates. The only unbiased IRT-based method was the group covariate Wald's test, performed on the random effects Rasch model. This model displayed the highest observed power, which was similar to the power using the score t-test. These results need to be extended to the case frequently encountered in practice where data are missing and possibly informative.