Identification of sources of DIF using covariates in patient-reported outcome measures: a simulation study comparing two approaches based on Rasch family models

Abstract

When analyzing patient-reported outcome (PRO) data, sources of differential item functioning (DIF) can be multiple and there may be more than one covariate of interest. Hence, it could be of great interest to disentangle their effects. Yet, in the literature on PRO measures, there are many studies where DIF detection is applied separately and independently for each covariate under examination. With such an approach, the covariates under investigation are not introduced together in the analysis, preventing from simultaneously studying their potential DIF effects on the questionnaire items. One issue, among others, is that it may lead to the detection of false-positive effects when covariates are correlated. To overcome this issue, we developed two new algorithms (namely ROSALI-DIF FORWARD and ROSALI-DIF BACKWARD). Our aim was to obtain an iterative item-by-item DIF detection method based on Rasch family models that enable to adjust group comparisons for DIF in presence of two binary covariates. Both algorithms were evaluated through a simulation study under various conditions aiming to be representative of health research contexts. The performance of the algorithms was assessed using: (i) the rates of false and correct detection of DIF, (ii) the DIF size and form recovery, and (iii) the bias in the latent variable level estimation. We compared the performance of the ROSALI-DIF algorithms to the one of another approach based on likelihood penalization. For both algorithms, the rate of false detection of DIF was close to 5%. The DIF size and form influenced the rates of correct detection of DIF. Rates of correct detection was higher with increasing DIF size. Besides, the algorithm fairly identified homogeneous differences in the item threshold parameters, but had more difficulties identifying non-homogeneous differences. Over all, the ROSALI-DIF algorithms performed better than the penalized likelihood approach. Integrating several covariates during the DIF detection process may allow a better assessment and understanding of DIF. This study provides valuable insights regarding the performance of different approaches that could be undertaken to fulfill this aim.

Keywords: LASSO; Rasch measurement theory (RMT); differential item functioning (DIF); measurement invariance (MI); patient-reported outcome (PRO); regularization.