Tree-based structural equation model for assessing measurement invariance in patient-reported outcome measures

Evidence of measurement invariance (MI) is essential to ensure that scores based on patient-reported outcome measures (PROMs) are comparable across groups or over time. Conventional methods for evaluating MI in PROMs are mostly group-based methods that require that relevant differences pertaining mainly to the lack of MI in the target populations are known a priori. Tree-based latent variable models can be used to evaluate MI in PROMs when the covariates associated with MI violation are unknown a priori. This study illustrates the implementation of a tree-based structural equation model (SEMTree) based on recursive partitioning for evaluating MI in PROMs and identifies patient characteristics associated with MI violation. Data were from 4,027 patients with coronary artery disease (CAD) who completed the 7-item Seattle Angina Questionnaire (SAQ-7) following a cardiac angiogram procedure. Structural equation modeling was used to examine factorial validity of the SAQ-7, and model fit was evaluated. SEMTree was used to identify subgroups on which the SAQ-7 items were not invariant using patients’ demographic and disease/comorbid characteristics as explanatory (i.e., splitting) variables. The median (IQR) age was 64.0 (15.1) years, while 3,172 (78.8%) patients were male. A 3-factor measurement model for the SAQ-7 had an acceptable fit to the data. The SEMTree analysis showed that the SAQ-7 measurement model was not invariant across subgroups defined by age, disease indication (whether acute coronary syndrome or stable angina), sex, and comorbid hypertension as splitting variables. Patients’ demographic and disease characteristics are associated with the lack of MI of the SAQ-7 in patients with CAD. SEMTree is a promising methodology for exploratory investigation of variables associated with the lack of MI of PROMs used in heterogeneous populations. Future research will use computer simulations to assess its statistical power to detect MI in PROMs under various data distributions and design characteristics.