Multidimensional latent trait linear mixed model: an application in clinical studies with multivariate longitudinal outcomes.

Multilevel item response theory (MLIRT) models have been widely used to analyze the multivariate longitudinal data of mixed types (e.g., categorical and continuous) in clinical studies. The MLIRT models often have unidimensional assumption, that is, the multiple outcomes are clinical manifestations of a univariate latent variable. However, the unidimensional assumption may be unrealistic because some diseases may be heterogeneous and characterized by multiple impaired domains with variable clinical symptoms and disease progressions. We relax this assumption and propose a multidimensional latent trait linear mixed model (MLTLMM) to allow multiple latent variables and within-item multidimensionality (one outcome can be a manifestation of more than one latent variable). We conduct extensive simulation studies to assess the unidimensional MLIRT model and the proposed MLTLMM model. The simulation studies suggest that the MLTLMM model outperforms unidimensional model when the multivariate longitudinal outcomes are manifested by multiple latent variables. The proposed model is applied to two motivating studies of amyotrophic lateral sclerosis: a clinical trial of ceftriaxone and the Pooled Resource Open-Access ALS Clinical Trials database.