Analysis of Longitudinal Lupus Data Using Multivariate t-Linear Models

Analysis of healthcare utilization, such as hospitalization duration and medical costs, is crucial for policymakers and doctors in experimental and epidemiological investigations. Herein, we examine the healthcare utilization data of patients with systemic lupus erythematosus (SLE). The characteristics of the SLE data were measured over a 10-year period with outliers. Multivariate linear models with multivariate normal error distributions are commonly used to evaluate long series of multivariate longitudinal data. However, when there are outliers or heavy tails in the data, such as those based on healthcare utilization, the assumption of multivariate normality may be too strong, resulting in biased estimates. To address this, we propose multivariate t-linear models (MTLMs) with an autoregressive moving-average (ARMA) covariance matrix. Modeling the covariance matrix for multivariate longitudinal data is difficult since the covariance matrix is high dimensional and must be positive-definite. To address these, we employ a modified ARMA Cholesky decomposition and hypersphere decomposition. Several simulation studies are conducted to demonstrate the performance, robustness, and flexibility of the proposed models. The proposed MTLMs with ARMA structured covariance matrix are applied to analyze the healthcare utilization data of patients with SLE.