Large-Vector Autoregression for Multilayer Spatially Correlated Time Series

<div><p>One of the most commonly used methods for modeling multivariate time series is the vector autoregressive model (VAR). VAR is generally used to identify lead, lag, and contemporaneous relationships describing Granger causality within and between time series. In this article, we investigate the VAR methodology for analyzing data consisting of multilayer time series that are spatially interdependent. When modeling VAR relationships for such data, the dependence between time series is both a curse and a blessing. The former because it requires modeling the between time-series correlation or the contemporaneous relationships which may be challenging when using likelihood-based methods. The latter because the spatial correlation structure can be used to specify the lead–lag relationships within and between time series, within and between layers. To address these challenges, we propose an <i>L</i>₁\<i>L</i>₂ regularized likelihood estimation method. The lead, lag, and contemporaneous relationships are estimated using an efficient algorithm that exploits sparsity in the VAR structure, accounts for the spatial dependence, and models the error dependence. We consider a case study to illustrate the applicability of our method. In the supplementary materials available online, we assess the performance of the proposed VAR model and compare it with existing methods within a simulation study.</p></div

Modeling Heterogeneity in Healthcare Utilization Using Massive Medical Claims Data

<p>We introduce a modeling approach for characterizing heterogeneity in healthcare utilization using massive medical claims data. We first translate the medical claims observed for a large study population and across five years into individual-level discrete events of care called <i>utilization sequences</i>. We model the utilization sequences using an exponential proportional hazards mixture model to capture heterogeneous behaviors in patients’ healthcare utilization. The objective is to cluster patients according to their longitudinal utilization behaviors and to determine the main drivers of variation in healthcare utilization while controlling for the demographic, geographic, and health characteristics of the patients. Due to the computational infeasibility of fitting a parametric proportional hazards model for high-dimensional, large-sample size data we use an iterative one-step procedure to estimate the model parameters and impute the cluster membership. The approach is used to draw inferences on utilization behaviors of children in the Medicaid system with persistent asthma across six states. We conclude with policy implications for targeted interventions to improve adherence to recommended care practices for pediatric asthma. Supplementary materials for this article are available online.</p