Markov-Switching Vector Autoregression for Latent Glycaemic Regimes in Real-World Diabetes Self-Monitoring Data: An Out-of-Sample Evaluation

Abstract

Self-monitoring records of blood glucose and insulin dose form irregular time series whose physiological regime is not observed. This study fits a Markov-switching vector autoregression, MS-VAR(1), with regime-specific intercepts, autoregressive matrices and covariances to raw event logs of the public UCI AIM’94 data and asks what regime switching adds to out-of-sample prediction. Each patient is modelled separately by expectation–maximisation with exact forward–backward smoothing, without any regime label; 20 of 70 patients (2189 glucose-recording days) met a priori recording criteria. Models were compared by one-step-ahead predictive log-likelihood per day on the final 20% of each series against a single-regime VAR(1), a Gaussian hidden Markov model (HMM), a single-pass switching model and a static Gaussian, using paired Wilcoxon tests with Holm correction and BIC. A feature set containing both levels and first differences is degenerate for a firstorder autoregression: two features are exact linear functions of the lagged state, and the smallest residual-covariance eigenvalue equalled the regularisation floor in all 20 patients. In that specification the advantage over the HMM was reproduced, but a single-regime VAR(1) did equally well. After removing the redundant features, MS-VAR(3) was not better than the single-regime VAR(1) (median paired difference −0.31 nats/day, 95% CI [−1.11, 0.89]), BIC selected at most two regimes in 17 of 20 patients, and the advantage over the HMM (+2.33 nats/day) did not survive Holm correction (???? = 0.069). The fitted regimes were persistent (mean dwell time 10.2 days) and ordered in mean glucose (137, 160, 194 mg/dL), but day-level labels were noise-sensitive (ARI 0.78 at noise SD 0.05). Regime switching is thus supported as a descriptive segmentation, not as a predictive improvement.