A statistical model for inter‐temporal causal dynamics of glucose production and disposal with insulin level in diabetic patients

Abstract

This paper provides a useful tool to examine inter-temporal behaviour in glucose and insulin level in diabetic patients. The primary thrust of this paper is to model inter-temporal causal dynamics of endogenous and ingested glucose production and disposal with insulin in diabetic patients. A short-run compartmental dynamics of glucose and insulin was introduced with their stochastic relationship through a vector autoregressive (VAR) scheme. This study also aims to develop glucose variability indices and test for their independence, homogeneity and symmetry at steady-state condition. The model also empirically identifies the significant prognostic factors and other exogenous variables affecting the dynamics. An empirical application provides more compelling evidence of such dynamics. The estimated model reconfirms the fact that pre-prandial PM glucose level has statistically significant effects on post-prandial PM glucose level in diabetic patients. Also, pre-prandial PM insulin level shows a significant impact on post-prandial PM insulin in this study. In addition, results also indicate statistical significance of body mass index (BMI) and haemoglobin on post-prandial PM glucose level. It is interesting to note that the pattern of glucose variability indices in pre- and post-prandial AM time points is different from those at PM period. The results also show interdependence between the glucose variability indices. Only the pre- and post-meal PM variations of glucose are homogenous to its pre- and post-meal AM variations.