Evaluation of nonlinear regression approaches to estimation of insulin sensitivity by the minimal model with reference to Bayesian hierarchical analysis

Abstract

Minimal model analysis of intravenous glucose tolerance test (IVGTT) glucose and insulin concentrations offers a validated approach to measuring insulin sensitivity, but model identification is not always successful. Improvements may be achieved by using alternative settings in the modeling process, although results may differ according to setting, and care must be exercised in combining results. IVGTT data (12 samples, regular test) from 533 men without diabetes was modeled by the traditional nonlinear regression (NLR) approach, using five different permutations of settings. Results were evaluated with reference to the more robust Bayesian hierarchical (BH) approach to model identification and to the proportion of variance they explained in known correlates of insulin sensitivity (age, BMI, blood pressure, fasting glucose and insulin, serum triglyceride, HDL cholesterol, and uric acid concentration). BH analysis was successful in all cases. With NLR analysis, between 17 and 35 IVGTTs were associated with parameter coefficients of variation (PCVs) for minimal model parameters SI(insulin sensitivity) and SG(glucose effectiveness) of >100%. Systematic use of each different approach in combination reduced this number to five. Mean (interquartile range) SINLRwas then 3.14 (2.29–4.63) min−1·mU−1·l × 10−4and 2.56 (1.74–3.83) min−1·mU−1·l × 10−4for SIBH(correlation 0.86, P < 0.0001). SINLRexplained, on average, 10.6% of the variance in known correlates of insulin sensitivity, whereas SIBHexplained 8.5%. In a large body of data, which BH analysis demonstrated could be fully identified, use of alternative modeling settings in NLR analysis could substantially reduce the number of analyses with PCVs >100%. SINLRcompared favorably with SIBHin the proportion of variance explained in known correlates of insulin sensitivity.