Hyperbolic Relationship Between Insulin Secretion and Sensitivity on Oral Glucose Tolerance Test

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Abstract
The utility of the disposition index as a measure of β‐cell compensatory capacity rests on the established hyperbolic relationship between its component insulin secretion and sensitivity measures as derived from the intravenous glucose tolerance test (IVGTT). If one is to derive an analogous measure of β‐cell compensation from the oral glucose tolerance test (OGTT), it is thus necessary to first establish the existence of this hyperbolic relationship between OGTT‐based measures of insulin secretion and insulin sensitivity. In this context, we tested five OGTT‐based measures of secretion (insulinogenic index, Stumvoll first phase, Stumvoll second phase, ratio of total area‐under‐the‐insulin‐curve to area‐under‐the‐glucose‐curve (AUCins/gluc), and incremental AUCins/gluc) with two measures of sensitivity (Matsuda index and 1/Homeostasis Model of Assessment for insulin resistance (HOMA‐IR)). Using a model of log(secretion measure) = constant + β × log(sensitivity measure), a hyperbolic relationship can be established if β is approximately equal to −1, with 95% confidence interval (CI) excluding 0. In 277 women with normal glucose tolerance (NGT), the pairing of total AUCins/gluc and Matsuda index was the only combination that satisfied these criteria (β = −0.99, 95% CI (−1.66, −0.33)). This pairing also satisfied hyperbolic criteria in 53 women with impaired glucose tolerance (IGT) (β = −1.02, (−1.72, −0.32)). In a separate data set, this pairing yielded distinct hyperbolae for NGT (n = 245) (β = −0.99, (−1.67, −0.32)), IGT (n = 116) (β = −1.18, (−1.84, −0.53)), and diabetes (n = 43) (β = −1.37, (−2.46, −0.29)). Moreover, the product of AUCins/gluc and Matsuda index progressively decreased from NGT (212) to IGT (193) to diabetes (104) (P < 0.001), consistent with declining β‐cell function. In summary, a hyperbolic relationship can be demonstrated between OGTT‐derived AUCins/gluc and Matsuda index across a range of glucose tolerance. Based on these findings, the product of these two indices emerges as a potential OGTT‐based measure of β‐cell function.

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