Department of Information Engineering, University of Padua, Padua, Italy.
Am J Physiol Endocrinol Metab. 2012 Sep 1;303(5):E576-86. doi: 10.1152/ajpendo.00139.2011. Epub 2012 Jun 5.
To correctly evaluate the glucose control system, it is crucial to account for both insulin sensitivity and secretion. The disposition index (DI) is the most widely accepted method to do so. The original paradigm (hyperbolic law) consists of the multiplicative product of indices related to insulin sensitivity and secretion, but more recently, an alternative formula has been proposed with the exponent α (power function law). Traditionally, curve-fitting approaches have been used to evaluate the DI in a population: the algorithmic implementations often introduce some critical issues, such as the assumption that one of the two indices is error free or the effects of the log transformation on the measurement errors. In this work, we review the commonly used approaches and show that they provide biased estimates. Then we propose a novel nonlinear total least square (NLTLS) approach, which does not need to use the approximations built in the previously proposed alternatives, and show its superiority. All of the traditional fit procedures, including NLTLS, account only for uncertainty affecting insulin sensitivity and secretion indices when they are estimated from noisy data. Thus, they fail when part of the observed variability is due to inherent differences in DI values between individuals. To handle this inevitable source of variability, we propose a nonlinear mixed-effects approach that describes the DI using population hyperparameters such as the population typical values and covariance matrix. On simulated data, this novel technique is much more reliable than the curve-fitting approaches, and it proves robust even when no or small population variability is present in the DI values. Applying this new approach to the analysis of real IVGTT data suggests a value of α significantly smaller than 1, supporting the importance of testing the power function law as an alternative to the simpler hyperbolic law.
要正确评估血糖控制系统，必须同时考虑胰岛素敏感性和胰岛素分泌。胰岛素分泌指数（DI）是最广泛接受的方法。原始范式（双曲线定律）由与胰岛素敏感性和分泌相关的指数的乘积组成，但最近提出了一种具有指数α（幂函数定律）的替代公式。传统上，使用曲线拟合方法来评估人群中的 DI：算法实现通常会引入一些关键问题，例如假设两个指数之一是无误差的，或者对数变换对测量误差的影响。在这项工作中，我们回顾了常用的方法，并表明它们提供了有偏差的估计。然后，我们提出了一种新的非线性总体最小二乘法（NLTLS）方法，该方法不需要使用之前提出的替代方法中的近似值，并展示了其优越性。所有传统的拟合程序，包括 NLTLS，仅在从噪声数据估计胰岛素敏感性和分泌指数时考虑影响它们的不确定性。因此，当部分观察到的变异性归因于个体之间 DI 值的固有差异时，它们会失败。为了处理这种不可避免的变异性来源，我们提出了一种非线性混合效应方法，该方法使用群体超参数（例如群体典型值和协方差矩阵）来描述 DI。在模拟数据上，这项新技术比曲线拟合方法可靠得多，即使 DI 值没有或只有很小的群体变异性，它也证明是稳健的。将这种新方法应用于真实 IVGTT 数据的分析表明，α 值显著小于 1，这支持了作为更简单的双曲线定律的替代方案测试幂函数定律的重要性。
