### Abstract

The minimal model of glucose kinetics, in conjunction with an insulin-modified intravenous glucose tolerance test, is widely used to estimate insulin sensitivity (S _{I}). Parameter estimation usually resorts to nonlinear least squares (NLS), which provides a point estimate, and its precision is expressed as a standard deviation. Applied to type 2 diabetic subjects, NLS implemented in MINMOD software often predicts S _{I}= 0 (the so-called "zero" S _{I} problem), whereas general purpose modeling software systems, e.g., SAAM II, provide a very small S _{I} but with a very large uncertainty, which produces unrealistic negative values in the confidence interval. To overcome these difficulties, in this article we resort to Bayesian parameter estimation implemented by a Markov chain Monte Carlo (MCMC) method. This approach provides in each individual the S _{I} a posteriori probability density function, from which a point estimate and its confidence interval can be determined. Although NLS results are not acceptable in four out of the ten studied subjects, Bayes estimation implemented by MCMC is always able to determine a nonzero point estimate of S _{I} together with a credible confidence interval. This Bayesian approach should prove useful in reanalyzing large databases of epidemiological studies.

Original language | English |
---|---|

Journal | American Journal of Physiology - Endocrinology and Metabolism |

Volume | 282 |

Issue number | 3 45-3 |

Publication status | Published - 2002 |

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### Keywords

- Insulin resistance
- Insulin sensitivity
- Mathematical model
- Parameter estimation
- Type 2 diabetes

### ASJC Scopus subject areas

- Physiology
- Endocrinology
- Biochemistry

### Cite this

_{I}=0 problem in NIDDM subjects: Nonzero Bayesian estimates with credible confidence intervals.

*American Journal of Physiology - Endocrinology and Metabolism*,

*282*(3 45-3).

**Minimal model S _{I}=0 problem in NIDDM subjects : Nonzero Bayesian estimates with credible confidence intervals.** / Pillonetto, Gianluigi; Sparacino, Giovanni; Magni, Paolo; Bellazzi, Riccardo; Cobelli, Claudio.

Research output: Contribution to journal › Article

_{I}=0 problem in NIDDM subjects: Nonzero Bayesian estimates with credible confidence intervals',

*American Journal of Physiology - Endocrinology and Metabolism*, vol. 282, no. 3 45-3.

_{I}=0 problem in NIDDM subjects: Nonzero Bayesian estimates with credible confidence intervals. American Journal of Physiology - Endocrinology and Metabolism. 2002;282(3 45-3).

}

TY - JOUR

T1 - Minimal model S I=0 problem in NIDDM subjects

T2 - Nonzero Bayesian estimates with credible confidence intervals

AU - Pillonetto, Gianluigi

AU - Sparacino, Giovanni

AU - Magni, Paolo

AU - Bellazzi, Riccardo

AU - Cobelli, Claudio

PY - 2002

Y1 - 2002

N2 - The minimal model of glucose kinetics, in conjunction with an insulin-modified intravenous glucose tolerance test, is widely used to estimate insulin sensitivity (S I). Parameter estimation usually resorts to nonlinear least squares (NLS), which provides a point estimate, and its precision is expressed as a standard deviation. Applied to type 2 diabetic subjects, NLS implemented in MINMOD software often predicts S I= 0 (the so-called "zero" S I problem), whereas general purpose modeling software systems, e.g., SAAM II, provide a very small S I but with a very large uncertainty, which produces unrealistic negative values in the confidence interval. To overcome these difficulties, in this article we resort to Bayesian parameter estimation implemented by a Markov chain Monte Carlo (MCMC) method. This approach provides in each individual the S I a posteriori probability density function, from which a point estimate and its confidence interval can be determined. Although NLS results are not acceptable in four out of the ten studied subjects, Bayes estimation implemented by MCMC is always able to determine a nonzero point estimate of S I together with a credible confidence interval. This Bayesian approach should prove useful in reanalyzing large databases of epidemiological studies.

AB - The minimal model of glucose kinetics, in conjunction with an insulin-modified intravenous glucose tolerance test, is widely used to estimate insulin sensitivity (S I). Parameter estimation usually resorts to nonlinear least squares (NLS), which provides a point estimate, and its precision is expressed as a standard deviation. Applied to type 2 diabetic subjects, NLS implemented in MINMOD software often predicts S I= 0 (the so-called "zero" S I problem), whereas general purpose modeling software systems, e.g., SAAM II, provide a very small S I but with a very large uncertainty, which produces unrealistic negative values in the confidence interval. To overcome these difficulties, in this article we resort to Bayesian parameter estimation implemented by a Markov chain Monte Carlo (MCMC) method. This approach provides in each individual the S I a posteriori probability density function, from which a point estimate and its confidence interval can be determined. Although NLS results are not acceptable in four out of the ten studied subjects, Bayes estimation implemented by MCMC is always able to determine a nonzero point estimate of S I together with a credible confidence interval. This Bayesian approach should prove useful in reanalyzing large databases of epidemiological studies.

KW - Insulin resistance

KW - Insulin sensitivity

KW - Mathematical model

KW - Parameter estimation

KW - Type 2 diabetes

UR - http://www.scopus.com/inward/record.url?scp=0036084772&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036084772&partnerID=8YFLogxK

M3 - Article

C2 - 11832358

AN - SCOPUS:0036084772

VL - 282

JO - American Journal of Physiology

JF - American Journal of Physiology

SN - 0363-6119

IS - 3 45-3

ER -