Predictive performance for population models using stochastic differential equations applied on data from an oral...

Area of Science:

• Pharmacokinetics/Pharmacodynamics (PK/PD)
• Mathematical modeling
• Metabolic research

Background:

• Accurate estimation of first-phase insulin secretion is crucial for assessing beta-cell function.
• Existing models for oral glucose tolerance tests (OGTT) have limitations in predictive performance.
• Stochastic differential equations (SDEs) offer a potential advancement for PK/PD modeling.

Purpose of the Study:

• To investigate the predictive power of SDEs for first-phase insulin secretion (AIR (0-8)) using parameters from the oral minimal model (OMM).
• To quantitatively assess the benefits of SDE-based models on real data predictive performance.
• To evaluate the Ornstein-Uhlenbeck (OU) process within SDE models for improved data description.

Main Methods:

• Utilized data from 174 subjects undergoing both OGTT and tolbutamide-modified IVGTT.
• Estimated OMM parameters using the FOCE method in NONMEM VI with insulin and C-peptide measurements.
• Implemented SDE models based on the Ornstein-Uhlenbeck process and extended Kalman filter for parameter estimation.

Main Results:

• The inclusion of the OU process in SDE models improved data description, evidenced by the autocorrelation function (ACF) of prediction errors.
• SDE models significantly enhanced the correlation between individual first-phase indexes from OGTT and AIR (0-8) (r=0.36 to 0.49; r=0.32 to 0.47).
• SDE models provided a more accurate assessment of first-phase insulin secretion indexes compared to traditional methods.

Conclusions:

• The SDE approach effectively reduces autocorrelation of errors in PK/PD models.
• This methodology improves the estimation of clinical measures derived from glucose tolerance tests.
• The SDE approach demonstrates high theoretical and practical relevance due to improved accuracy and minimal increase in estimation time.