Population stochastic modelling (PSM)--an R package for mixed-effects models based on stochastic differential...

Area of Science:

• Pharmacometrics and Systems Pharmacology
• Computational Statistics
• Biomathematics

Background:

• Pharmacokinetic and pharmacodynamic (PK/PD) models traditionally use ordinary differential equations (ODEs), incorporating only observation noise.
• This limitation excludes system noise, which can lead to autocorrelated residuals due to natural variation or model error.
• Autocorrelated residuals are often overlooked in PK/PD modeling, potentially violating statistical test assumptions.

Purpose of the Study:

• To present an R package designed for handling stochastic differential equations (SDEs) within a mixed-effects modeling framework.
• To enable the incorporation of system noise in PK/PD models, thereby accounting for autocorrelated residuals.
• To provide a robust tool for advanced PK/PD analysis.

Main Methods:

• Implementation of SDEs in a mixed-effects setting using the R statistical programming language.
• Utilizes the First-Order Conditional Estimation (FOCE(1)) approximation for population likelihood estimation.
• Employs the Extended Kalman Filter's one-step predictions to approximate individual likelihoods.

Main Results:

• The developed R package effectively handles SDEs in mixed-effects PK/PD models.
• The FOCE(1) method combined with the Extended Kalman Filter provides a viable estimation strategy.
• The approach allows for the modeling of system noise and autocorrelated residuals, offering a more comprehensive analysis.

Conclusions:

• The R package offers a significant advancement for PK/PD modeling by incorporating SDEs.
• This methodology improves the handling of complex error structures, including system noise and autocorrelated residuals.
• The tool facilitates more accurate and reliable PK/PD model development and analysis.