Non-Linear Mixed-Effects Modelling using Stochastic Differential Equations
Functions for fitting linear and non-linear mixed-effects models using stochastic differential equations (SDEs). The package allows for any multivariate non-linear time-variant model to be specified, and it also handles multidimensional input, covariates, missing observations, and specification of dosage regimen. The provided pipeline relies on the coupling of the FOCE algorithm and Kalman filtering as outlined by Klim et al. (2009) and has been validated against the proprietary software 'NONMEM' (Tornoe et al., 2005). Further functions are provided for finding smoothed estimates of model states and for simulation.
Function overview:
PSM.estimate
Estimate population parameters for any linear or non-linear model.
PSM.smooth
Optimal estimates of model states based on estimated parameters.
PSM.simulate
Simulate data for multiple individuals.
PSM.plot
Plot data, state estimates ect. for multiple individuals.
PSM.template
Creates a template with R-syntax to help setup a model in PSM.
Klim, S., Mortensen, S. B., Kristensen, N. R., Overgaard, R. V., & Madsen, H. (2009). Population stochastic modelling (PSM)<U+2014>an R package for mixed-effects models based on stochastic differential equations. Computer Methods and Programs in Biomedicine, 94:279-289.
Moler, C., & Van Loan, C. (2003). Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later. SIAM Review, 45:3-49.
Mortensen, S. B., Klim, S., Dammann, B., Kristensen, N. R., Madsen, H., Overgaard, R. V. (2007). A matlab framework for estimation of NLME models using stochastic differential equations: Application for estimation of insulin secretion rates. Journal of Pharmacokinetics and Pharmacodynamics, 34:623-642.
Tornoe, C. W., Overgaard, R. V., Agersoe, H., Nielsen, H. A., Madsen, H., & Jonsson, E. N. (2005). Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations. Pharmaceutical Research, 22:1247-1258.
PSM.estimate, PSM.smooth,
PSM.simulate, PSM.plot, PSM.template