@MASTERSTHESIS\{IMM2007-05174,
    author       = "A. S. Christensen",
    title        = "A Next Generation Method For {PK}/{PD} Modeling",
    year         = "2007",
    keywords     = "stochastic differential equation (SDE); non-linear mixed-effects; {FOCE} approximation; Kalman filter; maximum likelihood estimation; pharmacokinetic; pharmacodynamic; {PK}/{PD} modeling.",
    school       = "Informatics and Mathematical Modelling, Technical University of Denmark, {DTU}",
    address      = "Richard Petersens Plads, Building 321, {DK-}2800 Kgs. Lyngby",
    type         = "",
    note         = "Supervised by Bernd Dammann and Henrik Madsen, {IMM,} {DTU}. External supervisor: Niels Rode Kristensen",
    url          = "http://www2.compute.dtu.dk/pubdb/pubs/5174-full.html",
    abstract     = "This thesis describes the development of a software prototype implemented in Fortran 95 for population pharmacokinetic/pharmacodynamic (PK/PK) modeling based on non-linear mixed-effects models using stochastic differential equations (SDEs). An advantage of using SDEs is that it allows residual errors to be separated into two fundamentally different types of noise, namely (1) correlated system noise attributed to unmodelled dynamics of the system, and (2) uncorrelated observation noise.

A maximum likelihood method for estimating the fixed- and random-effects parameters in the model is adopted. The likelihood function is approximated numerically using a First-Order Conditional Estimate (FOCE) method and Kalman filtering. The prototype handles linear time-invariant and linear timevarying models.

The choice of Fortran 95 as programming language is motivated by high computational speed, availability of scientific software packages and support of OpenMP shared-library multiprocessing {API} for parallel computing. With the intent of aiding future model extensions and modifications, the thesis attempts to provide extensive documentation of the program interface and, at the same time, raise awareness of known weaknesses in the implementation."
}