The System for Population Kinetics: Open Source Software for Population Analysis

Introduction

Population kinetic analysis is an increasingly important tool for modeling and analyzing biomedical kinetic (time series) data affected by an unfavorable signal-to-noise ratio and relatively short duration. Population kinetics is characterized by the simultaneous modeling of population “typical values” of kinetic parameters and the variability of these kinetic parameters (between subjects) as well as the residual errors in measurement. Its historical development and use, especially in drug development, has been extensively reviewed elsewhere (Pillai et al., 2005). Since the pioneering work of Beal and Sheiner (Beal and Sheiner, 1982) and the development of the NONMEM software (Beal et al, 1989-2006), population kinetics has been invoked as a useful, and sometimes essential, step in understanding the determinants (demographic, clinical and genetic) of biological variation among experimental subjects. This is particularly useful in presence of sparse data at the individual level. What appears at first to be random variability is gradually explained by invoking deterministic covariates in a process often described as model building (Mandema et al., 1992; Ette and Ludden, 1995). Population kinetic analysis describes the information available at the population level: both typical values and variability estimates. By providing reliable population estimates, these can also be used to inform likely kinetic profiles at the individual subject level. An application where this concept has been applied is individualized, pharmacokinetic-based dosing (Jelliffe et al., 1998; Salinger et al., 2006, among others). Indeed, it can be argued that the first step towards individualized medicine is the understanding of the magnitude of variation among subjects in drug disposition and effect, the knowledge of which then allows one to deploy statistical models that link such observed, quantified variation to other covariates more amenable to direct measurement. The next step is the individualization of models of drug disposition and effect through the availability of individual covariates, thus allowing customized prediction of the events surrounding dose administration (Sheiner and Beal, 1992). Population kinetics is complicated by the fact that the underlying models for drug disposition and effect (termed pharmacokinetics and pharmacodynamics, or PK-PD, respectively), or indeed any other biological phenomenon, are nonlinear in their parameters. That the parameters vary among subjects according to unknown probability distributions adds further layers of complexity. The nonlinear dependence on the parameters prevents the likelihood function required for model fitting from being written in closed form (Davidian and Giltinan, 1995). Thus, since its optimization requires the solution of a multidimensional integral. Indeed, even numerical evaluation of the likelihood is extremely demanding, so much so that optimization of the true likelihood function remains to a large degree impractical.