An adaptive grid non-parametric approach to pharmacokinetic and dynamic (PK/PD) population models

Our NPEM (Non-Parametric Expectation Maximization) software for non-parametric PK/PD (pharmacokinetic/pharmacodynamic) population modeling employs the classical expectation maximization (EM) algorithm to compute a maximum-likelihood distribution on a large multi-dimensional grid. In order to achieve good resolution, a large number of grid points must be chosen, which can lead to high computational demands requiring a large-scale parallel supercomputer. We describe an improved method, called NPAG (Non-Parametric Adaptive Grid), that uses a sequence of adaptively refined grids as well as a new, state-of-the-art interior point algorithm for solving the associated maximum-likelihood problem on each successive grid. The combination of the adaptive grid strategy with the interior point algorithm is far faster than the original NPEM method. Also, NPAG requires much less memory, thus making many computations feasible on a PC or workstation that previously required supercomputer resources. Finally, the new algorithm easily and naturally accommodates the simultaneous maximum-likelihood estimation of both intra-individual and inter-individual variability, thus improving usability and removing a major limitation of the original NPEM program.