Improved Computational Methods for Statistically Consistent and Efficient PK/PD Population Analysis
Robert Leary [1], Roger Jelliffe [2], Alan Schumitzky[2], Michael Van Guilder [2]
[1] San Diego Supercomputer Center, University Of California, San Diego [2] Laboratory Of Applied Pharmacokinetics, USC School Of Medicine, Los Angeles
Objectives: Most current PK/PD population analysis methodologies are based on parametric maximum likelihood estimators that use approximations such as FO, FOCE, and Laplace in the parametric likelihood function to reduce computational effort. Such approximations can severely compromise statistical quality in terms of both statistical consistency (bias) and statistical efficiency. Nonparametric (NP) maximum likelihood methods use exact likelihood functions but require the solution of a much higher dimensional likelihood optimization problem. Here we investigate an NP algorithm which uses principles of optimal design to decompose this high-dimensional problem into a sequence of low dimensional problems that can be easily solved numerically.
Methods: The nonparametric adaptive grid (NPAG) PK/PD population analysis program developed by our laboratory was modified to replace the local grid refinement strategy at each iteration with an optimization over the relatively low-dimensional PK/PD model parameter space to identify coordinates of new support points to introduce at each successive iteration. The form of this optimization problem is defined by the Fedorov optimal design methodology [1] applied to the convex NP maximum likelihood problem.
Results: NPOD (NP optimal design) strongly outperformed NPAG in terms of computational efficiency in comparative nonparametric analyses, often with 10-fold or greater speedups. For example, on a small nonlinear 3-compartment model with 19 subjects, NPOD reached the same optimal solution as NPAG in 10 vs. 180 minutes on a current generation PC. A large 641-subject model was converged in 1.5 days with NPOD as opposed to over 2 weeks with NPAG. When tested against PEM, a new consistent parametric analysis program developed by our laboratory, NPOD achieved comparable statistical efficiency at significantly lower computational expense.
Conclusion: The NPOD methodology is computationally much more efficient than NPAG. It can be used both for parametric and NP analyses to provide statistically efficient and consistent estimators by avoiding the likelihood approximations that degrade the statistical performance of other methods.
Reference:
[1] Fedorov, V.V: Theory of Optimal Experiments, translated and edited by W.J. Studden and E.M. Klimko, New York: Academic Press, 1972.