A survey of population analysis methods and software for complex pharmacokinetic and pharmacodynamic models with examples

Abstract

An overview is provided of the present population analysis methods and an assessment of which software packages are most appropriate for various PK/PD modeling problems. Four PK/PD example problems were solved using the programs NONMEM VI beta version, PDx-MCPEM, S-ADAPT, MONOLIX, and WinBUGS, informally assessed for reasonable accuracy and stability in analyzing these problems. Also, for each program we describe their general interface, ease of use, and abilities. We conclude with discussing which algorithms and software are most suitable for which types of PK/ PD problems. NONMEM FO method is accurate and fast with 2-compartment models, if intra-individual and interindividual variances are small. The NONMEM FOCE method is slower than FO, but gives accurate population values regardless of size of intra-and interindividual errors. However, if data are very sparse, the NONMEM FOCE method can lead to inaccurate values, while the Laplace method can provide more accurate results. The exact EM methods (performed using S-ADAPT, PDx-MCPEM, and MONOLIX) have greater stability in analyzing complex PK/PD models, and can provide accurate results with sparse or rich data. MCPEM methods perform more slowly than NONMEM FOCE for simple models, but perform more quickly and stably than NONMEM FOCE for complex models. WinBUGS provides accurate assessments of the population parameters, standard errors and 95% confi dence intervals for all examples. Like the MCPEM methods, WinBUGS's effi ciency increases relative to NONMEM when solving the complex PK/PD models.

Performance and Robustness of the Monte Carlo Importance Sampling Algorithm Using Parallelized S-ADAPT for Basic and Complex Mechanistic Models

“…Gradient search algorithms such as the FOCE method can also be parallelized; however, to our knowledge the fraction of the computations of the FOCE method that can be parallelized (and therefore accelerated) is notably less than 99%. Among the parametric EM algorithms (1)(2)(3)(4)(5)(6)13,15,19,52,53), the MC-PEM method requires the fewest number of iterations (often 80-300, depending on the model complexity and data), since the MC-PEM algorithm spends most of its computation time on exploring potential parameter values for each subject per iteration. The MC-PEM algorithm typically uses 1,000-3,000 random samples per subject and iteration for the multidimensional integration to compute the conditional means and conditional var-cov matrices.…”

“…Expectation maximization (EM) algorithms are robust, as they use integration instead of gradient search methods to optimize (update) parameter estimates. State-of-the-art EM algorithms (1)(2)(3)(4)(5)(6) provide the additional advantage that they can approximate the true log-likelihood as precisely as needed by increasing the number of Monte Carlo samples used to approximate the integrals for calculation of the true loglikelihood. Importantly, algorithms, such as the FOCE method, which calculate the exact solution of a formula that approximates the log-likelihood can only improve the quality of the approximation by changing the algorithm (i.e., by using a more complex formula that approximates the loglikelihood more closely).…”

“…A comprehensive review of the MC-PEM algorithm as published by Schumitzky (2) and Bauer et al (4) is beyond the scope of this paper. The MC-PEM algorithm and its implementation in S-ADAPT are described in detail in the S-ADAPT manuals (12,19).…”

Population Pharmacokinetics of Therapeutic Monoclonal Antibodies: Examples and Estimation Method Performance Differences

“…Despite the more accurate approximation of the nonlinear mixed effects model used by LAP, the estimation performance of LAP and FOCE were very similar under the informative and uninformative 600 mg study designs (Tables 4-1 through , although the LAP method did show improvement over FOCE under the uninformative 600 mg study design for the bias in V max and the between-subject variance for V max and V 2 . A detailed discussion of the theory behind the approximate maximum likelihood methods in NONMEM (FO, FOCE, LAP) and Bayesian MCMC methods, such as that used by WinBUGS, is not within the scope of this text but are discussed elsewhere (112,113,115,116,150,152). Although, it is worth noting that Bayesian MCMC methods do not rely on analytical approximations of the nonlinear mixed effects model like with FO, FOCE, and LAP, but instead use Monte Carlo integration techniques to obtain parameter estimates for the exact model (115,116).…”

“…A one-compartment model with nonlinear elimination was used in the analysis by Hashimoto et al Although Hashimoto et al used a PK model with nonlinear elimination, in most of the therapeutic mAb population PK analyses a two-compartment model was used (Table 1-1). Bauer et al recently evaluated various population estimation methods and software when applied to different PK/PD models (150). One of the PK models included in the study was a one-compartment model with parallel linear and nonlinear elimination pathways.…”