Performance and robustness of the Monte Carlo importance sampling algorithm using parallelized S-ADAPT for basic and complex mechanistic models

Abstract

The Monte Carlo Parametric Expectation Maximization (MC-PEM) algorithm can approximate the true log-likelihood as precisely as needed and is efficiently parallelizable. Our objectives were to evaluate an importance sampling version of the MC-PEM algorithm for mechanistic models and to qualify the default estimation settings in SADAPT-TRAN. We assessed bias, imprecision and robustness of this algorithm in S-ADAPT for mechanistic models with up to 45 simultaneously estimated structural parameters, 14 differential equations, and 10 dependent variables (one drug concentration and nine pharmacodynamic effects). Simpler models comprising 15 parameters were estimated using three of the ten dependent variables. We set initial estimates to 0.1 or 10 times the true value and evaluated 30 bootstrap replicates with frequent or sparse sampling. Datasets comprised three dose levels with 16 subjects each. For simultaneous estimation of the full model, the ratio of estimated to true values for structural model parameters (median [5-95% percentile] over 45 parameters) was 1.01 [0.94-1.13] for means and 0.99 [0.68-1.39] for between-subject variances for frequent sampling and 1.02 [0.81-1.47] for means and 1.02 [0.47-2.56] for variances for sparse sampling. Imprecision was ≤25% for 43 of 45 means for frequent sampling. Bias and imprecision was well comparable for the full and simpler models. Parallelized estimation was 23-fold (6.9-fold) faster using 48 threads (eight threads) relative to one thread. The MC-PEM algorithm was robust and provided unbiased and adequately precise means and variances during simultaneous estimation of complex, mechanistic models in a 45 dimensional parameter space with rich or sparse data using poor initial estimates.

Fig. 1

Structure of the full model containing a two-compartment PK model, four indirect response (IDR) models, a direct effect model, and four precursor indirect response models

Fig. 2

Illustration of one dataset with frequent sampling for the full model including plasma concentrations and nine different pharmacodynamic effects at three dose levels (the dependent variable identifiers [DVIDs] refer to the respective model part number shown in Table I; doses were given at 0, 24, and 48 h)

Fig. 3

SADAPT-TRAN model code to define the full mechanistic model for simultaneous estimation

Fig. 3

SADAPT-TRAN model code to define the full mechanistic model for simultaneous estimation