Ordway Research Institute, Albany, New York 12208, USA.
AAPS J. 2011 Jun;13(2):212-26. doi: 10.1208/s12248-011-9258-9. Epub 2011 Mar 4.
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.
蒙特卡罗参数期望最大化 (MC-PEM) 算法可以根据需要精确逼近真实对数似然，并且能够有效地进行并行化。我们的目标是评估用于机械模型的重要性抽样版本的 MC-PEM 算法，并对 SADAPT-TRAN 中的默认估计设置进行资格认证。我们评估了在 S-ADAPT 中，这种算法在多达 45 个同时估计的结构参数、14 个微分方程和 10 个因变量（一个药物浓度和 9 个药效学效应）的机械模型中的偏差、不精确性和稳健性。使用十个因变量中的三个，我们对包含 15 个参数的更简单的模型进行了估计。我们将初始估计值设置为真实值的 0.1 或 10 倍，并使用频繁或稀疏采样评估了 30 次自举复制。数据集由三个剂量水平组成，每个剂量水平有 16 个受试者。对于完整模型的同时估计，结构模型参数的估计值与真实值之比（45 个参数的中位数 [5-95% 分位数]）对于频繁采样，均值为 1.01 [0.94-1.13]，个体间方差为 0.99 [0.68-1.39]，稀疏采样的均值为 1.02 [0.81-1.47]，个体间方差为 1.02 [0.47-2.56]。对于频繁采样，43 个均值的不精确性≤25%。对于完整和更简单的模型，偏差和不精确性具有可比性。使用 48 个线程（8 个线程）进行并行化估计比使用 1 个线程分别快 23 倍（6.9 倍）和 1.5 倍。MC-PEM 算法在使用较差的初始估计值，对具有丰富或稀疏数据的 45 维参数空间中的复杂机械模型进行同时估计时具有稳健性，并提供无偏和足够精确的均值和方差。
