Department of Pharmaceutical Biosciences, Uppsala University, Box 591, 75124, Uppsala, Sweden.
J Pharmacokinet Pharmacodyn. 2011 Feb;38(1):63-82. doi: 10.1007/s10928-010-9177-x. Epub 2010 Nov 13.
When parameter estimates are used in predictions or decisions, it is important to consider the magnitude of imprecision associated with the estimation. Such imprecision estimates are, however, presently lacking for nonparametric algorithms intended for nonlinear mixed effects models. The objective of this study was to develop resampling-based methods for estimating imprecision in nonparametric distribution (NPD) estimates obtained in NONMEM. A one-compartment PK model was used to simulate datasets for which the random effect of clearance conformed to a (i) normal (ii) bimodal and (iii) heavy-tailed underlying distributional shapes. Re-estimation was conducted assuming normality under FOCE, and NPDs were estimated sequential to this step. Imprecision in the NPD was then estimated by means of two different resampling procedures. The first (full) method relies on bootstrap sampling from the raw data and a re-estimation of both the preceding parametric (FOCE) and the nonparametric step. The second (simplified) method relies on bootstrap sampling of individual nonparametric probability distributions. Nonparametric 95% confidence intervals (95% CIs) were obtained and mean errors (MEs) of the 95% CI width were computed. Standard errors (SEs) of nonparametric population estimates were obtained using the simplified method and evaluated through 100 stochastic simulations followed by estimations (SSEs). Both methods were successfully implemented to provide imprecision estimates for NPDs. The imprecision estimates adequately reflected the reference imprecision in all distributional cases and regardless of the numbers of individuals in the original data. Relative MEs of the 95% CI width of CL marginal density when original data contained 200 individuals were equal to: (i) -22 and -12%, (ii) -22 and -9%, (iii) -13 and -5% for the full and simplified (n = 100), respectively. SEs derived from the simplified method were consistent with the ones obtained from 100 SSEs. In conclusion, two novel bootstrapping methods intended for nonparametric estimation methods are proposed. In addition of providing information about the precision of nonparametric parameter estimates, they can serve as diagnostic tools for the detection of misspecified parameter distributions.
当参数估计用于预测或决策时，重要的是要考虑与估计相关的不精确程度。然而，目前缺乏用于非线性混合效应模型的非参数算法的不精确估计。本研究的目的是开发基于重采样的方法，用于估计 NONMEM 中获得的非参数分布 (NPD) 估计的不精确性。使用一室 PK 模型模拟数据集，其中清除的随机效应符合 (i) 正态 (ii) 双峰和 (iii) 重尾的潜在分布形状。在 FOCE 下假设正态性进行重新估计，并在此步骤之后顺序估计 NPD。然后通过两种不同的重采样过程来估计 NPD 的不精确性。第一种（完整）方法依赖于从原始数据中进行引导抽样，并重新估计前面的参数（FOCE）和非参数步骤。第二种（简化）方法依赖于对个体非参数概率分布进行引导抽样。获得了非参数 95%置信区间 (95%CI)，并计算了 95%CI 宽度的平均误差 (ME)。使用简化方法获得了非参数群体估计的标准误差 (SE)，并通过 100 次随机模拟进行了评估（SSEs）。两种方法都成功实施，为 NPD 提供了不精确估计。在所有分布情况下，不精确估计都充分反映了参考不精确性，并且与原始数据中的个体数量无关。当原始数据包含 200 个个体时，CL 边际密度的 95%CI 宽度的相对 ME 分别为：(i)-22 和-12%，(ii)-22 和-9%，(iii)-13 和-5%，对于完整和简化（n=100）。简化方法得出的 SE 与从 100 个 SSE 中得出的 SE 一致。总之，提出了两种用于非参数估计方法的新引导抽样方法。除了提供关于非参数参数估计精度的信息外，它们还可以作为检测参数分布指定不当的诊断工具。
