Department of Pharmacy & Pharmacology, The Netherlands Cancer Institute/Slotervaart Hospital, Amsterdam, the Netherlands.
AAPS J. 2012 Sep;14(3):601-11. doi: 10.1208/s12248-012-9373-2. Epub 2012 May 31.
In population pharmacokinetic analyses, missing categorical data are often encountered. We evaluated several methods of performing covariate analyses with partially missing categorical covariate data. Missing data methods consisted of discarding data (DROP), additional effect parameter for the group with missing data (EXTRA), and mixture methods in which the mixing probability was fixed to the observed fraction of categories (MIX(obs)), based on the likelihood of the concentration data (MIX(conc)), or combined likelihood of observed covariate data and concentration data (MIX(joint)). Simulations were implemented to study bias and imprecision of the methods in datasets with equal-sized and unbalanced category ratios for a binary covariate as well as datasets with non-random missingness (MNAR). Additionally, the performance and feasibility of implementation was assessed in two real datasets. At either low (10%) or high (50%) levels of missingness, all methods performed similarly well. Performance was similar for situations with unbalanced datasets (3:1 covariate distribution) and balanced datasets. In the MNAR scenario, the MIX methods showed a higher bias in the estimation of CL and covariate effect than EXTRA. All methods could be applied to real datasets, except DROP. All methods perform similarly at the studied levels of missingness, but the DROP and EXTRA methods provided less bias than the mixture methods in the case of MNAR. However, EXTRA was associated with inflated type I error rates of covariate selection, while DROP handled data inefficiently.
在群体药代动力学分析中,经常会遇到缺失的分类数据。我们评估了几种方法,用于对部分缺失的分类协变量数据进行协变量分析。缺失数据方法包括丢弃数据(DROP)、为缺失数据的组添加额外的效应参数(EXTRA)以及混合方法,其中混合概率固定为观察到的类别分数(MIX(obs)),基于浓度数据的似然性(MIX(conc))或观察到的协变量数据和浓度数据的联合似然性(MIX(joint))。我们进行了模拟,以研究在具有相同大小和不平衡分类比例的二元协变量数据集以及具有非随机缺失(MNAR)的数据集的方法中的偏差和不精确性。此外,我们还在两个真实数据集评估了实施的性能和可行性。在缺失率较低(10%)或较高(50%)的情况下,所有方法的性能都非常相似。在不平衡数据集(3:1 协变量分布)和平衡数据集的情况下,性能相似。在 MNAR 情况下,与 EXTRA 相比,MIX 方法在 CL 和协变量效应的估计中显示出更高的偏差。除 DROP 外,所有方法都可应用于真实数据集。在研究的缺失水平下,所有方法的性能都相似,但在 MNAR 的情况下,DROP 和 EXTRA 方法比混合方法提供的偏差更小。然而,EXTRA 与协变量选择的膨胀Ⅰ型错误率相关,而 DROP 则低效地处理数据。