Department of Pharmacy and Pharmaceutical Technology, School of Pharmacy, University of Navarra, Pamplona, Spain.
J Pharmacokinet Pharmacodyn. 2009 Oct;36(5):461-77. doi: 10.1007/s10928-009-9131-y. Epub 2009 Oct 2.
The number of counts (events) per unit of time is a discrete response variable that is generally analyzed with the Poisson distribution (PS) model. The PS model makes two assumptions: the mean number of counts (lambda) is assumed equal to the variance, and counts occurring in non-overlapping intervals are assumed independent. However, many counting outcomes show greater variability than predicted by the PS model, a phenomenon called overdispersion. The purpose of this study was to implement and explore, in the population context, different distribution models accounting for overdispersion and Markov patterns in the analysis of count data. Daily seizures count data obtained from 551 subjects during the 12-week screening phase of a double-blind, placebo-controlled, parallel-group multicenter study performed in epileptic patients with medically refractory partial seizures, were used in the current investigation. The following distribution models were fitted to the data: PS, Zero-Inflated PS (ZIP), Negative Binomial (NB), and Zero-Inflated Negative Binomial (ZINB) models. Markovian features were introduced estimating different lambdas and overdispersion parameters depending on whether the previous day was a seizure or a non-seizure day. All analyses were performed with NONMEM VI. All models were successfully implemented and all overdispersed models improved the fit with respect to the PS model. The NB model resulted in the best description of the data. The inclusion of Markovian features in lambda and in the overdispersion parameter improved the fit significantly (P < 0.001). The plot of the variance versus mean daily seizure count profiles, and the number of transitions, are suggested as model performance tools reflecting the capability to handle overdispersion and Markovian features, respectively.
单位时间内的计数（事件）数量是一个离散的响应变量，通常使用泊松分布（PS）模型进行分析。PS 模型做出了两个假设：计数的平均值（lambda）被假设等于方差，并且在非重叠的时间间隔内发生的计数被假设是独立的。然而，许多计数结果显示出比 PS 模型预测的更大的可变性，这种现象称为过离散。本研究的目的是在人群背景下实施和探索不同的分布模型，这些模型考虑了计数数据分析中的过离散和马尔可夫模式。本研究使用了在患有医学难治性部分性癫痫发作的患者中进行的双盲、安慰剂对照、平行组多中心研究的 12 周筛选阶段中从 551 名受试者获得的每日发作计数数据。对数据进行了 PS、零膨胀 PS（ZIP）、负二项式（NB）和零膨胀负二项式（ZINB）模型拟合。引入了马尔可夫特征，根据前一天是发作日还是非发作日，估计不同的 lambda 和过离散参数。所有分析均使用 NONMEM VI 进行。所有模型均成功实施，所有过离散模型均改善了 PS 模型的拟合度。NB 模型对数据的描述最佳。在 lambda 和过离散参数中包含马尔可夫特征显著改善了拟合度（P<0.001）。方差与每日发作计数的均值图，以及跃迁的数量，被建议作为模型性能工具，分别反映了处理过离散和马尔可夫特征的能力。
