Biological and medical researchers often collect count data in clusters at multiple time points. The data can exhibit excessive zeros and a wide range of dispersion levels. In particular, our research was motivated by a dental dataset with such complex data features: the Iowa Fluoride Study (IFS). The study was designed to investigate the effects of various dietary and nondietary factors on the caries development of a cohort of Iowa school children at the ages of 5, 9, and 13. To analyze the multiyear IFS data, we propose a novel longitudinal method of a generalized estimating equations based marginal regression model. We use a zero-inflated model with a Conway-Maxwell-Poisson (CMP) distribution, which has the flexibility to account for all levels of dispersion. The parameters of interest are estimated through a modified expectation-solution algorithm to account for the clustered and temporal correlation structure. We fit the proposed zero-inflated CMP model and perform a comprehensive secondary analysis of the IFS dataset. It resulted in a number of notable conclusions that also make clinical sense. Additionally, we demonstrated the superiority of this modeling approach over two other popular competing models: the zero-inflated Poisson and negative binomial models. In the simulation studies, we further evaluate the performance of our point estimators, the variance estimators, and that of the large sample confidence intervals for the parameters of interest. It is also demonstrated that our longitudinal CMP model can correctly identify the time-varying dispersion patterns.

中文翻译：

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分析零膨胀的纵向聚类计数数据：使用 Conway-Maxwell-Poisson 分布的边际建模

生物和医学研究人员经常在多个时间点以集群的形式收集计数数据。数据可能表现出过多的零和广泛的分散水平。特别是，我们的研究受到具有如此复杂数据特征的牙科数据集的推动：爱荷华州氟化物研究 (IFS)。该研究旨在调查各种饮食和非饮食因素对爱荷华州 5、9 和 13 岁学龄儿童龋齿发展的影响。为了分析多年 IFS 数据，我们提出了一种新的纵向方法基于广义估计方程的边际回归模型。我们使用具有 Conway-Maxwell-Poisson (CMP) 分布的零膨胀模型，该模型可以灵活地考虑所有级别的分散。通过修改的期望解算法估计感兴趣的参数，以解释聚类和时间相关结构。我们拟合了所提出的零膨胀 CMP 模型，并对 IFS 数据集进行了全面的二次分析。它得出了许多值得注意的结论，这些结论也具有临床意义。此外，我们证明了这种建模方法优于其他两种流行的竞争模型：零膨胀泊松模型和负二项式模型。在模拟研究中，我们进一步评估了我们的点估计器、方差估计器以及感兴趣参数的大样本置信区间的性能。还证明了我们的纵向 CMP 模型可以正确识别随时间变化的色散模式。