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Double Poisson-Tweedie Regression Models
International Journal of Biostatistics ( IF 1.2 ) Pub Date : 2019-04-18 , DOI: 10.1515/ijb-2018-0119
Ricardo R Petterle 1 , Wagner H Bonat 2 , Célestin C Kokonendji 3 , Juliane C Seganfredo 4 , Atamai Moraes 4 , Monica G da Silva 4
Affiliation  

In this paper, we further extend the recently proposed Poisson-Tweedie regression models to include a linear predictor for the dispersion as well as for the expectation of the count response variable. The family of the considered models is specified using only second-moments assumptions, where the variance of the count response has the form μ + ϕ μ p $\mu + \phi \mu^p$ , where µ is the expectation, ϕ and p are the dispersion and power parameters, respectively. Parameter estimations are carried out using an estimating function approach obtained by combining the quasi-score and Pearson estimating functions. The performance of the fitting algorithm is investigated through simulation studies. The results showed that our estimating function approach provides consistent estimators for both mean and dispersion parameters. The class of models is motivated by a data set concerning CD4 counting in HIV-positive pregnant women assisted in a public hospital in Curitiba, Paraná, Brazil. Specifically, we investigate the effects of a set of covariates in both expectation and dispersion structures. Our results showed that women living out of the capital Curitiba, with viral load equal or larger than 1000 copies and with previous diagnostic of HIV infection, present lower levels of CD4 cell count. Furthermore, we detected that the time to initiate the antiretroviral therapy decreases the data dispersion. The data set and R code are available as supplementary materials.

中文翻译:

双 Poisson-Tweedie 回归模型

在本文中,我们进一步扩展了最近提出的 Poisson-Tweedie 回归模型,以包括离散度的线性预测器以及计数响应变量的期望值。所考虑的模型族仅使用二阶矩假设来指定,其中计数响应的方差具有以下形式 μ + φ μ p $\mu + \phi \mu^p$ , 在哪里微米是期望,φp分别是色散和功率参数。使用通过结合准分数和皮尔逊估计函数获得的估计函数方法进行参数估计。通过仿真研究来研究拟合算法的性能。结果表明,我们的估计函数方法为均值和离散参数提供了一致的估计量。此类模型的动机是关于在巴西巴拉那州库里提巴的一家公立医院协助的 HIV 阳性孕妇的 CD4 计数数据集。具体来说,我们研究了一组协变量在期望和色散结构中的影响。我们的研究结果表明,居住在首都库里提巴以外,病毒载量等于或大于 1000 拷贝且先前诊断为 HIV 感染的女性,呈现较低水平的 CD4 细胞计数。此外,我们检测到启动抗逆转录病毒治疗的时间减少了数据分散。数据集和R代码可作为补充材料。
更新日期:2019-04-18
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