Marginal modeling in community randomized trials with rare events: Utilization of the negative binomial regression model.
Marginal modeling in community randomized trials with rare events: Utilization of the negative binomial regression model.
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DOI：
10.1177/17407745211063479
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发表时间：
2022-04
期刊：
影响因子：
2.7
通讯作者：
Vandergrift, Nathan
中科院分区：
文献类型：
--
作者：
Westgate, Philip M.;Cheng, Debbie M.;Feaster, Daniel J.;Fernandez, Soledad;Shoben, Abigail B.;Vandergrift, Nathan
关键词：
这项工作是由 HEALing 社区研究推动的，这是一项仅进行后测试的聚类随机试验，其中社区被随机分配到两个不同的试验组。主要兴趣是减少阿片类药物过量死亡，这将作为社区一级的计数结果进行收集。社区规模从数千人到超过一百万居民不等，预计死亡人数很少。聚类随机试验文献中的传统边际建模方法包括在利用受试者级数据时使用具有可交换相关结构的广义估计方程，或者在利用社区级数据时使用基于过度分散二项式方差的类似拟似然法。这些方法解释并估计簇内相关系数，该系数应在簇随机试验的结果中提供。或者，可以报告变异系数或 R 系数。在这篇手稿中，我们表明，当社区很大且事件很少时，也可以使用负二项式回归。本手稿的目的是：1）表明负二项式回归方法的目标是与过度分散二项式模型相同的边际回归参数，并解释为什么估计值可能不同； 2)推导负二项式过分散参数k与簇内相关系数、变异系数和R系数的关系式； 3) 分析来自 HEALing 社区研究的干预前数据，以演示和对比模型，并展示如何在利用负二项式回归时报告簇内相关系数、变异系数和 R 系数。负二项式和过分散二项式回归模型在模型设置、回归参数估计和过分散参数的公式方面进行了对比。使用三个特定模型来说明概念并解决第三个目标。负二项式回归方法的目标是与过度分散二项式模型相同的边际回归参数，尽管估计值可能有所不同。在如何对过度分散以及簇内相关系数进行建模方面存在实际差异。负二项式过度离散参数大约等于簇内相关系数与边际概率之比、变异系数的平方和 R 系数负 1。因此，在利用负二项式回归时，可以报告与所有四种不同类型的过度离散参数化相对应的估计值。负二项式回归提供了一种有效、实用的替代方法来分析计数数据以及相应的过度离散参数报告，这些数据来自社区规模较大且事件罕见的社区随机试验。
This work is motivated by the HEALing Communities Study, which is a post-test only cluster randomized trial in which communities are randomized to two different trial arms. The primary interest is in reducing opioid overdose fatalities, which will be collected as a count outcome at the community level. Communities range in size from thousands to over one million residents, and fatalities are expected to be rare. Traditional marginal modeling approaches in the cluster randomized trial literature include the use of generalized estimating equations with an exchangeable correlation structure when utilizing subject-level data, or analogously quasi-likelihood based on an over-dispersed binomial variance when utilizing community-level data. These approaches account for and estimate the intra-cluster correlation coefficient, which should be provided in the results from a cluster randomized trial. Alternatively, the coefficient of variation or R coefficient could be reported. In this manuscript, we show that negative binomial regression can also be utilized when communities are large and events are rare. The objectives of this manuscript are: 1) to show that the negative binomial regression approach targets the same marginal regression parameter(s) as an over-dispersed binomial model, and to explain why the estimates may differ; 2) to derive formulas relating the negative binomial overdispersion parameter k with the intra-cluster correlation coefficient, coefficient of variation and R coefficient; and 3) analyze pre-intervention data from the HEALing Communities Study to demonstrate and contrast models as well as to show how to report the intra-cluster correlation coefficient, coefficient of variation and R coefficient when utilizing negative binomial regression. Negative binomial and over-dispersed binomial regression modeling are contrasted in terms of model setup, regression parameter estimation, and formulation of the overdispersion parameter. Three specific models are used to illustrate concepts and address the third objective. The negative binomial regression approach targets the same marginal regression parameter(s) as an over-dispersed binomial model, although estimates may differ. Practical differences arise in regard to how overdispersion, and hence the intra-cluster correlation coefficient, is modeled. The negative binomial overdispersion parameter is approximately equal to the ratio of the intra-cluster correlation coefficient and marginal probability, the square of the coefficient of variation, and the R coefficient minus 1. As a result, estimates corresponding to all four of these different types of overdispersion parameterizations can be reported when utilizing negative binomial regression. Negative binomial regression provides a valid, practical, alternative approach to the analysis of count data, and corresponding reporting of overdispersion parameters, from community randomized trials in which communities are large and events are rare.
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