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首页> 外文期刊>Journal of applied statistics >Hybrid-based confidence intervals for the ratio of two treatment means in the over-dispersed Poisson data
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Hybrid-based confidence intervals for the ratio of two treatment means in the over-dispersed Poisson data

机译：泊松数据中两种处理方法之比的基于混合的置信区间

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摘要

In many clinical trials and epidemiological studies, comparing the mean count response of an exposed group to a control group is often of interest. This type of data is often over-dispersed with respect to Poisson variation, and previous studies usually compared groups using confidence intervals (CIs) of the difference between the two means. However, in some situations, especially when the means are small, interval estimation of the mean ratio (MR) is preferable. Moreover, Cox and Lewis pointed out many other situations where the MR is more relevant than the difference of means. In this paper, we consider CI construction for the ratio of means between two treatments for over-dispersed Poisson data. We develop several CIs for the situation by hybridizing two separate CIs for two individual means. Extensive simulations show that all hybrid-based CIs perform reasonably well in terms of coverage. However, the CIs based on the delta method using the logarithmic transformation perform better than other intervals in the sense that they have slightly shorter interval lengths and show better balance of tail errors. These proposed CIs are illustrated with three real data examples.
机译：在许多临床试验和流行病学研究中，经常需要比较暴露人群与对照组的平均计数反应。这类数据通常相对于Poisson变异过于分散，以前的研究通常使用两种方法之间差异的置信区间（CI）比较各组。但是，在某些情况下，尤其是在均值较小的情况下，均值（MR）的区间估计是优选的。此外，考克斯和刘易斯指出，在其他许多情况下，MR比手段差异更重要。在本文中，对于过度分散的Poisson数据，我们考虑使用CI构造两次处理之间的均值比。通过将两个单独的CI混合为两种单独的方式，我们针对这种情况开发了几个CI。大量的仿真表明，所有基于混合的配置项在覆盖范围方面均表现良好。但是，基于使用对数变换的增量法的CI表现出比其他间隔更好的意义，因为它们的间隔长度略短，并且显示出更好的尾部误差平衡。这些提出的配置项用三个真实数据示例进行了说明。

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