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Methods for confidence interval estimation of a ratio parameter with application to location quotients

机译:用于位置商的比率参数的置信区间估计方法

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Background The location quotient (LQ) ratio, a measure designed to quantify and benchmark the degree of relative concentration of an activity in the analysis of area localization, has received considerable attention in the geographic and economics literature. This index can also naturally be applied in the context of population health to quantify and compare health outcomes across spatial domains. However, one commonly observed limitation of LQ is its widespread use as only a point estimate without an accompanying confidence interval. Methods In this paper we present statistical methods that can be used to construct confidence intervals for location quotients. The delta and Fieller's methods are generic approaches for a ratio parameter and the generalized linear modelling framework is a useful re-parameterization particularly helpful for generating profile-likelihood based confidence intervals for the location quotient. A simulation experiment is carried out to assess the performance of each of the analytic approaches and a health utilization data set is used for illustration. Results Both the simulation results as well as the findings from the empirical data show that the different analytical methods produce very similar confidence limits for location quotients. When incidence of outcome is not rare and sample sizes are large, the confidence limits are almost indistinguishable. The confidence limits from the generalized linear model approach might be preferable in small sample situations. Conclusion LQ is a useful measure which allows quantification and comparison of health and other outcomes across defined geographical regions. It is a very simple index to compute and has a straightforward interpretation. Reporting this estimate with appropriate confidence limits using methods presented in this paper will make the measure particularly attractive for policy and decision makers.
机译:背景技术位置商(LQ)比率是一种旨在量化和基准化区域定位分析中某项活动的相对集中程度的措施,在地理和经济学文献中引起了极大的关注。该指数自然也可以应用于人口健康状况,以量化和比较跨空间域的健康结果。但是,LQ的一个普遍观察到的局限性是LQ仅作为点估计而没有伴随置信区间的广泛应用。方法在本文中,我们介绍了可用于构造位置商的置信区间的统计方法。 delta和Fieller方法是比率参数的通用方法,而广义线性建模框架是有用的重新参数化,特别有助于生成位置商的基于轮廓似然的置信区间。进行了仿真实验以评估每种分析方法的性能,并使用健康利用数据集进行说明。结果仿真结果以及经验数据的结果都表明,不同的分析方法对位置商产生非常相似的置信限。当结果的发生率并不罕见且样本量很大时,置信度极限几乎是无法区分的。在小样本情况下,广义线性模型方法的置信度限制可能更可取。结论LQ是一种有用的量度,可以量化和比较定义的地理区域中的健康状况和其他结果。它是计算非常简单的索引,并且具有简单的解释。使用本文中介绍的方法以适当的置信度限制报告此估计值,将使该措施对政策制定者和决策者特别有吸引力。

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