Division of Research and Methodology, National Center for Health Statistics, Centers for Disease Control and Prevention, 3311 Toledo Road, Hyattsville, MD, 20782, USA.
University of Porto Institute of Public Health, Porto, Portugal.
Popul Health Metr. 2022 May 7;20(1):13. doi: 10.1186/s12963-022-00288-1.
Equal-tailed confidence intervals that maintain nominal coverage (0.95 or greater probability that a 95% confidence interval covers the true value) are useful in interval-based statistical reliability standards, because they remain conservative. For age-adjusted death rates, while the Fay-Feuer gamma method remains the gold standard, modifications have been proposed to streamline implementation and/or obtain more efficient intervals (shorter intervals that retain nominal coverage).
This paper evaluates three such modifications for use in interval-based statistical reliability standards, the Anderson-Rosenberg, Tiwari, and Fay-Kim intervals, when data are sparse and sample size-based standards alone are overly coarse. Initial simulations were anchored around small populations (P = 2400 or 1200), the median crude all-cause US mortality rate in 2010-2019 (833.8 per 100,000), and the corresponding age-specific probabilities of death. To allow for greater variation in the age-adjustment weights and age-specific probabilities, a second set of simulations draws those at random, while holding the mean number of deaths at 20 or 10. Finally, county-level mortality data by race/ethnicity from four causes are selected to capture even greater variation: all causes, external causes, congenital malformations, and Alzheimer disease.
The three modifications had comparable performance when the number of deaths was large relative to the denominator and the age distribution was as in the standard population. However, for sparse county-level data by race/ethnicity for rarer causes of death, and for which the age distribution differed sharply from the standard population, coverage probability in all but the Fay-Feuer method sometimes fell below 0.95. More efficient intervals than the Fay-Feuer interval were identified under specific circumstances. When the coefficient of variation of the age-adjustment weights was below 0.5, the Anderson-Rosenberg and Tiwari intervals appeared to be more efficient, whereas when it was above 0.5, the Fay-Kim interval appeared to be more efficient.
As national and international agencies reassess prevailing data presentation standards to release age-adjusted estimates for smaller areas or population subgroups than previously presented, the Fay-Feuer interval can be used to develop interval-based statistical reliability standards with appropriate thresholds that are generally applicable. For data that meet certain statistical conditions, more efficient intervals could be considered.
在基于区间的统计可靠性标准中，保持名义覆盖率（95%置信区间覆盖真实值的概率大于等于 0.95）的等尾置信区间是有用的，因为它们保持保守。对于年龄调整死亡率，虽然 Fay-Feuer 伽马方法仍然是金标准，但已经提出了一些修改方法，以简化实施和/或获得更有效的区间（保留名义覆盖率的更短区间）。
本文评估了三种用于基于区间的统计可靠性标准的修改方法，即 Anderson-Rosenberg、Tiwari 和 Fay-Kim 区间，当数据稀疏且仅基于样本量的标准过于粗糙时。初始模拟以小人群（P=2400 或 1200）为基础，以 2010-2019 年美国中值粗全因死亡率（每 10 万人 833.8 人）和相应的特定年龄死亡概率为中心。为了允许在年龄调整权重和特定年龄死亡概率方面有更大的变化，第二组模拟随机抽取这些数据，同时保持死亡人数为 20 或 10。最后，选择四个种族/族裔的县死亡率数据，以捕捉更大的变化：所有原因、外部原因、先天性畸形和阿尔茨海默病。
当死亡人数相对于分母较大且年龄分布与标准人群相同时，三种修改方法的性能相当。然而，对于罕见死因的种族/族裔的稀疏县级数据，以及年龄分布与标准人群明显不同的情况，除 Fay-Feuer 方法外，所有方法的覆盖率概率有时都低于 0.95。在特定情况下，确定了比 Fay-Feuer 区间更有效的区间。当年龄调整权重的变异系数低于 0.5 时，Anderson-Rosenberg 和 Tiwari 区间似乎更有效，而当变异系数高于 0.5 时，Fay-Kim 区间似乎更有效。
随着国家和国际机构重新评估现行的数据呈现标准，以发布以前未呈现的较小区域或人口亚组的年龄调整估计值，Fay-Feuer 区间可用于制定普遍适用的基于区间的统计可靠性标准，具有适当的阈值。对于符合某些统计条件的数据，可以考虑更有效的区间。
