Lui K J
Department of Mathematical and Computer Sciences, College of Sciences, San Diego State University, San Diego, CA 92182-7720, USA.
J Epidemiol Community Health. 2001 Dec;55(12):885-90. doi: 10.1136/jech.55.12.885.
The attributable risk (AR), which represents the proportion of cases who can be preventable when we completely eliminate a risk factor in a population, is the most commonly used epidemiological index to assess the impact of controlling a selected risk factor on community health. The goal of this paper is to develop and search for good interval estimators of the AR for case-control studies with matched pairs.
This paper considers five asymptotic interval estimators of the AR, including the interval estimator using Wald's statistic suggested elsewhere, the two interval estimators using the logarithmic transformations: log(x) and log(1-x), the interval estimator using the logit transformation log(x/(1-x)), and the interval estimator derived from a simple quadratic equation developed in this paper. This paper compares the finite sample performance of these five interval estimators by calculation of their coverage probability and average length in a variety of situations.
This paper demonstrates that the interval estimator derived from the quadratic equation proposed here can not only consistently perform well with respect to the coverage probability, but also be more efficient than the interval estimator using Wald's statistic in almost all the situations considered here. This paper notes that although the interval estimator using the logarithmic transformation log(1-x) may also perform well with respect to the coverage probability, using this estimator is likely to be less efficient than the interval estimator using Wald's statistic. Finally, this paper notes that when both the underlying odds ratio (OR) and the prevalence of exposure (PE) in the case group are not large (OR < or =2 and PE < or =0.10), the application of the two interval estimators using the transformations log(x) and log(x/(1-x)) can be misleading. However, when both the underlying OR and PE in the case group are large (OR > or =4 and PE > or =0.50), the interval estimator using the logit transformation can actually outperform all the other estimators considered here in terms of efficiency.
When there is no prior knowledge of the possible range for the underlying OR and PE, the interval estimator derived from the quadratic equation developed here for general use is recommended. When it is known that both the OR and PE in the case group are large (OR > or =4 and PE > or =0.50), it is recommended that the interval estimator using the logit transformation is used.
归因风险（AR）表示在人群中完全消除一个风险因素时可预防的病例比例，是评估控制选定风险因素对社区健康影响时最常用的流行病学指标。本文的目的是为配对病例对照研究开发并寻找AR的优良区间估计量。
本文考虑了AR的五个渐近区间估计量，包括别处建议的使用Wald统计量的区间估计量、使用对数变换log(x)和log(1 - x)的两个区间估计量、使用logit变换log(x/(1 - x))的区间估计量，以及本文基于一个简单二次方程推导的区间估计量。本文通过计算这五个区间估计量在各种情况下的覆盖概率和平均长度，比较了它们的有限样本性能。
本文表明，由此处提出的二次方程推导的区间估计量不仅在覆盖概率方面始终表现良好，而且在本文考虑的几乎所有情况下都比使用Wald统计量的区间估计量更有效。本文指出，尽管使用对数变换log(1 - x)的区间估计量在覆盖概率方面也可能表现良好，但使用该估计量可能不如使用Wald统计量的区间估计量有效。最后，本文指出，当病例组中的潜在比值比（OR）和暴露患病率（PE）都不大（OR≤2且PE≤0.10）时，使用变换log(x)和log(x/(1 - x))的两个区间估计量可能会产生误导。然而，当病例组中的潜在OR和PE都很大（OR≥4且PE≥0.50）时，使用logit变换的区间估计量在效率方面实际上可能优于本文考虑的所有其他估计量。
当对潜在OR和PE的可能范围没有先验知识时，建议使用此处为一般用途开发的二次方程推导的区间估计量。当已知病例组中的OR和PE都很大（OR≥4且PE≥0.50）时，建议使用使用logit变换的区间估计量。
