Benichou J, Gail M H
Département de Biostatistique et Informatique Médicale, Hôpital Saint-Louis, Paris, France.
Biometrics. 1990 Dec;46(4):991-1003.
The attributable risk (AR), defined as AR = [Pr(disease) - Pr(disease/no exposure)]/Pr(disease), measures the proportion of disease risk that is attributable to an exposure. Recently Bruzzi et al. (1985, American Journal of Epidemiology 122, 904-914) presented point estimates of AR based on logistic models for case-control data to allow for confounding factors and secondary exposures. To produce confidence intervals, we derived variance estimates for AR under the logistic model and for various designs for sampling controls. Calculations for discrete exposure and confounding factors require covariances between estimates of the risk parameters of the logistic model and the proportions of cases with given levels of exposure and confounding factors. These covariances are estimated from Taylor series expansions applied to implicit functions. Similar calculations for continuous exposures are derived using influence functions. Simulations indicate that those asymptotic procedures yield reliable variance estimates and confidence intervals with near nominal coverage. An example illustrates the usefulness of variance calculations in selecting a logistic model that is neither so simplified as to exhibit systematic lack of fit nor so complicated as to inflate the variance of the estimate of AR.
归因风险（AR）定义为AR = [Pr（疾病）- Pr（疾病/无暴露）]/Pr（疾病），用于衡量可归因于某种暴露的疾病风险比例。最近，布鲁齐等人（1985年，《美国流行病学杂志》122卷，904 - 914页）基于病例对照数据的逻辑模型给出了AR的点估计值，以考虑混杂因素和二次暴露。为了生成置信区间，我们推导了逻辑模型下以及各种对照抽样设计下AR的方差估计值。对于离散暴露和混杂因素的计算，需要逻辑模型风险参数估计值与给定暴露和混杂因素水平的病例比例之间的协方差。这些协方差通过应用于隐函数的泰勒级数展开来估计。对于连续暴露，使用影响函数进行类似的计算。模拟表明，那些渐近程序产生可靠的方差估计值和具有接近名义覆盖范围的置信区间。一个例子说明了方差计算在选择逻辑模型中的有用性，该模型既不会过于简化而表现出系统性的拟合不足，也不会过于复杂而使AR估计值的方差膨胀。
