Whittemore A S
Stat Med. 1982 Jul-Sep;1(3):229-43. doi: 10.1002/sim.4780010305.
This paper extends Levin's measure of attributable risk to adjust for confounding by aetiologic factors other than the exposure of interest. One can estimate this extended measure from case-control data provided either (i) from the control data one can estimate exposure prevalence within each stratum of the confounding factor; or (ii) one has additional information available concerning the confounder distribution and the stratum-specific disease rates. In both cases we give maximum likelihood estimates and their estimated asymptotic variances, and show them to be independent of the sampling design (matched vs. random). Computer simulations investigate the behaviour of these estimates and of three types of confidence intervals when sample size is small relative to the number of confounder strata. The simulations indicate that attributable risk estimates tend to be too low. The bias is not serious except when exposure prevalence is high among controls. In this case the estimates and their standard error estimates are also highly unstable. In general, the asymptotic standard error estimates performed quite well, even in small samples, and even when the true asymptotic standard error was too small. By contrast, the bootstrap estimate tended to be too large. None of the three confidence intervals proved superior in accuracy to the other two. Thus there appears no advantage in using the log-based interval suggested by Walter which is always longer than the simpler symmetric interval.
本文扩展了莱文的归因风险度量方法，以调整除感兴趣的暴露因素之外的病因因素造成的混杂。可以根据病例对照数据估计这种扩展度量，条件是：（i）从对照数据中可以估计混杂因素各层内的暴露患病率；或者（ii）有关于混杂因素分布和各层特定疾病率的额外信息。在这两种情况下，我们给出最大似然估计及其估计的渐近方差，并表明它们与抽样设计（匹配抽样与随机抽样）无关。计算机模拟研究了在样本量相对于混杂因素层数较小的情况下这些估计以及三种类型置信区间的表现。模拟表明归因风险估计往往过低。除了对照中暴露患病率较高的情况外，偏差并不严重。在这种情况下，估计值及其标准误差估计值也非常不稳定。一般来说，渐近标准误差估计即使在小样本中，甚至当真实的渐近标准误差过小时，表现也相当不错。相比之下，自助法估计往往过大。三种置信区间在准确性方面均未证明比其他两种更具优势。因此，使用沃尔特建议的基于对数的区间似乎没有优势，该区间总是比更简单的对称区间长。
