Taylor J M
Stat Med. 1986 Jan-Feb;5(1):29-36. doi: 10.1002/sim.4780050106.
This paper investigates the efficiency of using multiple controls in a case-control study, when there is a single binary exposure variable. Specifically, we consider the asymptotic power of the Cochran test statistic against non-local alternatives of interest. When it is desirable to take multiple controls per case, we show that the marginal return rapidly diminishes as the number of controls per case increases. The effect is as strong, if not stronger, for non-local alternatives as it is for local alternatives. Hence, it is rarely worth choosing more than three controls per case. We also provide a table of sample sizes necessary to achieve 80 per cent power for some odds ratios not equal to one. We extend the results to a special case when there are two binary exposure variables.
本文研究了在单一个二元暴露变量的病例对照研究中使用多个对照的效率。具体而言，我们考虑了针对感兴趣的非局部备择假设的 Cochr an检验统计量的渐近功效。当希望每个病例采用多个对照时，我们表明随着每个病例对照数量的增加，边际回报会迅速减少。对于非局部备择假设，这种效应与局部备择假设一样强烈，甚至更强。因此，每个病例选择超过三个对照很少有价值。我们还提供了一个样本量表格，对于一些不等于1的优势比，该表格给出了达到80%功效所需的样本量。我们将结果扩展到存在两个二元暴露变量的特殊情况。
