Lubin J H, Gail M H, Ershow A G
Biostatistics Branch, National Cancer Institute, Bethesda, Maryland 20205.
Stat Med. 1988 Mar;7(3):363-76. doi: 10.1002/sim.4780070302.
In estimating the sample size for a case-control study, epidemiologic texts present formulae that require a binary exposure of interest. Frequently, however, important exposures are continuous and dichotomization may result in a 'not exposed' category that has little practical meaning. In addition, if risks vary monotonically with exposure, then dichotomization will obscure risk effects and require a greater number of subjects to detect differences in the exposure distributions among cases and controls. Starting from the usual score statistic to detect differences in exposure, this paper develops sample size formulae for case-control studies with arbitrary exposure distributions; this includes both continuous and dichotomous exposure measurements as special cases. The score statistic is appropriate for general differentiable models for the relative odds, and, in particular, for the two forms commonly used in prospective disease occurrence models: (1) the odds of disease increase linearly with exposure; or (2) the odds increase exponentially with exposure. Under these two models we illustrate calculation of sample sizes for a hypothetical case-control study of lung cancer among non-smokers who are exposed to radon decay products at home.
在估计病例对照研究的样本量时，流行病学文献中给出的公式要求感兴趣的暴露因素为二元变量。然而，通常重要的暴露因素是连续的，二分类可能会导致一个“未暴露”类别，而该类别几乎没有实际意义。此外，如果风险随暴露因素单调变化，那么二分类会掩盖风险效应，并且需要更多的研究对象来检测病例组和对照组之间暴露分布的差异。本文从用于检测暴露差异的常用得分统计量出发，推导出了具有任意暴露分布的病例对照研究的样本量公式；连续和二分类暴露测量均作为特殊情况包含在内。得分统计量适用于相对比值的一般可微模型，尤其适用于前瞻性疾病发生模型中常用的两种形式：（1）疾病的比值随暴露因素呈线性增加；或（2）比值随暴露因素呈指数增加。在这两种模型下，我们举例说明了一项假设的病例对照研究的样本量计算，该研究对象为在家中接触氡衰变产物的非吸烟者中的肺癌患者。
