Optimal selection of controls in nested case-control studies

流行病学研究对于发现人类疾病的原因很重要。队列研究是比较典型的研究方法，但对于罕见疾病，由于随访时间长，队列规模大，费用高，故本研究采用巢式病例对照研究设计。我们发现，当暴露率较低时，随机抽样的渐近效率不佳，而反匹配设计优于随机抽样，并提出了一种新的方法，称之为配对方法，并检验了该方法的性质。结果表明，当每种情况下使用多个对照时，成对方法优于普通的反向匹配设计。我们在日本数学学会的一次年会上报告了这一结果。不幸的是，除了少数研究外，都采用了计数器匹配设计。因此，我们对计数匹配法进行了调查，并将其提交给学术期刊，并根据审稿人的意见对其进行了修改。在本研究中，我们意识到我们需要研究计算检验程序的功效并定义样本量。关于这一点，我们想检查的方法，使用理论推导和模拟方法作为未来的问题。

Epidemiologic studies are important to discover a cause of disease for Homo sapiens. The cohort study is typical method but there is demerit that it needs high cost when the disease is rare because it needs long time follow-up and large cohort.We consider the nested case-control study design in this study. We found that the random sampling was not good method when the exposure rate was low with respect to the asymptotic efficiency and that the counter-matching design is better than it. We also developed the new method, so call pairwise method, and examined the characteristics of the method. As the results we showed that the pairwise method is better than ordinary counter-matching design when we use several controls per case. We reported the result in an annual meeting of Mathematical Society of Japan.Unfortunately the counter matching design is used except for a few studies. So we survey the counter matching method and submit it an academic journal and revised it about comment of reviewers. In this study we realized that we need to study to calculate the power of the testing procedure and define the sample size. About the point, we want to examine the methods that used theoretical derivation and simulation methods as a future problem.