Rosenbaum Paul R
Department of Statistics, The Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6340, USA.
Biometrics. 2007 Dec;63(4):1164-71. doi: 10.1111/j.1541-0420.2007.00783.x. Epub 2007 Apr 9.
A small literature discusses locally most powerful rank tests when only a fraction of treated subjects respond to treatment. The ranks used in these tests are very different from conventional ranks, being relatively flat for low responses and then rising steeply, and the associated tests are much more powerful than conventional rank tests when, indeed, only a small fraction of treated subjects exhibit dramatic responses. Because the tests are derived from considerations of local power, they do not yield a plausible family of models for effect, and therefore they do not yield confidence intervals for the magnitude of effect formed by inverting the tests. There is a similarity between these tests and another family of tests, originally motivated by different considerations involving peak performance in small subsets. Exploiting this similarity, a method for obtaining confidence statements is proposed. In the case of observational studies, sensitivity to unobserved bias from nonrandom assignment of treatments is also examined. Two examples are used as illustrations: (i) a study of smoking during pregnancy and its effects on birth weight, in which smokers are matched to six controls, and (ii) a matched pair study of damage to DNA among workers at aluminum production plants.
一小部分文献探讨了仅一部分接受治疗的受试者对治疗有反应时的局部最强大秩检验。这些检验中使用的秩与传统秩有很大不同，对于低反应相对平缓，然后急剧上升，并且当实际上只有一小部分接受治疗的受试者表现出显著反应时，相关检验比传统秩检验更强大。由于这些检验是基于局部功效的考虑得出的，它们没有产生一个合理的效应模型族，因此也没有通过反转检验得出效应大小的置信区间。这些检验与另一类检验有相似之处，另一类检验最初是由涉及小子集中峰值表现的不同考虑因素推动的。利用这种相似性，提出了一种获得置信陈述的方法。在观察性研究的情况下，还研究了对治疗非随机分配产生的未观察到的偏差的敏感性。使用了两个例子进行说明：（i）一项关于孕期吸烟及其对出生体重影响的研究，其中吸烟者与六个对照组进行匹配，以及（ii）一项铝生产厂工人DNA损伤的配对研究。
