Nam J M, Fears T R
Biostatistics Branch, National Cancer Institute, Rockville, Maryland 20892.
Stat Med. 1992 Sep 30;11(13):1759-66. doi: 10.1002/sim.4780111309.
Strata-matched case-control studies based on a given number of cases and k times as many controls are common. We obtain a necessary and sufficient condition for there to exist a numerical solution for k with a desired level of a power. We derive the maximum power of the Cochran test, which may be less than one, when the number of cases is fixed. We provide an approximate formula for the minimum number of cases required for a specified power. There exists a numerical solution (that is, convergence of an iterative method) for k if the number of cases given is greater than this minimum number and no such a solution otherwise. We also show that the incremental gain in relative efficiency of the test with respect to k is diminished as k gets large.
基于给定数量的病例以及病例数k倍的对照进行分层匹配病例对照研究很常见。我们得到了一个必要且充分的条件，即在给定的检验效能水平下存在k的数值解。当病例数固定时，我们推导出了Cochran检验的最大效能，其可能小于1。我们给出了达到特定效能所需的最小病例数的近似公式。如果给定的病例数大于这个最小病例数，则存在k的数值解（即迭代方法收敛），否则不存在这样的解。我们还表明，随着k增大，检验相对于k的相对效率的增量增益会减小。
