Département de Biostatistique et Informatique Médicale, Hôpital Saint-Louis, AP-HP, Paris, France.
Stat Med. 2010 Aug 15;29(18):1900-9. doi: 10.1002/sim.3947.
The cumulative summation (CUSUM) test is increasingly being used in medicine to monitor a wide variety of processes such as cardiac surgery or disease outbreaks. The CUSUM sequentially tests the null hypothesis that the process is in control, i.e. its mean is equal to a given target. Thus, it detects when the process changes to an out of control state. Conversely, monitoring the learning curve requires detecting the time when the process reaches an in control state. In this work we develop an alternative to the CUSUM, the learning curve CUSUM (LC-CUSUM), that serves to detect when a process deviates from an out of control state to an in control state. The test is based on a two one-sided tests procedure where the null hypothesis is that the process is out of control. This can be written as H(0): |mu-mu(0)|> or =delta tested against H(1): |mu-mu(0)|< delta. The null hypothesis is thus the union of two one-sided hypotheses and is rejected when both are rejected. A CUSUM test statistic is then constructed for each hypothesis in a traditional way. The properties of the test are investigated through numerical simulations, and are illustrated on the learning curve of an endoscopist performing endoscopic retrograde cholangiopancreatographies for biliary tract disorders.
累积和 (CUSUM) 检验越来越多地被用于医学领域，以监测各种过程，如心脏手术或疾病爆发。CUSUM 连续检验过程是否处于控制状态的零假设，即其均值等于给定的目标值。因此，它可以检测到过程何时变为失控状态。相反，监测学习曲线需要检测到过程达到控制状态的时间。在这项工作中，我们开发了一种替代 CUSUM 的方法，即学习曲线 CUSUM（LC-CUSUM），用于检测过程何时从失控状态转变为控制状态。该检验基于双边检验程序，零假设是过程失控。这可以表示为 H(0): |mu-mu(0)|> or = delta，检验针对 H(1): |mu-mu(0)|< delta。因此，零假设是两个单边假设的并集，当两个假设都被拒绝时，零假设被拒绝。然后，以传统方式为每个假设构建 CUSUM 检验统计量。通过数值模拟研究了检验的性质，并在一位内窥镜医生进行胆道疾病的内镜逆行胰胆管造影术的学习曲线上进行了说明。
