Lui Kung-Jong, Chang Kuang-Chao
Department of Mathematics and Statistics, College of Sciences, San Diego State University, San Diego, California 92182-7720, USA.
J Biopharm Stat. 2009 Sep;19(5):916-32. doi: 10.1080/10543400903105497.
The odds ratio (OR) has been recommended to measure the relative treatment effect in therapeutic equivalence or meta-analysis. When controlling the confounding effect due to strata formed by centers (or trials) on patients' response in a multicenter study (or a meta-analysis), we commonly employ stratified analysis and obtain a summary estimate of the treatment effect. In practice, it is not uncommon to come across data in which there are patients not complying with their assigned treatment. To avoid obtaining a misleading summary estimate due to overlooking the interaction between the stratum and treatment effects as well as the selection bias from noncompliance, it is important to develop test statistics accounting for noncompliance for testing the homogeneity of the OR across strata. In this article, we develop five asymptotic test statistics and employ Monte Carlo simulation to evaluate the performance of these statistics in a variety of situations. We note that the weighted-least-squares (WLS) test statistic can be liberal when the number of strata is moderate or large (>/=5). We find that the logarithmic transformation of the WLS (LWLS) test statistic, the squared-root transformation of the LWLS (SLWLS) test statistic, and Fisher's logarithmic transformation of LWLS (LLWLS) test statistic can perform well with respect to Type I error in all the situations considered here. We further find that the Z-transformation of LWLS (ZLWLS) test statistic can be liberal when the number of strata is small or moderate. We note that the LWLS test statistic is likely preferable to the others for a small number of strata, while the ZLWLS test statistic can be the best for a moderate or large number of strata. Finally, we use the data taken from a multiple-risk-factor intervention trial to illustrate the use of these test statistics.
比值比（OR）已被推荐用于衡量治疗等效性或荟萃分析中的相对治疗效果。在多中心研究（或荟萃分析）中，当控制因中心（或试验）形成的分层对患者反应产生的混杂效应时，我们通常采用分层分析并获得治疗效果的汇总估计值。在实际中，遇到存在患者不依从分配治疗的数据并不罕见。为避免因忽视分层与治疗效果之间的相互作用以及不依从导致的选择偏倚而获得误导性的汇总估计值，开发考虑不依从情况的检验统计量以检验各层间OR的同质性非常重要。在本文中，我们开发了五个渐近检验统计量，并采用蒙特卡罗模拟来评估这些统计量在各种情况下的性能。我们注意到，当层数适中或较大（≥5）时，加权最小二乘法（WLS）检验统计量可能会宽松。我们发现，WLS检验统计量的对数变换（LWLS）、LWLS检验统计量的平方根变换（SLWLS）以及LWLS检验统计量的费舍尔对数变换（LLWLS）在本文考虑的所有情况下，在I型错误方面表现良好。我们进一步发现，当层数较小或适中时，LWLS检验统计量的Z变换（ZLWLS）可能会宽松。我们注意到，对于层数较少的情况，LWLS检验统计量可能比其他统计量更可取，而对于层数适中或较大的情况，ZLWLS检验统计量可能是最佳的。最后，我们使用来自一项多危险因素干预试验的数据来说明这些检验统计量的使用。
