Matthews J N S, Badi N H
School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne, U.K.
Statistics Department, Benghazi University, Benghazi, Libya.
Stat Med. 2015 Aug 30;34(19):2681-94. doi: 10.1002/sim.6508. Epub 2015 Apr 14.
When the difference between treatments in a clinical trial is estimated by a difference in means, then it is well known that randomization ensures unbiassed estimation, even if no account is taken of important baseline covariates. However, when the treatment effect is assessed by other summaries, for example by an odds ratio if the outcome is binary, then bias can arise if some covariates are omitted, regardless of the use of randomization for treatment allocation or the size of the trial. We present accurate closed-form approximations for this asymptotic bias when important normally distributed covariates are omitted from a logistic regression. We compare this approximation with ones in the literature and derive more convenient forms for some of these existing results. The expressions give insight into the form of the bias, which simulations show is usable for distributions other than the normal. The key result applies even when there are additional binary covariates in the model.
当通过均值差异来估计临床试验中各治疗组之间的差异时，众所周知，即使不考虑重要的基线协变量，随机化也能确保无偏估计。然而，当通过其他汇总指标来评估治疗效果时，例如，如果结局是二元的，则通过比值比来评估，那么无论治疗分配是否采用随机化或试验规模大小，若遗漏某些协变量，就可能会产生偏差。当逻辑回归中遗漏重要的正态分布协变量时，我们给出了这种渐近偏差的精确闭式近似。我们将此近似与文献中的近似进行比较，并为其中一些现有结果推导了更方便的形式。这些表达式揭示了偏差的形式，模拟结果表明，该偏差形式适用于正态分布以外的其他分布。即使模型中存在额外的二元协变量，关键结果仍然适用。
