Schmoor C, Schumacher M
Institute of Medical Biometry and Informatics, University of Freiburg, Germany.
Stat Med. 1997;16(1-3):225-37. doi: 10.1002/(sici)1097-0258(19970215)16:3<225::aid-sim482>3.0.co;2-c.
When analysing the survival of patients in comparative randomized clinical trials using the Cox proportional hazards model, important prognostic factors may be included for the adjustment of the treatment effect. In this paper we examine two of the most common misspecifications of the model: (i) an important prognostic factor is omitted from the analysis; and (ii) an important prognostic factor originally present on continuous scale is included in categorized form. Both situations may emerge from the occurrence of missing values. We investigate the properties of the maximum partial likelihood estimator of the treatment effect under this kind of misspecification. The estimate of the treatment effect is found to be asymptotically biased toward zero. For its asymptotic variance we obtain a quantity with the so-called 'sandwich' structure. Thus, variance estimation by the inverse of the second-order derivative of the likelihood is not consistent. The magnitude of overestimation or underestimation is evaluated numerically for specific settings. The precision of the treatment effect estimate under covariate omission or categorization is compared with the precision of the estimate in the correct and not misspecified model. It turns out that correct adjustment does not lead to a higher precision of the treatment effect estimate, but due to the resulting underestimation, covariate omission or categorization lead to loss of power of the test of no treatment effect.
在使用Cox比例风险模型分析比较随机临床试验中患者的生存情况时，可能会纳入重要的预后因素以调整治疗效果。在本文中，我们研究了该模型最常见的两种错误设定：（i）分析中遗漏了一个重要的预后因素；（ii）原本以连续尺度呈现的一个重要预后因素以分类形式纳入。这两种情况都可能因缺失值的出现而产生。我们研究了在这种错误设定下治疗效果的最大偏似然估计量的性质。发现治疗效果的估计值在渐近意义上偏向于零。对于其渐近方差，我们得到了一个具有所谓“三明治”结构的量。因此，通过似然函数二阶导数的逆来进行方差估计是不一致的。针对特定设置，对高估或低估的程度进行了数值评估。将协变量遗漏或分类情况下治疗效果估计的精度与正确且未错误设定模型中估计的精度进行了比较。结果表明，正确的调整并不会导致治疗效果估计具有更高的精度，但由于由此产生的低估，协变量遗漏或分类会导致无治疗效果检验的功效丧失。
