Magder Laurence S
Department of Epidemiology and Preventive Medicine, University of Maryland, Baltimore, Maryland 21201-1596, USA.
Control Clin Trials. 2003 Aug;24(4):411-21. doi: 10.1016/s0197-2456(03)00021-7.
Often in clinical trials, the primary outcome is binary and the impact of an intervention is summarized using risk ratios (RRs), odds ratios (ORs), or risk differences (RDs). It is typical that in such studies, the binary outcome variable is not observed for some study participants. When there is missing data, it is well known that analyses based on those participants with complete data can be biased unless it can be assumed that the probability of a missing outcome is unrelated to the value of the missing binary outcome (i.e., missing at random). Unfortunately, this assumption cannot be assessed with the data since the missing outcomes, by definition, are not observed. One approach to this problem is to perform a sensitivity analysis to see the degree to which conclusions based only on the complete data would be affected given various degrees of departure from the missing at random assumption. In this paper we provide researchers formulae for doing such a sensitivity analysis. We quantify the departure from the missing at random assumption with a parameter we call the "response probability ratio" (RPR). This is the ratio between the probability of a nonmissing outcome among those with one value of the binary outcome and the probability of a nonmissing outcome among those with the other value of the outcome. Then we provide simple formulae for the estimation of the RRs, ORs, and RDs given any specific values of the RPRs. In addition to being useful for sensitivity analyses, these formulae provide some insight into the conditions that are necessary for bias to occur. In particular, it can be seen that, under certain plausible assumptions, OR estimates based on participants with complete data will be asymptotically unbiased, even if the probability of missing outcome depends on both the treatment and the outcome.
在临床试验中，主要结局通常是二元的，干预措施的影响用风险比（RRs）、比值比（ORs）或风险差（RDs）来概括。在这类研究中，一些研究参与者未观察到二元结局变量是很常见的。当存在缺失数据时，众所周知，基于那些具有完整数据的参与者进行的分析可能会产生偏差，除非可以假设缺失结局的概率与缺失二元结局的值无关（即随机缺失）。不幸的是，由于定义上缺失的结局未被观察到，所以无法用这些数据来评估这个假设。解决这个问题的一种方法是进行敏感性分析，以了解在偏离随机缺失假设的不同程度下，仅基于完整数据得出的结论会受到何种程度的影响。在本文中，我们为研究人员提供了进行这种敏感性分析的公式。我们用一个我们称为“反应概率比”（RPR）的参数来量化偏离随机缺失假设的程度。这是二元结局具有一个值的人群中未缺失结局的概率与结局具有另一个值的人群中未缺失结局的概率之比。然后，我们给出了在RPR的任何特定值下估计RRs、ORs和RDs的简单公式。除了对敏感性分析有用外，这些公式还提供了一些对偏差发生所需条件的见解。特别是，可以看出，在某些合理的假设下，基于具有完整数据的参与者的OR估计将是渐近无偏的，即使缺失结局的概率取决于治疗和结局两者。
