Asymptotic separability in sensitivity analysis
Asymptotic separability in sensitivity analysis
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DOI：
10.1111/1467-9868.00249
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发表时间：
2000-01-01
影响因子：
5.8
通讯作者：
Rosenbaum, PR
中科院分区：
文献类型：
--
作者：
Gastwirth, JL;Krieger, AM;Rosenbaum, PR
在一项观察性研究中，通过使用观察到的治疗前协变量将每例接受治疗的受试者与几例未接受治疗的对照组进行匹配，敏感性分析询问未观察到的协变量导致的隐藏偏倚如何改变结论。灵敏度分析所需的边界是优化问题的解。一般来说，这个优化问题是不可分离的，在这个意义上，人们不能通过在每个匹配集合中执行单独的优化并组合结果来找到所需的最佳值。然而，我们证明了这个优化问题是渐进可分的，因此当有许多匹配集时，可以在每个匹配集中执行单独的优化，并将结果组合起来，以产生正确的最佳值，误差可以忽略不计。当Wilcoxon秩和检验或Hodges-Lehmann对齐秩检验应用于与多个对照匹配时，这是正确的。数值计算表明，渐近近似表现良好，只有10个匹配集。在秩和检验的情况下，给出一个包含可分解的表。使用此表，仅需简单的运算即可进行敏感度分析。该方法还提供估计值，如Hodges-Lehmann估计值，以及与秩检验相关的置信区间。该方法在一项关于美国高中辍学及其对认知测试成绩影响的研究中得到了说明。
In an observational study in which each treated subject is matched to several untreated controls by using observed pretreatment covariates, a sensitivity analysis asks how hidden biases due to unobserved covariates might alter the conclusions. The bounds required for a sensitivity analysis are the solution to an optimization problem. In general, this optimization problem is not separable, in the sense that one cannot find the needed optimum by performing a separate optimization in each matched set and combining the results. We show, however, that this optimization problem is asymptotically separable, so that when there are many matched sets a separate optimization may be performed in each matched set and the results combined to yield the correct optimum with negligible error. This is true when the Wilcoxon rank sum test or the Hodges-Lehmann aligned rank test is applied in matching with multiple controls. Numerical calculations show that the asymptotic approximation performs well with as few as 10 matched sets. In the case of the rank sum test, a table is given containing the separable solution. With this table, only simple arithmetic is required to conduct the sensitivity analysis. The method also supplies estimates, such as the Hodges-Lehmann estimate, and confidence intervals associated with rank tests. The method is illustrated in a study of dropping out of US high schools and the effects on cognitive test scores.