Gustafson P, McCandless L C, Levy A R, Richardson S
Department of Statistics, University of British Columbia, Vancouver, British Columbia, Canada.
Biometrics. 2010 Dec;66(4):1129-37. doi: 10.1111/j.1541-0420.2009.01377.x.
We examine situations where interest lies in the conditional association between outcome and exposure variables, given potential confounding variables. Concern arises that some potential confounders may not be measured accurately, whereas others may not be measured at all. Some form of sensitivity analysis might be employed, to assess how this limitation in available data impacts inference. A Bayesian approach to sensitivity analysis is straightforward in concept: a prior distribution is formed to encapsulate plausible relationships between unobserved and observed variables, and posterior inference about the conditional exposure-disease relationship then follows. In practice, though, it can be challenging to form such a prior distribution in both a realistic and simple manner. Moreover, it can be difficult to develop an attendant Markov chain Monte Carlo (MCMC) algorithm that will work effectively on a posterior distribution arising from a highly nonidentified model. In this article, a simple prior distribution for acknowledging both poorly measured and unmeasured confounding variables is developed. It requires that only a small number of hyperparameters be set by the user. Moreover, a particular computational approach for posterior inference is developed, because application of MCMC in a standard manner is seen to be ineffective in this problem.
我们研究在给定潜在混杂变量的情况下，结果变量与暴露变量之间的条件关联情况。人们担心一些潜在的混杂因素可能无法准确测量，而另一些则可能根本未被测量。可能会采用某种形式的敏感性分析，以评估可用数据中的这种局限性如何影响推断。贝叶斯敏感性分析方法在概念上很直接：形成一个先验分布来概括未观察到的变量与观察到的变量之间的合理关系，然后对条件暴露 - 疾病关系进行后验推断。然而，在实践中，以现实且简单的方式形成这样的先验分布可能具有挑战性。此外，开发一个能有效处理由高度未识别模型产生的后验分布的伴随马尔可夫链蒙特卡罗（MCMC）算法可能很困难。在本文中，我们开发了一种简单的先验分布，用于承认测量不佳和未测量的混杂变量。它只要求用户设置少量的超参数。此外，还开发了一种用于后验推断的特定计算方法，因为在这个问题中，以标准方式应用MCMC被认为是无效的。
