McCandless Lawrence C, Gustafson Paul, Austin Peter C
Faculty of Health Sciences, Simon Fraser University, Canada.
Stat Med. 2009 Jan 15;28(1):94-112. doi: 10.1002/sim.3460.
In the analysis of observational data, stratifying patients on the estimated propensity scores reduces confounding from measured variables. Confidence intervals for the treatment effect are typically calculated without acknowledging uncertainty in the estimated propensity scores, and intuitively this may yield inferences, which are falsely precise. In this paper, we describe a Bayesian method that models the propensity score as a latent variable. We consider observational studies with a dichotomous treatment, dichotomous outcome, and measured confounders where the log odds ratio is the measure of effect. Markov chain Monte Carlo is used for posterior simulation. We study the impact of modelling uncertainty in the propensity scores in a case study investigating the effect of statin therapy on mortality in Ontario patients discharged from hospital following acute myocardial infarction. Our analysis reveals that the Bayesian credible interval for the treatment effect is 10 per cent wider compared with a conventional propensity score analysis. Using simulations, we show that when the association between treatment and confounders is weak, then this increases uncertainty in the estimated propensity scores. Bayesian interval estimates for the treatment effect are longer on average, though there is little improvement in coverage probability. A novel feature of the proposed method is that it fits models for the treatment and outcome simultaneously rather than one at a time. The method uses the outcome variable to inform the fit of the propensity model. We explore the performance of the estimated propensity scores using cross-validation.
在观察性数据分析中，根据估计的倾向得分对患者进行分层可减少测量变量带来的混杂。治疗效果的置信区间通常在不考虑估计倾向得分不确定性的情况下计算，直观地讲，这可能会得出虚假精确的推断。在本文中，我们描述了一种将倾向得分建模为潜在变量的贝叶斯方法。我们考虑具有二分治疗、二分结局和测量混杂因素的观察性研究，其中对数比值比是效应的度量。马尔可夫链蒙特卡罗用于后验模拟。我们在一项调查他汀类药物治疗对安大略省急性心肌梗死后出院患者死亡率影响的案例研究中，研究了对倾向得分建模不确定性的影响。我们的分析表明，与传统倾向得分分析相比，治疗效果的贝叶斯可信区间宽10%。通过模拟，我们表明当治疗与混杂因素之间的关联较弱时，这会增加估计倾向得分的不确定性。治疗效果的贝叶斯区间估计平均更长，不过覆盖概率几乎没有改善。所提出方法的一个新颖特点是它同时拟合治疗和结局模型，而不是一次拟合一个。该方法使用结局变量来指导倾向模型的拟合。我们使用交叉验证来探索估计倾向得分的性能。
