Standard regression adjustment gives inconsistent estimates of causal effects when there are time-varying treatment effects and time-varying covariates. Loosely speaking, the issue is that some covariates are post-treatment variables because they may be affected by prior treatment status, and regressing out post-treatment variables causes bias. More precisely, the bias is due to certain non-confounding latent variables that create colliders in the causal graph. These latent variables, which we call phantoms, do not harm the identifiability of the causal effect, but they render naive regression estimates inconsistent. Motivated by this, we ask: how can we modify regression methods so that they hold up even in the presence of phantoms? We develop an estimator for this setting based on regression modeling (linear, log-linear, probit and Cox regression), proving that it is consistent for the causal effect of interest. In particular, the estimator is a regression model fit with a simple adjustment for collinearity, making it easy to understand and implement with standard regression software. From a causal point of view, the proposed estimator is an instance of the parametric g-formula. Importantly, we show that our estimator is immune to the null paradox that plagues most other parametric g-formula methods.
翻译:标准回归调整给出了在有时间变化的治疗效果和时间变化的共变时的因果关系的不一致性估计。 粗略地说, 问题在于有些共变是后处理变量, 因为他们可能受到先前治疗状况的影响, 而后退则造成偏差。 更准确地说, 偏差是由于某些不固定的潜在变量造成的, 在因果图中产生相撞效应。 这些潜在变量, 我们称之为幻影, 并不损害因果关系的可识别性, 但是它们使天真回归估计不一致。 受此影响, 我们问: 我们如何能够修改回归方法, 使它们在出现幻影时也能坚持下去? 我们为这一设置开发了一个基于回归模型( 线性、 线性线性线性、 probit 和 Cox 回归) 的估算符, 证明它符合因果效应。 具体地说, 估计值是一种回归模型, 适合简单的对因果关系的调整, 使得它容易理解和实施标准回归软件。 我们问: 我们如何修改回归方法, 从一个因果点上, 我们的估算模型是其它的估量模型。