论文标题
残留物的非线性回归:随时间变化和协变量的因果估计
Nonlinear Regression with Residuals: Causal Estimation with Time-varying Treatments and Covariates
论文作者
论文摘要
当存在时间变化的治疗效果和随时间变化的协变量时,标准回归调整会产生因果效应的不一致估计。宽松地说,问题是某些协变量是治疗后变量,因为它们可能会受到先前的治疗状况的影响,并且会导致治疗后变量会导致偏见。更确切地说,偏差是由于某些非共鸣的潜在变量引起的,这些变量在因果图中创建了山脉。我们称之为幻象的这些潜在变量不会损害因果效应的可识别性,但它们使天真的回归估计不一致。在此激励的情况下,我们问:我们如何修改回归方法,以便即使在幻象存在的情况下也要坚持?我们基于回归建模(线性,log-linear,Probit和Cox回归)开发了此设置的估计器,证明了合理的因果估计和合理的因果关系一致。尤其是,估算器是一个回归模型,可以简单地调整共线性,从而易于理解和使用标准回归软件实现。提出的估计量是参数G形式的实例,将遗传性的回归方法扩展到了几种规范的非线性模型。
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 a reasonable causal estimand. 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. The proposed estimators are instances of the parametric g-formula, extending the regression-with-residuals approach to several canonical nonlinear models.