In observational studies, potential confounders may distort the causal relationship between an exposure and an outcome. However, under some conditions, a causal dose–response curve can be recovered by using the G ‐computation formula. Most classical methods for estimating such curves when the exposure is continuous rely on restrictive parametric assumptions, which carry significant risk of model misspecification. Non‐parametric estimation in this context is challenging because in a non‐parametric model these curves cannot be estimated at regular rates. Many available non‐parametric estimators are sensitive to the selection of certain tuning parameters, and performing valid inference with such estimators can be difficult. We propose a non‐parametric estimator of a causal dose–response curve known to be monotone. We show that our proposed estimation procedure generalizes the classical least squares isotonic regression estimator of a monotone regression function. Specifically, it does not involve tuning parameters and is invariant to strictly monotone transformations of the exposure variable. We describe theoretical properties of our proposed estimator, including its irregular limit distribution and the potential for doubly robust inference. Furthermore, we illustrate its performance via numerical studies and use it to assess the relationship between body mass index and immune response in human immunodeficiency virus vaccine trials.

中文翻译：

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因果等渗回归


在观察性研究中，潜在的混杂因素可能会扭曲暴露与结果之间的因果关系。然而，在某些情况下，可以通过使用G计算公式来恢复因果剂量反应曲线。当暴露连续时估计此类曲线的大多数经典方法都依赖于限制性参数假设，这会带来模型错误指定的重大风险。在这种情况下，非参数估计具有挑战性，因为在非参数模型中，这些曲线无法以常规速率估计。许多可用的非参数估计器对某些调整参数的选择很敏感，并且使用此类估计器执行有效的推理可能很困难。我们提出了一种已知单调的因果剂量反应曲线的非参数估计量。我们表明，我们提出的估计过程概括了单调回归函数的经典最小二乘等渗回归估计器。具体来说，它不涉及调整参数，并且对于曝光变量的严格单调变换是不变的。我们描述了我们提出的估计器的理论特性，包括其不规则极限分布和双鲁棒推理的潜力。此外，我们通过数值研究说明了其性能，并用它来评估人类免疫缺陷病毒疫苗试验中体重指数与免疫反应之间的关系。