The R-learner has been popular in causal inference as a flexible and efficient meta-learning approach for heterogeneous treatment effect estimation. In this article, we show the identifiability transition of the generalized R-learning framework from a binary treatment to continuous treatment. To resolve the non-identification issue with continuous treatment, we propose a novel identification strategy named T-identification, acknowledging the use of Tikhonov regularization rooted in the nonlinear functional analysis. Following the new identification strategy, we introduce an $\ell_2$-penalized R-learner framework to estimate the conditional average treatment effect with continuous treatment. The new R-learner framework accommodates modern, flexible machine learning algorithms for both nuisance function and target estimand estimation. Asymptotic properties are studied when the target estimand is approximated by sieve approximation, including general error bounds, asymptotic normality, and inference. Simulations illustrate the superior performance of our proposed estimator. An application of the new method to the medical information mart for intensive care data reveals the heterogeneous treatment effect of oxygen saturation on survival in sepsis patients.

中文翻译：

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使用连续处理实现条件平均处理效果的 R 学习器：T 识别、估计和推理

R-learner 作为一种灵活高效的元学习方法用于异质治疗效果估计，在因果推理中很受欢迎。在本文中，我们展示了广义 R 学习框架从二元处理到连续处理的可识别性转变。为了解决连续处理的非识别问题，我们提出了一种新的识别策略，称为 T 识别，承认使用植根于非线性泛函分析的 Tikhonov 正则化。遵循新的识别策略，我们引入了一个 $\ell_2$-penalized R-learner 框架来估计连续治疗的条件平均治疗效果。新的 R-learner 框架适应现代、灵活的机器学习算法，用于滋扰函数和目标估计。当目标估计量通过筛逼近来逼近时，研究渐近性质，包括一般误差界限、渐近正态性和推理。模拟说明了我们提出的估计器的优越性能。将新方法应用于重症监护数据的医疗信息市场，揭示了氧饱和度对脓毒症患者生存率的异质性治疗效果。