Targeted Data Adaptive Estimation of the Causal Dose-Response Curve
Targeted Data Adaptive Estimation of the Causal Dose-Response Curve
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DOI：
10.1515/jci-2012-0005
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发表时间：
2013-12-01
影响因子：
1.4
通讯作者：
Van der Laan, Mark J.
中科院分区：
文献类型：
--
作者：
Diaz, Ivan;Van der Laan, Mark J.
因果剂量-反应曲线的估计是统计学中的一个老问题。在非参数模型中，如果治疗是连续的，则剂量-反应曲线不是路径可微参数，并且没有ffiffi pn相容估计器可用。然而，用于估计剂量-反应曲线的候选算法的风险是路径可微参数，其一致和有效的估计是可能的。在这项工作中，我们回顾了风险的交叉验证的增广治疗逆概率加权估计(CV A-IPTW)，并提出了一个交叉验证的基于目标最小损失的估计(CV-TMLE)。在某些一致性和正则性条件下，这些估计量被证明是关于结果和治疗机制的初始估计量的一致和有效的。我们还提出了一种方法，使用这些估计的风险来从候选算法库中进行选择。这些选择器被证明是最优的，因为在一定的一致性条件下，它们在治疗和结果机制的估计量上与Oracle选择器渐近等价。由于CV-TMLE是一种替代估计量，因此它比CV-AIPTW对违反正性假设的经验更稳健。这一点以及CV-TMLE和CV-AIPTW之间的其他小样本大小差异在模拟研究中得到了探索。
Estimation of the causal dose-response curve is an old problem in statistics. In a non-parametric model, if the treatment is continuous, the dose-response curve is not a pathwise differentiable parameter, and no ffiffiffi pn-consistent estimator is available. However, the risk of a candidate algorithm for estimation of the dose-response curve is a pathwise differentiable parameter, whose consistent and efficient estimation is possible. In this work, we review the cross-validated augmented inverse probability of treatment weighted estimator (CV A-IPTW) of the risk and present a cross-validated targeted minimum loss-based estimator (CV-TMLE) counterpart. These estimators are proven consistent and efficient under certain consistency and regularity conditions on the initial estimators of the outcome and treatment mechanism. We also present a methodology that uses these estimated risks to select among a library of candidate algorithms. These selectors are proven optimal in the sense that they are asymptotically equivalent to the oracle selector under certain consistency conditions on the estimators of the treatment and outcome mechanisms. Because the CV-TMLE is a substitution estimator, it is more robust than the CV-AIPTW against empirical violations of the positivity assumption. This and other small sample size differences between the CV-TMLE and the CV-AIPTW are explored in a simulation study.