Pham Cuong T, Baer Benjamin R, Ertefaie Ashkan
Department of Biostatistics and Computational Biology, University of Rochester Medical Center, Rochester, NY, 14620, United States.
School of Mathematics and Statistics, University of St Andrews, St Andrews, KY16 9SS, Scotland.
Biometrics. 2025 Apr 2;81(2). doi: 10.1093/biomtc/ujaf066.
In the framework of dynamic marginal structural models, regimen-response curve is a function that describes the relation between the mean outcome and the parameters in the class of decision rules. The modeling choice of the regimen-response curve is crucial in constructing an optimal regime, as a misspecified model can lead to a biased estimate with questionable causal interpretability. However, the existing literature lacks methods to evaluate and compare different working models. To address this problem, we will leverage risk to assess the "goodness-of-fit" of an imposed working model. We consider the counterfactual risk as our target parameter and derive inverse probability weighting and canonical gradients to map it to the observed data. We provide asymptotic properties of the resulting risk estimators, considering both fixed and data-dependent target parameters. We will show that the inverse probability weighting estimator can be efficient and asymptotic linear when the weight functions are estimated using a sieve-based estimator. The proposed method is implemented on the LS1 study to estimate a regimen-response curve for patients with Parkinson's disease.
在动态边际结构模型的框架下，治疗方案-反应曲线是一种描述平均结局与决策规则类中的参数之间关系的函数。治疗方案-反应曲线的建模选择对于构建最优治疗方案至关重要，因为错误指定的模型可能导致有偏差的估计，其因果解释性也存在问题。然而，现有文献缺乏评估和比较不同工作模型的方法。为了解决这个问题，我们将利用风险来评估所施加工作模型的“拟合优度”。我们将反事实风险视为目标参数，并推导逆概率加权和规范梯度以将其映射到观测数据。我们给出了所得风险估计量的渐近性质，同时考虑了固定的和依赖于数据的目标参数。我们将表明，当使用基于筛法的估计量来估计权重函数时，逆概率加权估计量可以是有效的且渐近线性的。所提出的方法在LS1研究中得以实施，以估计帕金森病患者的治疗方案-反应曲线。
