Marginal structural models have been widely used in causal inference to estimate mean outcomes under either a static or a prespecified set of treatment decision rules. This approach requires imposing a working model for the mean outcome given a sequence of treatments and possibly baseline covariates. In this paper, we introduce a dynamic marginal structural model that can be used to estimate an optimal decision rule within a class of parametric rules. Specifically, we will estimate the mean outcome as a function of the parameters in the class of decision rules, referred to as a regimen-response curve. In general, misspecification of the working model may lead to a biased estimate with questionable causal interpretability. To mitigate this issue, we will leverage risk to assess "goodness-of-fit" of the 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.

翻译：边际结构模型已广泛应用于因果推断中，用于估计静态或预设治疗决策规则下的平均结局。该方法需要基于一组治疗序列及可能的基线协变量，对平均结局施加一个工作模型。本文提出一种动态边际结构模型，可用于在参数规则类中估计最优决策规则。具体而言，我们将平均结局估计为决策规则类中参数的函数，即治疗方案反应曲线。通常，工作模型的错误设定可能导致有偏估计，且其因果可解释性存疑。为解决这一问题，我们将利用风险来评估所施加工作模型的"拟合优度"。将反事实风险作为目标参数，并推导出逆概率加权和典型梯度以将其映射至观测数据。针对固定目标和数据依赖目标参数，给出了所得风险估计量的渐近性质。结果表明，当权重函数使用基于筛子的估计量进行估计时，逆概率加权估计量可具备有效性和渐近线性性。该方法在LS1研究中实施，用于估计帕金森病患者的治疗方案反应曲线。