Unmeasured confounding and selection bias are often of concern in observational studies and may invalidate a causal analysis if not appropriately accounted for. Under outcome-dependent sampling, a latent factor that has causal effects on the treatment, outcome, and sample selection process may cause both unmeasured confounding and selection bias, rendering standard causal parameters unidentifiable without additional assumptions. Under an odds ratio model for the treatment effect, Li et al. 2022 established both proximal identification and estimation of causal effects by leveraging a pair of negative control variables as proxies of latent factors at the source of both confounding and selection bias. However, their approach relies exclusively on the existence and correct specification of a so-called treatment confounding bridge function, a model that restricts the treatment assignment mechanism. In this article, we propose doubly robust estimation under the odds ratio model with respect to two nuisance functions -- a treatment confounding bridge function and an outcome confounding bridge function that restricts the outcome law, such that our estimator is consistent and asymptotically normal if either bridge function model is correctly specified, without knowing which one is. Thus, our proposed doubly robust estimator is potentially more robust than that of Li et al. 2022. Our simulations confirm that the proposed proximal estimators of an odds ratio causal effect can adequately account for both residual confounding and selection bias under stated conditions with well-calibrated confidence intervals in a wide range of scenarios, where standard methods generally fail to be consistent. In addition, the proposed doubly robust estimator is consistent if at least one confounding bridge function is correctly specified.

中文翻译：

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混杂结果依赖抽样下的双重稳健近端因果推理

未测量的混杂和选择偏倚在观察性研究中经常受到关注，如果没有适当考虑，可能会使因果分析无效。在结果依赖抽样下，对治疗、结果和样本选择过程有因果影响的潜在因素可能会导致无法测量的混杂和选择偏差，从而在没有额外假设的情况下无法识别标准因果参数。在治疗效果的优势比模型下，Li 等人。2022 通过利用一对负控制变量作为混杂和选择偏差来源的潜在因素的代理，建立了近端识别和因果效应估计。然而，他们的方法完全依赖于所谓的治疗混淆桥函数的存在和正确规范，限制治疗分配机制的模型。在本文中，我们提出了在优势比模型下关于两个讨厌函数的双重稳健估计——一个治疗混杂桥函数和一个限制结果定律的结果混杂桥函数，这样我们的估计量是一致的且渐近正态，如果任何一个正确指定了桥功能模型，但不知道是哪一个。因此，我们提出的双重稳健估计器可能比 Li 等人的更稳健。2022. 我们的模拟证实，所提出的优势比因果效应的近端估计量可以充分考虑在规定条件下的残余混杂和选择偏差，并在广泛的情景中具有良好校准的置信区间，标准方法通常无法保持一致。此外，如果正确指定了至少一个混杂桥函数，则所提出的双重稳健估计器是一致的。