Estimating treatment effects using observation data often relies on the assumption of no unmeasured confounders. However, unmeasured confounding variables may exist in many real-world problems. It can lead to a biased estimation without incorporating the unmeasured confounding effect. To address this problem, this paper proposes a new mixed-effects joint modeling approach to identifying and estimating the OR function and the PS function in the presence of unmeasured confounders in longitudinal data settings. As a result, we can obtain the estimators of the average treatment effect and heterogeneous treatment effects. In our proposed setting, we allow interaction effects of the treatment and unmeasured confounders on the outcome. Moreover, we propose a new Laplacian-variant EM algorithm to estimate the parameters in the joint models. We apply the method to a real-world application from the CitieS-Health Barcelona Panel Study, in which we study the effect of short-term air pollution exposure on mental health.

翻译：利用观测数据估计处理效应通常依赖于不存在未测量混杂因素的假设。然而，在许多现实问题中可能存在未测量的混杂变量。若不考虑未测量混杂效应，则可能导致估计偏差。为解决此问题，本文提出一种新的混合效应联合建模方法，用于在纵向数据设置中存在未测量混杂因素的情况下识别和估计OR函数与PS函数。由此，我们可以获得平均处理效应和异质性处理效应的估计量。在我们提出的设置中，我们允许处理与未测量混杂因素对结果存在交互效应。此外，我们提出一种新的拉普拉斯变体EM算法来估计联合模型中的参数。我们将该方法应用于CitieS-Health Barcelona Panel Study的实际案例，研究短期空气污染暴露对心理健康的影响。