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.

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