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Assessing the robustness of combining propensity theory and methods to assess the impact of unmeasured confounders on the estimation of causal effects
Keegan Korthauer, University of Wisconsin 
*David Nelson, VA Medical Center, University of Minnesota 
Siamak Noorbaloochi, VA Medical Center, University of Minnesota 

Keywords: propensity theory, missing confounders

Propensity methods can be effective in reducing confounder dimension and, thereby, simplifying the estimation of causal intervention effects. Application of these methods requires measurement of all relevant confounders. In observational studies it is common to know, or strongly suspect, that relevant confounders have not been measured. Several sensitivity analysis methods have been developed to assess the impact of an unmeasured confounder on the estimation of intervention effects. However, little theory has been developed assessing whether these sensitivity methods can be combined with propensity methods to simultaneously assess the impact of an unmeasured confounder and reduce the dimension of the measured confounders to simplify the overall estimation process.

We have shown that when the unmeasured and measured confounders are conditionally independent given intervention status these methods are readily combined. However, this condition is typically violated if the unmeasured and measured confounders are independent. We present results of simulations examining whether, in such a situation, combining propensity theory with missing confounder methods may be robust to violation of the conditional independence requirement. The scenarios examined in these simulation studies considered dichotomous outcomes, confounders, and interventions but the magnitudes of association between these variables are representative of those likely to be encountered in health services research and related fields.

In these simulation studies, we examined whether the conditional associations between the outcome and intervention conditional on the estimated propensity and the value of the unmeasured confounder tended to be equivalent to the underlying population level conditional association given the values of the observed covariates and the value of the unmeasured confounder. For the scenarios considered here combining propensity theory and methods for addressing unmeasured confounders were not substantively affected by violation of the conditional independence criteria.