  Causal inference in observational studies can be challenging when confounders
are subject to missingness. Generally, the identification of causal effects is
not guaranteed even under restrictive parametric model assumptions when
confounders are missing not at random. To address this, We propose a general
framework to establish the identification of causal effects when confounders
are subject to treatment-independent missingness, which means that the missing
data mechanism is independent of the treatment, given the outcome and possibly
missing confounders. We give special consideration to commonly-used models for
continuous and binary outcomes and provide counterexamples when identification
fails. For estimation, we provide a weighted estimation equation estimating
method for model parameters and purpose three estimators for the average causal
effect based on the estimated models. We evaluate the finite-sample performance
of the estimators via simulations. We further illustrate the proposed method
with real data sets from the National Health and Nutrition Examination Survey.
