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Estimating the average treatment causal effect in clustered data ofteninvolves dealing with unmeasured cluster-specific confounding variables. Suchvariables may be correlated with the measured unit covariates and outcome. Whenthe correlations are ignored, the causal effect estimation can be biased. Byutilizing sufficient statistics, we propose an inverse conditional probabilityweighting (ICPW) method, which is robust to both (i) the correlation betweenthe unmeasured cluster-specific confounding variable and the covariates and(ii) the correlation between the unmeasured cluster-specific confoundingvariable and the outcome. Assumptions and conditions for the ICPW method arepresented. We establish the asymptotic properties of the proposed estimators.Simulation studies and a case study are presented for illustration.

Inverse Conditional Probability Weighting with Clustered Data in Causal Inference