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