Should we drop covariate cells with attrition problems?

It is well known that sample attrition can lead to inconsistent treatment effect estimators even in randomized control trials. Standard solutions to attrition problems either rely on strong assumptions on the attrition mechanisms or consider the estimation of bounds, which may be uninformative if attrition problems are severe. In this paper, we analyze strategies of focusing the analysis on subsets of the data with less observed attrition problems. We show that these strategies are asymptotically valid when the number of observations in each covariate cell goes to infinity. However, they can lead to important distortions when the number of observations per covariate cell is finite.