Treatment effect identification using two-level designs with partially ignorable missing data

. These data often have two characteristics: (a) missing in the framework of counterfactual outcomes; (b) missing responses arising from dropouts. One challenge is to identify the treatment effect in three-way arrays of outcomes with missing data.Thus, this paper proposes a novel method, PIM estimator (PIME), for inferring the differential effect of treatment. This method aims to estimate the average treatment effect using the three-way outcome array of a two-level design. This method can identify the selection bias and quantify it with the difference in outcome means between complete and incomplete cases. With the sensitivity analysis of dropout fractions, the results suggest there exists a minimum point of the upper bound of the difference estimation with the specified models. The results with real applications show that the proposed method is efficient for the treatment effect estimation. The proposed method was compared with the related methods (with dropouts imputed or removed). The results indicate that patients with higher blood glucose levels are more likely to drop out than the others.