Nonignorable Missing Data, Single Index Propensity Score and Profile Synthetic Distribution Function

In missing data problems, missing not at random is difficult to handle since the response probability or propensity score is confounded with the outcome data model in the likelihood. Existing works often assume the propensity score is known up to a finite dimensional parameter. We relax this assumption and consider an unspecified single index model for the propensity score. A pseudo-likelihood based on the complete data is constructed by profiling out a synthetic distribution function that involves the unknown propensity score. The pseudo-likelihood gives asymptotically normal estimates. Simulations show the method compares favorably with existing methods.

Automated summary

In this study, we address the challenge of non-random missing data by considering an unspecified single index model for the propensity score and constructing a pseudo-likelihood based on complete data. The pseudo-likelihood provides asymptotically normal estimates and simulations demonstrate its favorable performance compared to existing methods.