A novel semiparametric approach to nonignorable missing data by catching covariate marginal information

Nonignorable missing data problems are challenging because of the parameter identifiability issue. Existing methods designed for handling nonignorable missing data often struggle to fully utilize covariate marginal information, leading to potential efficiency losses. We propose a novel approach that leverages both a logistic propensity score model and a semiparametric proportional likelihood ratio model (SPLRM) for the observed data. Our approach generally does not require instrumental variables or shadow variables, leading to improved identifiability in most scenarios. In the identifiable case, we use the density-ratio-model-based empirical likelihood to catch the covariate distribution information and estimate the target parameter. The proposed estimator is shown to be asymptotically normal and semiparametric efficient. In the exception case, we conduct a sensitivity analysis by making full use of the marginal covariate information. Our numerical results indicate that compared with existing estimators, the proposed estimator is more reliable and more robust to model mis-specification.