Statistical inferences for missing response problems based on modified empirical likelihood

In this paper, we advance the application of empirical likelihood (EL) for missing response problems. Inspired by remedies for the shortcomings of EL for parameter hypothesis testing, we modify the EL approach used for statistical inference on the mean response when the response is subject to missing behavior. We propose consistent mean estimators, and associated confidence intervals. We extend the approach to estimate the average treatment effect in causal inference settings. We detail the analogous estimators for average treatment effect, prove their consistency, and example their use in estimating the average effect of smoking on renal function of the patients with atherosclerotic renal-artery stenosis and elevated blood pressure, chronic kidney disease, or both. Our proposed estimators outperform the historical mean estimators under missing responses and causal inference settings in terms of simulated relative RMSE and coverage probability on average.