Estimation of the mean of a K-sample U-statistic with missing outcomes and auxiliaries

We propose estimators of the mean of a K-sample U-statistic when data on the outcomes of interest are missing in some sampled units and auxiliary variables are available in the entire sample. The proposed estimators exploit the information available in the auxiliaries without requiring assumptions about the joint distribution of the auxiliaries and outcomes. The properties of the proposed estimators are derived as a consequence of general results on efficient semiparametric estimation of the mean of a K-sample U-statistic with missing at random outcomes, observed auxiliary variables and known missingness probabilities. We illustrate the methods with the estimation of the area under a receiver operating characteristic curve when the biomarker data are observed only in subsamples of the diseased and healthy subjects.