Extending the DeLong algorithm for comparing areas under correlated receiver operating characteristic curves with missing data

A nonparametric method proposed by DeLong et al in 1988 for comparing areas under correlated receiver operating characteristic curves is used widely in practice. However, the DeLong method as implemented in popular software quietly deletes individuals with any missing values, yielding potentially invalid and/or inefficient results. We simplify the DeLong algorithm using ranks and extend it to accommodate missing data by using a mixed model approach for multivariate data. Simulation results demonstrate the validity and efficiency of our procedure for data missing at random. We illustrate our proposed procedure in SAS, Stata, and R using the original DeLong data.