There is a paper on the concordance statistic for competing risks models: Concordance for prognostic models with competing risks | Biostatistics | Oxford Academic. The authors themselves provided R code in the supplemental material of the paper: Supplementary material to “Concordance for prognostic models with competing risks”. Another person has also developed an R package for this calculation based upon the paper mentioned above: R: Concordance index in the Presence of Competing Risks. An issue to note is that independence of observations was assumed in the paper. Therefore, this method is not applicable in the analysis of clustered data with competing risks. ... View more