Time-dependent concordance index for prediction model of interval-censored competing risk data

Diverse measures have been proposed to assess the discriminative ability of prognostic survival models. In this paper, we consider a C-index and a time-dependent C-index to evaluate the prognostic models of interval-censored competing risk data where patients are at risk of several terminal events and the occurrence of an event is declared only at the sequential observation times. In this article, two approaches are proposed to reflect the effect of competing events on discriminating the occurrence of event of interest in the context of interval censored data. The first approach is an imputation method using the conditional occurrence probability for including incomparable pairs. The second one is based on the cumulative incidence function directly calculated from the prognostic model. Furthermore, to consider the covariate-dependent censoring, an inverse probability of censoring weighting (IPCW) technique is employed. A simulation study is performed to compare those estimators under several scenarios. We apply the suggested methodology to two AIDS data sets to evaluate the predictive accuracy of a prognostic risk score.