A New Correlation Measure for Interval‐Censored Failure Time Data and Application

Measuring the correlation between two random vectors is required and plays an important role in almost every scientific field and correspondingly many criteria have been proposed in the literature. In this paper, we investigate a new correlation measure and propose an empirical estimator for interval‐censored failure time data. The theoretical guarantee of the new measure and the asymptotic properties of the estimator are established and in particular, the estimator is shown to be consistent and asymptotically normally distributed. One main advantage of the new correlation is that it significantly reduces the computational burden compared to some existing criteria for high‐dimensional data. By using the new measure, a model‐free feature screening procedure is proposed and both sure screening property and rank consistency of the proposed approach are established. An extensive simulation study indicates that the screening procedure works well in practical situations and an illustration is provided.