Abstract: Canonical correlation analysis (CCA) is widely applied in statistical analysis of multivariate data to find associations between two sets of multidimensional variables. However, we often cannot use CCA directly for survival data or their monotone transformations, owing to right-censoring in the data. In this paper, we propose a new robust rank CCA (RRCCA) method based on Kendall's τ correlation, and adjust it to deal with multivariate survival data, without requiring any model assumptions. Owing to the nature of rank correlation, the RRCCA is invariant against monotone transformations of the data. We establish the estimation consistency of the RRCCA approach under weak conditions. Simulation studies demonstrate the superior performance of the RRCCA in terms of estimation accuracy and empirical power. Lastly, we demonstrate the proposed method by applying it to Stanford heart transplant data.

Key words and phrases: Canonical correlation analysis, inverse probability of censoring weighting, Kendall's τ correlation, right-censoring.