SPAJoint: A Multivariate Saddlepoint Approximation for Time-to- Event and Response Joint Analysis

Time-to-event and response endpoints are typical phenotypes in association studies that often exhibit stochastic correlation within the same individual. However, current analytic methods do not take the inherent correlation into account. Separate or fixed-connected endpoints assumptions can yield unreliable and prejudiced outcomes. Saddlepoint approximation is commonly used in association analysis to calibrate the type I error rate, but it is mostly applied in the univariate domain. Applying binary saddlepoint approximation to analyze joint models poses significant technical challenges. The bivariate saddlepoint approximation, considering natural correlations, necessitates intricate mathematical derivations. Therefore, we propose the a multivariate saddlepoint approximation method SPAJoint for time-to-event and response joint analysis, which constructs a joint model and applies binary saddlepoint approximation to calibrate test statistics, and the experimental results demonstrate that SPAJoint can control the type I error rate and more accurately identify genomic variants associated with multiple endpoints. The SPAJoint method incorporates random effects using the generalized linear mixed model to account for the correlation between time-to-event and tumour response. Bivariate saddlepoint approximation is utilized to calibrate test statistics for improved accuracy. By examining bladder cancer, kidney cancer, and lung cancer, we demonstrate that SPAJoint effectively manages type I error rates.