Partial sufficient dimension reduction on additive rates model for recurrent event data with high-dimensional covariates

Recurrent event data with an additive marginal rates function have been extensively studied in the literature. The existing statistical inference, however, faces the difficulty with high-dimensional covariates due to “curse of dimensionality”. Examples include gene expression and single nucleotide polymorphism data which have revolutionized our understanding of disease such as cancer recurrence. In this paper, a technique of partial sufficient dimension reduction is applied to an additive rates model for recurrent event data. A two-step procedure is proposed to estimate parameters. First, partial sufficient dimension reduction is used to estimate the basis of the partial central subspace and the structural dimension. Then the second step estimates the baseline and the regression function of covariates based on the estimated partial central subspace using the average surface method. Simulation is performed to confirm and assess the theoretical findings, and an application on a set of chronic granulomatous disease data is demonstrated.