SUFFICIENT DIMENSION REDUCTION WITH SIMULTANEOUS ESTIMATION OF EFFECTIVE DIMENSIONS FOR TIME-TO-EVENT DATA

When researchers do not have enough scientific knowledge to assume a particular regression model, suficient dimension reduction is a exible yet parsimonious nonparametric framework to study how covariates are associated with an outcome. We propose a novel estimator of low-dimensional composite scores that summarizes the contribution of covariates on a right-censored survival outcome. The proposed estimator determines the degree of dimension reduction adaptively from the data; it estimates the structural dimension, the central subspace, and a rate-optimal smoothing bandwidth parameter simultaneously from a single criterion. The methodology is formulated in a counting process framework. Furthermore, the estimation is free of the inverse probability weighting employed in existing methods, which often leads to instability in small samples. We derive the large-sample properties for the estimated central subspace with a data-adaptive structural dimension and bandwidth. The estimation can be implemented easily using a forward selection algorithm; this implementation is justified by the asymptotic convexity of the criterion in working dimensions. Numerical simulations and two real examples are given to illustrate the proposed method.