Parsimonious covariate selection with censored outcomes

A new objective methodology is proposed to select the parsimonious set of important covariates that are associated with a censored outcome variable Y; the method simplifies to accommodate uncensored outcomes. Covariate selection proceeds in an iterated forward manner and is controlled by the pre-chosen upper bound for the number of covariates to be selected and the global false selection rate and level. A sequence of working regression models for the event (Y≤y) given a covariate set is fit among subjects not censored before y and the corresponding process (through y) of conditional prediction error estimated; the direction and magnitude of covariate effects can arbitrarily change with y. The newly proposed adequacy measure for the covariate set is the slope coefficient resulting from a regression (with no intercept) between the baseline prediction error process for the intercept-only model and that process corresponding to the covariate set. Under quite general conditions on the censoring variable, the methods are shown to asymptotically control the false selection rate at the nominal level while consistently ranking covariate sets which permits recruitment of all important covariates from those available with probability tending to 1. A simulation study confirms these analytical results and compares the proposed methods to recent competitors. Two real data illustrations are provided.