Quantile regression for competing risks data from stratified case-cohort studies: an induced-smoothing approach

A case-cohort design offers an economical way of investigating an association between exposure variables and risks of disease outcomes compared to a large-scale full cohort study. A stratified sampling in such designs based on the information available for the entire cohort is often considered for improving efficiencies of estimators. In this paper, we consider fitting censored quantile regression models for competing risks data arising from stratified case-cohort designs. We model quantiles for cumulative incidence functions that provide desirable interpretation for competing risks data and flexible ways of assessing covariates effects. For estimation of regression parameters, we consider weighted estimating equations with two-types of weights: the inverses of censoring probabilities and sampling probabilities to account for censoring in competing risks data and biased features in stratified case-cohort samplings, respectively. An induced smoothing approach is applied to obtain computationally more reliable estimates. The resulting estimating functions are smooth in regression parameters, so standard numerical algorithms for point estimation can be readily applied and variances can be estimated via a closed-form expression or computationally efficient resampling method. An iterative algorithm is proposed to simultaneously estimate regression parameters and their variances. Asymptotic properties of the proposed estimators are established. The finite sample properties of the proposed estimators are investigated through extensive simulation studies. They perform reasonably well under practical settings considered. The proposed methods are illustrated with Hodgkin's disease data.