Quantile residual life regression with longitudinal biomarker measurements for dynamic prediction

Residual life is of great interest to patients with life threatening disease. It is also important for clinicians who estimate prognosis and make treatment decisions. Quantile residual life has emerged as a useful summary measure of the residual life. It has many desirable features, such as robustness and easy interpretation. In many situations, the longitudinally collected biomarkers during patients' follow-up visits carry important prognostic value. In this work, we study quantile regression methods that allow for dynamic predictions of the quantile residual life, by flexibly accommodating the post-baseline biomarker measurements in addition to the baseline covariates. We propose unbiased estimating equations that can be solved via existing L1-minimization algorithms. The resulting estimators have desirable asymptotic properties and satisfactory finite sample performance. We apply our method to a study of chronic myeloid leukaemia to demonstrate its usefulness as a dynamic prediction tool.