Super-efficient estimation of future conditional hazards based on time-homogeneous high-quality marker information

SummaryWe introduce a new concept for forecasting future events based on marker information. The model is developed in the nonparametric counting process setting under the assumptions that the marker is of so-called high quality and with a time-homogeneous conditional distribution. Despite the model having nonparametric parts, it is established herein that it attains a parametric rate of uniform consistency and uniform asymptotic normality. In usual nonparametric scenarios, reaching such a fast convergence rate is not possible, so one can say that the proposed approach is super-efficient. These theoretical results are employed in the construction of simultaneous confidence bands directly for the hazard rate. Extensive simulation studies validate and compare the proposed methodology with the joint modelling approach and illustrate its robustness for mild violations of the assumptions. Its use in practice is illustrated in the computation of individual dynamic predictions in the context of primary biliary cirrhosis of the liver.