Martingale and counting process techniques are applied to the problem of inference for general conditional hazard functions. This problem was first studied by Beran, who introduced a class of estimators for the conditional cumulative hazard and survival functions in the special case of time-independent covariates. Here the covariate can be time dependent; the classical i.i.d. assumptions are relaxed by replacing them with certain asymptotic stability assumptions, and models involving recurrent failures are included. This is done within the framework of a general nonparametric counting process regression model. Important examples of the model include right-censored survival data, semi-Markov processes, an illness-death process with duration dependence, and age-dependent birth and death processes.
"Inference for a Nonlinear Counting Process Regression Model." Ann. Statist. 18 (3) 1172 - 1187, September, 1990. https://doi.org/10.1214/aos/1176347745