Abstract: Case-cohort design, an outcome-dependent sampling design for censored survival data, is increasingly used in biomedical research. The development of asymptotic theory for a case-cohort design in the current literature primarily relies on counting process stochastic integrals. Such an approach, however, is rather limited and lacks theoretical justification for outcome-dependent weighted methods due to non-predictability. Instead of stochastic integrals, we derive asymptotic properties for case-cohort studies based on a general Z-estimation theory for semiparametric models with bundled parameters using empirical process theory. Both the Cox model and the additive hazards model with time-dependent covariates are considered.
Key words and phrases: Additive hazards model, bundled parameters, case-cohort study, Cox model, Donsker class, empirical process, Glivenko-Cantelli class, missing covariates, semiparametric estimation function, Z-estimation.