A general semiparametric Z-estimation approach for case-cohort studies

TL;DR

This paper introduces a new Z-estimation framework for case-cohort studies, providing a more general and theoretically justified approach for analyzing censored survival data with outcome-dependent sampling.

Contribution

It develops a semiparametric Z-estimation method using empirical processes, extending asymptotic theory beyond counting process integrals for case-cohort designs.

Findings

Provides asymptotic properties for Cox and additive hazards models

Enables outcome-dependent weighted methods with theoretical support

Broadens the applicability of semiparametric inference in survival analysis

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 modern empirical processes. Both the Cox model and the additive hazards model with time-dependent covariates are considered.