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We propose a two-stage estimation procedure for a copula-based model with semi-competing risks data, where the non-terminal event is subject to dependent censoring by the terminal event, and both events are subject to independent censoring. With a copula-based model, the marginal survival functions of individual event times are specified by semiparametric transformation models, and the dependence between the bivariate event times is specified by a parametric copula function. For the estimation procedure, in the first stage, the parameters associated with the marginal of the terminal event are estimated using only the corresponding observed outcomes, and in the second stage, the marginal parameters for the non-terminal event time and the copula parameter are estimated together via maximizing a pseudo-likelihood function based on the joint distribution of the bivariate event times. We derived the asymptotic properties of the proposed estimator and provided an analytic variance estimator for inference. Through simulation studies, we showed that our approach leads to consistent estimates with less computational cost and more robustness than the one-stage procedure developed in Chen (2012), where all parameters were estimated simultaneously. In addition, our approach demonstrates more desirable finite-sample performances over another existing two-stage estimation method proposed in Zhu et al. (2021). An R package PMLE4SCR is developed to implement our proposed method.
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Estimation of the Cumulative Incidence Function under multiple dependent and independent censoring mechanisms
Competing risks occur in a time-to-event analysis in which a patient can experience one of several types of events. Traditional methods for handling competing risks data presuppose one censoring process, which is assumed to be independent. In a controlled clinical trial, censoring can occur for several reasons: some independent, others dependent. We propose an estimator of the cumulative incidence function in the presence of both independent and dependent censoring mechanisms. We rely on semi-parametric theory to derive an augmented inverse probability of censoring weighted (AIPCW) estimator. We demonstrate the efficiency gained when using the AIPCW estimator compared to a non-augmented estimator via simulations. We then apply our method to evaluate the safety and efficacy of two anti-HIV regimens in a randomized trial conducted by the AIDS Clinical Trial Group, ACTG A5095.
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- Award ID(s):
- 1854934
- PAR ID:
- 10357269
- Date Published:
- Journal Name:
- Lifetime data analysis
- Volume:
- 24
- Issue:
- 2
- ISSN:
- 1572-9249
- Page Range / eLocation ID:
- 201–223
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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