Consistency of The MMGLE under the piecewise proportional hazards models with interval-censored data

ABSTRACT

Wong et al. [(2018), ‘Piece-wise Proportional Hazards Models with Interval-censored Data’, Journal of Statistical Computation and Simulation, 88, 140–155] studied the piecewise proportional hazards (PWPH) model with interval-censored (IC) data under the distribution-free set-up. It is well known that the partial likelihood approach is not applicable for IC data, and Wong et al. (2018) showed that the standard generalised likelihood approach does not work either. They proposed the maximum modified generalised likelihood estimator (MMGLE) and the simulation results suggest that the MMGLE is consistent. We establish the consistency and asymptotically normality of the MMGLE.

KEYWORDS:

• Cox's model
• time-dependent covariates
• semi-parametric MLE
• consistency
• asymptotic normality

AMS 1991 SUBJECT CLASSIFICATIONS:

• Primary: 62 G07
• Secondary: 62 J99

Acknowledgments

The authors thank the editor, an associate editor and two referees for their invaluable comments.

Disclosure statement

No potential conflict of interest was reported by the authors.