Journal of Advanced Statistics

Download PDF (591 KB) PP. 58 - 70 Pub. Date: December 1, 2018

DOI: 10.22606/jas.2018.34002

• Qiqing Yu^*
  Department of Mathematical Sciences, SUNY, Binghamton, NY 13902, USA
• Qinggang Diao
  Department of Mathematical Sciences, SUNY, Binghamton, NY 13902, USA

The semi-parametric estimation under the proportional hazards (PH) model with a linearly time-dependent covariates and with interval-censored data has not been investigated before. The partial likelihood approach does not work and one has to use the generalized likelihood function (GLF). There is a challenge in this problem. The GLF must be in the form of the baseline hazard function, rather than the baseline survival function as in the PH model with time-independent covariates, and a feasible way to specify the hazard function is a piece-wise constant function. However, several naive ways do not yield a consistent estimator. We propose proper modifications of the GLF. Simulation results suggest that our method works. The generalization to other types of time-dependent covariates is also discussed.

Cox’s model, time-dependent covariates, modified likelihood function, semi-parametric MLE.

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