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The Lehmann Model with Time-dependent Covariates |
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| Authors: | Qiqing Yu George Y C Wong Michael P Osborne Yuting Hsu Xiaosong Ai |
| Institution: | 1. Department of Mathematical Sciences, SUNY, Binghamton, New York, USAqyu@math.binghamton.edu;3. Department of Integrative Medicine, Beth Israel Medical Center, New York, New York, USA;4. Continuum Cancer Centers of New York, Beth Israel Medical Center, New York, New York, USA;5. Department of Computer and Mathematical Sciences, Penn State Harrisburg, Harrisburg, Pennsylvania, USA;6. Department of Mathematical Sciences, SUNY, Binghamton, New York, USA |
| Abstract: | Consider the Lehmann model with time-dependent covariates, which is different from Cox’s model. We find out that (1) the parameter space for β under the Lehmann model is restricted, and the maximum point of the parametric likelihood for β may lie outside the parameter space; (2) for some particular time-dependent covariate, under the standard generalized likelihood the semiparametric maximum likelihood estimator (SMLE) is inconsistent and we propose a modified generalized likelihood which leads to the consistent SMLE. |
| Keywords: | Cox regression Restricted parameter space Semiparametric MLE Time-dependent covariates |