Efficient estimation for a semiparametric extended hazards model

We propose an alternative estimation for an extended hazards (EH) model by maximizing a kernel-smoothed profile likelihood function. The EH model includes the proportional hazards (PH) model and the accelerated failure time (AFT) model as special cases. Maximization is realized using conventional gradient-search methods. The nested structure of the EH model allows one to construct a goodness-of-fit for the PH model or the AFT model through a likelihood ratio test. We also establish asymptotic theories of the resulting estimators and the likelihood ratio test statistic.