Semiparametric models based on transformations and extremes
University of California, Berkeley and
University of Wisconsin, Madison
The proportional hazard model can be derived as the survival distribution of a unit whose survival depends on the survival of a fixed number of components. Nabeya and Miura (NAMI)(1972) describe the distribution of a unit whose survival depends on the survival of a random number of components, where the distribution of the number of components has a zero truncated Poisson distribution. The partial likelihood for a NAMI survival regression model is derived and compared to the partial likelihood for the proportional hazard model. The proportional hazard likelihood heavily weights the large survival times while the NAMI likelihood weights survival times more evenly. The proportional hazard model can also be interpreted as a linear transformation model with extreme value errors. We consider other transformation models including models where the response and covariates are transformed jointly by nonparametric transformations.