Inference for a family of survival models encompassing the proportional hazards and proportional odds models

For survival data regression, the Cox proportional hazards model is the most popular model, but in certain situations the Cox model is inappropriate. Various authors have proposed the proportional odds model as an alternative. Yang and Prentice recently presented a number of easily implemented estimators for the proportional odds model. Here we show how to extend the methods of Yang and Prentice to a family of survival models that includes the proportional hazards model and proportional odds model as special cases. The model is defined in terms of a Box-Cox transformation of the survival function, indexed by a transformation parameter rho. This model has been discussed by other authors, and is related to the Harrington-Fleming G(rho) family of tests and to frailty models. We discuss inference for the case where rho is known and the case where rho must be estimated. We present a simulation study of a pseudo-likelihood estimator and a martingale residual estimator. We find that the methods perform reasonably. We apply our model to a real data set.