with the coeffiicients of the various powers of time being possibly diffierent functions of the vector of covariables. Methods for fitting the model to data and testing hypotheses about model parameters are presented. The degree of the polynomial for the hazard is chosen in a step-wise manner as part of thefitting of the model. Specification of the survival curve with covariables is straightforward as a result of the parametric nature of the model. [Jse of the model and methods forfitting and hypothesis testing are illustrated by application to two diffierent cohort studies. For each analysis, a single covariate indicates in which of two treatment groups an individual belongs. It is found that a time-constant hazard and hence, the proportional hazards assumption are adequate for thefirst cohort examined. However, for the second cohort a time-varying hazard is required and the proportional hazards assumption is not suitable. Results obtained using other methods are compared with those of the proposed method for both of the cohorts. Good agreement among the diffierent approaches is observed.