The textbook by (Lawless 2003) is a good source for the study of parametric survival models. The parametric distribution functions that can be used as the baseline distribution in the function phreg are the Weibull, Piecewise constant hazards, Lognormal, Loglogistic, and the Gompertz distributions. The lognormal and loglogistic distributions allow for hazard functions that are first increasing to a maximum and then decreasing, while the other distributions all have monotone hazard functions. One of the advantages with parametric models is that it is easy to study and plot the hazard function, and not only the cumulative hazards function, which is the dominant tool for analysis in the case of the nonparametric model of Cox regression. For modeling survival data with parametric proportional hazards models, the distributions of the function phreg in the package eha are available. The problem of choosing between a proportional hazards and an accelerated failure time model can be solved by comparing the AIC of the models.