The PHREG procedure performs regression analysis of survival data based on the Cox proportional hazards model. Cox�s semiparametric model is widely used in the analysis of survival data to explain the effect of explanatory variables on hazard rates. The PHREG procedure's Bayesian analysis capabilities enable you to do the following:
To perform Bayesian analyses with PROC PHREG, you specify a model essentially the same way you do for a frequentist approach, but you add a BAYES statement to request Bayesian estimation methods for fitting the model. The BAYES statement requests that the parameters of the model be estimated by Markov chain Monte Carlo sampling techniques and provides options that enable you to specify prior information, control the sampling, and obtain posterior summary statistics and convergence diagnostics. You can also save the posterior samples to a SAS data set for further analysis.
The PHREG procedure supports the following sampling algorithms:
The PHREG procedure supports the following priors:
| Parameter | Prior |
| Regression coefficients | Normal, uniform, Zellner g-prior |
| g (Zellner) | Constant, gamma |
| Baseline hazards (original scale) | Improper, uniform, gamma, independent gamma, AR(1) |
| Baseline hazards (log scale) | Uniform, normal |
| Log-hazards and regression coefficients | Joint multivariate normal |
For a Cox model, the model parameters are the regression coefficients.
For a piecewise exponential model, the model parameters consist of the
regression coefficients and the hazards or log-hazards.