#
Bayesian Analysis Using the LIFEREG Procedure

The LIFEREG procedure fits
parametric models to failure-time data that can be uncensored, right-censored, left-censored, or interval-censored.
The models for the response variable consist of a linear effect (which is composed of the covariates) and a random disturbance term. The distribution of
the random disturbance can be taken from a class of distributions that includes the extreme value, normal, logistic, and, by using a log transformation,
the exponential, Weibull, lognormal, log-logistic, and three-parameter gamma distributions.
PROC LIFEREG uses either frequentist or Bayesian methods to fit models.

To perform Bayesian analyses with PROC LIFEREG, 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.

### Sampling Algorithms

The LIFEREG procedure supports the following sampling algorithms:

- The adaptive rejection Metropolis algorithm (Gilks and Wild 1992; Gilks, Best, and Tan 1995) along with Gibbs sampling is the default

### Priors

The LIFEREG procedure supports the following priors:

**Parameter** |
**Prior** |

Regression coefficients |
Normal, uniform |

Exponential scale |
Gamma, improper |

Location-scale model scale parameter |
Gamma |

Weibull scale |
Gamma |

Three-parameter gamma shape |
Normal |

Weibull shape |
Gamma |

#### Bayesian Analysis Examples