  Fully Bayesian methods for Cox models specify a model for the baseline hazard
function. Parametric approaches generally provide monotone estimations.
Semi-parametric choices allow for more flexible patterns but they can suffer
from overfitting and instability. Regularization methods through prior
distributions with correlated structures usually give reasonable answers to
these types of situations. We discuss Bayesian regularization for Cox survival
models defined via flexible baseline hazards specified by a mixture of
piecewise constant functions and by a cubic B-spline function. For those
"semiparametric" proposals, different prior scenarios ranging from prior
independence to particular correlated structures are discussed in a real study
with micro-virulence data and in an extensive simulation scenario that includes
different data sample and time axis partition sizes in order to capture risk
variations. The posterior distribution of the parameters was approximated using
Markov chain Monte Carlo methods. Model selection was performed in accordance
with the Deviance Information Criteria and the Log Pseudo-Marginal Likelihood.
The results obtained reveal that, in general, Cox models present great
robustness in covariate effects and survival estimates independent of the
baseline hazard specification. In relation to the "semi-parametric" baseline
hazard specification, the B-splines hazard function is less dependent on the
regularization process than the piecewise specification because it demands a
smaller time axis partition to estimate a similar behaviour of the risk.
