TITLE:
Estimation of the Piecewise Exponential Model by Bayesian P-Splines via Gibbs Sampling: Robustness and Reliability of Posterior Estimates
AUTHORS:
Giuseppe Marano, Patrizia Boracchi, Elia M. Biganzoli
KEYWORDS:
Survival Analysis, Hazard Smoothing, Bayesian P-Splines, Piecewise Exponential Model, Time-Dependent Effects
JOURNAL NAME:
Open Journal of Statistics,
Vol.6 No.3,
June
22,
2016
ABSTRACT: In the investigation of disease dynamics,
the effect of covariates on the hazard function is a major topic. Some recent
smoothed estimation methods have been proposed, both frequentist and Bayesian,
based on the relationship between penalized splines and mixed models theory.
These approaches are also motivated by the possibility of using automatic
procedures for determining the optimal amount of smoothing. However, estimation
algorithms involve an analytically intractable hazard function, and thus
require ad-hoc software routines. We propose a more user-friendly alternative,
consisting in regularized estimation of piecewise exponential models by
Bayesian P-splines. A further facilitation is that widespread Bayesian
software, such as WinBUGS, can be used. The aim is assessing the robustness of
this approach with respect to different prior functions and penalties. A large
dataset from breast cancer patients, where results from validated clinical
studies are available, is used as a benchmark to evaluate the reliability of
the estimates. A second dataset from a small case series of sarcoma patients is
used for evaluating the performances of the PE model as a tool for exploratory
analysis. Concerning breast cancer data, the estimates are robust with respect
to priors and penalties, and consistent with clinical knowledge. Concerning
soft tissue sarcoma data, the estimates of the hazard function are sensitive
with respect to the prior for the smoothing parameter, whereas the estimates of
regression coefficients are robust. In conclusion, Gibbs sampling results an
efficient computational strategy. The issue of the sensitivity with respect to
the priors concerns only the estimates of the hazard function, and seems more
likely to occur when non-large case series are investigated, calling for
tailored solutions.