Nonparametric Bayesian hazard rate models based on penalized splines

Extensions of the traditional Cox proportional hazard model,
concerning the following features are often desirable in
applications: Simultaneous nonparametric estimation of baseline
hazard and usual fixed covariate effects, modelling and detection
of time-varying covariate effects and nonlinear functional forms of
metrical covariates, and inclusion of frailty components. In this
paper, we develop Bayesian multiplicative hazard rate models for
survival and event history data that can deal with these issues in
a flexible and unified framework. Some simpler models, such as
piecewise exponential models with a smoothed baseline hazard, are
covered as special cases. Embedded in the counting process
approach, nonparametric estimation of unknown nonlinear functional
effects of time or covariates is based on Bayesian penalized
splines. Inference is fully Bayesian and uses recent MCMC sampling
schemes. Smoothing parameters are an integral part of the model and
are estimated automatically. We investigate performance of our
approach through simulation studies, and illustrate it with a real
data application.