Biomedical Engineering Reference
In-Depth Information
6.5
Discussion
In this chapter, we reviewed three recently proposed Bayesian methods for
analyzing interval-censored data under the semiparametric Probit, PO, and
PH models. These methods adopt monotone splines for modeling the unknown
nondecreasing functions and allow us to estimate the regression parameters
and spline coecients jointly.
Unlike the existing Bayesian methods on survival data, these methods
do not require imputing unobserved failure times or using any complicated
Metropolis-Hastings algorithm in the MCMC computation. The methods are
expected to be widely applicable for analyzing interval-censored data because
they do not require model assumptions on the observational process that
causes interval-censored data structure.
The methods discussed in this chapter allow one to conduct model compar-
ison and select the most appropriate model among the three commonly used
semiparametric models for a particular interval-censored data set. For this
purpose, one can use pseudo-marginal likelihood criteria (Geisser and Eddy,
1979; Gelfand and Dey, 1994; Sinha et al., 1999) or deviance information cri-
teria (Spiegelhalter et al., 2002) based on these estimation approaches.
The data augmentations in the proposed methods were developed based
on interval-censored data structure and each individual model structure. One
can develop a unified estimation method under these three models. One fea-
sible solution is to work on the linear transformation models and model the
unknown nondecreasing function H with monotone splines. A Gibbs sampler
can be developed using the adaptive rejection sampling for all unknown pa-
rameters as their full conditional densities are log-concave functions in this
case. However, we expect that this unified Gibbs sampler will be less ecient
than the methods mentioned in this chapter because the unified method does
not fully utilize each model structure.
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