Bayesian Inference of Interval-Censored Survival Data - Interval-Censored-Time-to-Event Data: Methods and Applications - page 168

does not change over time. For right-censored data, the Cox model has been
extended to allow time-varying coecients to break the reliance on this as-
sumption, which may not hold in practice.
Methodological development for varying-coecient survival models in-
cludes the histogram sieve estimator (Murphy and Sen, 1991), the penalized
partial likelihood (Hastie and Tibshirani, 1993), the weighted local partial
likelihood (Cai and Sun, 2003; Tian et al., 2005), estimating equations for
cumulative time-varying coecients (Martinussen and Scheike, 2002; Marti-
nussen et al., 2002), and sequential estimating equations for temporal effects
on the survival function (Peng and Huang, 2007). For interval-censored data,
however, the literature on Cox models with time-varying coecients is sparse.
Sinha et al. (1999) treated the unobserved exact event times as latent variables
and sampled from their full conditional posterior distribution via the Gibbs
sampling algorithm (Gelfand and Smith, 1990).
An autoregressive (AR) process prior was used for the regression coef-
ficients to allow the coecients to change over time and borrow strength
from adjacent intervals. The model comparison with the Cox proportional
hazards model was done via conditional predictive ordinate (CPO) (Gelfand
et al., 1992). Wang et al. (2011a) proposed a new Bayesian model for interval-
censored data where the regression coecients and baseline hazards functions
are both dynamic in time. A fine time grid is prespecified, covering all the
endpoints of the observed intervals whose right end is finite. The regression
coecients and the baseline hazards are piecewise constants on the grid, but
the numbers of pieces are covariate-specific and estimated from the data. This
is a natural but substantial extension of the time-varying coecient Cox model
of Sinha et al. (1999), where jumps are placed at every grid point.
In this chapter, we present a comprehensive discussion of Bayesian infer-
ence of interval-censored survival data. Various Bayesian models along with
likelihoods and priors are presented in Section 7.2. The MCMC algorithm is
developed in Section 7.3. In Section 7.4, we discuss two Bayesian model com-