Bayesian Inference of Interval-Censored Survival Data - Interval-Censored-Time-to-Event Data: Methods and Applications - page 190

that from M 1 , only excluding zero around time 20. Although M 3 is close to
M 2 in model comparison, it may still be preferred due to a smoother curve
and narrower 95% credible intervals of the treatment effect.

7.8 Discussion

We have discussed several regression models for interval-censored survival data
that extend the Cox model. With time-varying coecients, the AR and dy-

namic models have the flexibility of capturing the temporal nature of covariate

effects. Compared to the time-varying coecient model, the dynamic model

allows the data to determine the extent of temporal dynamics each covariate

coecient needs to be, and allows a dynamic baseline hazards function as well

as regression coecients. These differences may lead to a much reduced effec-

tive number of parameters and better Bayesian model comparison statistics.

The dynamic model avoids over-fitting and enables borrowing strength from

adjacent values.

As part of the Bayesian model specification, priors of the regression coe-

cients and baseline hazards are important in determining the structure of the

posterior distributions. We considered Markov-type process priors, whose the-

oretical properties with normal noise remain to be rigorously studied. Other

Markov-type process priors are worth further investigating. For example, a

Markov-type process with Laplace noise leads to a penalty in total variation
instead of quadratic variation of the coecients; a refined Markov-type pro-

cess with normal noise where the AR coecient and the size of noise are

location specific (Kim et al., 2007). In Section 7.2, the priors for the baseline

hazards and components of the regression coecient functions are assumed

to be independent. This assumption can, however, be relaxed, and correlated

Markov-type process priors can be developed. Further, for the time-varying