## Wednesday, 18 April 2012

### Bayesian inference of the fully specified subdistribution model for survival data with competing risks

Miaomiao Ge and Ming-Hui Chen have a new paper in Lifetime Data Analysis. This considers methods for Bayesian inference in the Fine-Gray model for competing risks. In order to perform the Bayesian analysis it is necessary to fully specify the model for the competing risk(s) that are not of direct interest in the analysis. Ge and Chen propose a model in which for failure time $\inline T^{*}$,
$F_2(t) = P(T^{*} \leq t, \delta = 2) = M_2(t)P(\delta = 2)$ and a proportional hazards model affects $\inline M_2(t)$ via
$M_2(t | \mathbf{x}) = 1 - \exp{\{-H_{20}(t)\exp{(\mathbf{x}^{T}\beta_2)}\}}$.
Note that $\inline \beta_2$ does not affect $\inline F_1(t)$ or $\inline P(\delta = 2)$.
The authors consider approaches to non-parametric Bayesian inference using Gamma process priors, but also use piecewise constant hazard models (with fixed cut points) where the hazard in each time period has an independent gamma prior.