A Bayesian approach for analyzing case 2 interval-censored data under the semiparametric proportional odds model

Analyzing interval-censored data is difficult due to its complex data structure containing left-, interval-, and right-censored observations. An easy-to-implement Bayesian approach is proposed under the proportional odds (PO) model for analyzing such data. The nondecreasing baseline log odds function is modeled with a linear combination of monotone splines. Two efficient Gibbs samplers are developed based on two different data augmentations using the relationship between the PO model and the logistic distribution. In the first data augmentation, the logistic distribution is achieved by the scaled normal mixture with the scale parameter related to the Kolmogorov–Smirnove distribution. In the second data augmentation, the logistic distribution is approximated by a Student’s t distribution up to a scale constant. The proposed methods are evaluated by simulation studies and illustrated with an application of an HIV data set.