A Bayesian accelerated failure time model for interval censored three-state screening outcomes

Women infected by the human papillomavirus are at an increased risk to develop cervical intraepithelial neoplasia lesions (CIN). CIN are classified into three grades of increasing severity (CIN-1, CIN-2, and CIN-3) and can eventually develop into cervical cancer. The main purpose of screening is detecting CIN-2 and CIN-3 cases which are usually removed surgically. Screening data from the POBASCAM trial involving 1454 HPV-positive women are analyzed with two objectives, estimate: (a) the transition time from HPV diagnosis to CIN-3 and (b) the transition time from CIN-2 to CIN-3. The screening data have two key characteristics. First, the CIN state is monitored in an interval censored sequence of screening times. Second, a woman’s progression to CIN-3 is only observed if the woman progresses to, both, CIN-2 and from CIN-2 to CIN-3 in the same screening interval. We propose a Bayesian accelerated failure time model for the two transition times in this three-state model. To deal with the unusual censoring structure of the screening data, we develop a Metropolis-within-Gibbs algorithm with data augmentation from the truncated transition time distributions.