Hidden mover‐stayer model for disease progression accounting for misclassified and partially observed diagnostic tests: Application to the natural history of human papillomavirus and cervical precancer

Hidden Markov models (HMMs) have been proposed to model the natural history of diseases while accounting for misclassification in state identification. We introduce a discrete time HMM for human papillomavirus (HPV) and cervical precancer/cancer where the hidden and observed state spaces are defined by all possible combinations of HPV, cytology, and colposcopy results. Because the population of women undergoing cervical cancer screening is heterogeneous with respect to sexual behavior, and therefore risk of HPV acquisition and subsequent precancers, we use a mover‐stayer mixture model that assumes a proportion of the population will stay in the healthy state and are not subject to disease progression. As each state is a combination of three distinct tests that characterize the cervix, partially observed data arise when at least one but not every test is observed. The standard forward‐backward algorithm, used for evaluating the E‐step within the E‐M algorithm for maximum‐likelihood estimation of HMMs, cannot incorporate time points with partially observed data. We propose a new forward‐backward algorithm that considers all possible fully observed states that could have occurred across a participant's follow‐up visits. We apply our method to data from a large management trial for women with low‐grade cervical abnormalities. Our simulation study found that our method has relatively little bias and out preforms simpler methods that resulted in larger bias.