Some extensions of hidden Markov models for estimating disease state transition rates using observational healthcare databases

Chronic diseases are often described by stages of severity. Clinical decisions about what to do are influenced by the stage, whether a patient is progressing, and the rate of progression. For chronic kidney disease (CKD), relatively little is known about the transition rates between stages. Since CKD is a slowly progressive disease, large samples with long follow-up times are needed to estimate these rare transitions. Data such as electronic health records (EHR) are informative for this purpose because such data have the advantage of having both sufficient follow-up time and sample size to reliably and accurately estimate the transition rates. However, there are challenges in using EHR. For example, the large amount of information itself may pose difficulty in estimation; data collected tend to have higher levels of measurement error due to having less regulated and consistent data collection methods than data that were collected as part of a research study; acute events (e.g., acute kidney injury) can also affect a laboratory measurement in a way that does not accurately characterize the chronic disease stages; the observed data process might be infor- mative; in addition, many researchers believe that the transition rates between CKD stages vary among individuals. Standard statistical methods for estimation of transition rates such as hidden Markov models (HMMs) do not address these challenges specifically and efficiently, hence, may not be feasible when applied to EHR data. In this dissertation, new methods are developed to estimate these transition rates using HMMs to address the issues mentioned above. We propose a discretization method that transforms daily transition probabilities into intervals of 30 days, 90 days, or 180 days in order to make estimating transition rates feasible when large observation data are used. An extended HMM that uses two error matrices to correlate the observed outcomes with the true disease states is developed. This new model addresses the contamination in data due to measurement errors or acute events more efficiently than a traditional HMM. Lastly, we develop a modified mover-stayer HMM that views the distribution of the transition rates of a CKD patient as a mixture of two different distributions. This method intents to inform us the prevalence of different groups of people in the CKD population and their transition rates. The accuracy and robustness of these methods are tested via simulation studies. We also applied our models to a large EHR data set from Geisinger Clinic, where the transition probabilities and the relationship between true CKD states and the observed outcomes are estimated