Latent multi-state models for non-equidistant longitudinal observations with finite and infinite mixture model-based clustering

Large amounts of data that exist in the form of longitudinal health records, such as electronic health records (EHRs), healthcare administrative databases and mobile health applications, are now available for dynamic monitoring of the underlying processes governing the observations. However, such latent progression generating the observations is not observed directly and so requires inferential methods to ascertain progression. Moreover, records are only observed when a subject interacts with the healthcare system, resulting in irregular visits where the observations are not collected at equidistant time intervals with possible sparsity. For example, in healthcare databases, chronic disease patients do not seek intensive care at early stage of the disease, and therefore the records may be sparse, and patients might seek care outside the healthcare system, which means that only a segment of the entire health trajectory might be observed. These considerations suggest that trajectories should be modeled as a latent continuous-time process. The progression usually depends on the evolution of different types of time-varying covariates. Incorporating these covariates into the model can advance our understanding of the development of the condition. However, no existing statistical method addresses these issues. To overcome these challenges, the first part of this thesis develops a continuous-time hidden Markov model (CTHMM) under the framework of generalized linear models (GLMs) to analyze the issues of irregular visits, different types of observations and multiple time-dependent covariates. Both likelihood and Bayesian inferences for the CTHMM-GLM are investigated via the expectation-maximization (EM) algorithm and Markov chain Monte Carlo (MCMC) respectively. Bayesian inference is appealing as simulation-based methods can be easily applied to make inference for each individual, and is more efficient when random effects or more complex settings are incorporated into the model. To provide a better understanding of dynamic changes in trajectories, it would be helpful to be able to cluster trajectories, allowing study of the pattern in each group to explore reasons for variation. The second part of this thesis extends the CTHMM-GLM to the finite and infinite mixture model-based clustering methods. We demonstrate that inference for finite mixture models can be inherited from one component CTHMM-GLM, where the EM algorithm and MCMC can be employed. The inference for infinite mixture models is a considerable research challenge, but the posterior distribution can be sampled by Gibbs sampling via Pólya urn schemes and and, more efficiently, split-merge proposals. All the proposed methods are applied to a healthcare administrative database in Montreal and specifically to study the progression of chronic obstructive pulmonary disease (COPD) and to group the trajectories of COPD patients. The description of the dataset and results are presented in the last part of this thesis. The application of the methodology demonstrate that the model can identify the meaningful latent states, the transition pattern and clusters to help the health system managers measure the performance of the healthcare system temporally.

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