Bayesian approaches of Markov models embedded in unbalanced panel data

[摘要] ENGLISH ABSTRACT: Multi-state models are used in this dissertation to model panel data, also known as longitudinalor cross-sectional time-series data. These are data sets which include units that are observedacross two or more points in time. These models have been used extensively in medical studieswhere the disease states of patients are recorded over time.A theoretical overview of the current multi-state Markov models when applied to panel datais presented and based on this theory, a simulation procedure is developed to generate paneldata sets for given Markov models. Through the use of this procedure a simulation studyis undertaken to investigate the properties of the standard likelihood approach when fittingMarkov models and then to assess its shortcomings. One of the main shortcomings highlightedby the simulation study, is the unstable estimates obtained by the standard likelihood models,especially when fitted to small data sets.A Bayesian approach is introduced to develop multi-state models that can overcome theseunstable estimates by incorporating prior knowledge into the modelling process. Two Bayesiantechniques are developed and presented, and their properties are assessed through the use ofextensive simulation studies.Firstly, Bayesian multi-state models are developed by specifying prior distributions for thetransition rates, constructing a likelihood using standard Markov theory and then obtainingthe posterior distributions of the transition rates. A selected few priors are used in thesemodels. Secondly, Bayesian multi-state imputation techniques are presented that make useof suitable prior information to impute missing observations in the panel data sets. Onceimputed, standard likelihood-based Markov models are fitted to the imputed data sets toestimate the transition rates. Two different Bayesian imputation techniques are presented.The first approach makes use of the Dirichlet distribution and imputes the unknown states atall time points with missing observations. The second approach uses a Dirichlet process toestimate the time at which a transition occurred between two known observations and then astate is imputed at that estimated transition time.The simulation studies show that these Bayesian methods resulted in more stable results, evenwhen small samples are available.

[发布机构] Stellenbosch University