Graduation Year


Document Type




Degree Name

Doctor of Philosophy (Ph.D.)

Degree Granting Department

Epidemiology and Biostatistics

Major Professor

Getachew Dagne, Ph.D.

Co-Major Professor

Wei Wang, Ph.D.

Committee Member

Kevin Kip, Ph.D.

Committee Member

Glenn Currier, M.D.


Directed graphs, Multilevel Models, Random Effects, Survival analysis


Healthcare systems have multistate processes. Such processes may be modeled using flowgraphs, which are directed graphs. Flowgraph models support a variety of transition time distributions, easily handle reversibility between states and allow alternate paths to the event or state of interest to be taken. However, estimation of flowgraph and first passage time distribution parameters can lead to incorrect inferences when interdependent data are treated as independent.

In this dissertation, we expand the flowgraph model to accommodate nested and correlated data structures. We develop a framework to incorporate random effects into transition probability and transition time components of a flowgraph model. By introducing cluster-level random effects, we show how conditional independence can be utilized to improve the accuracy and reliability of results from a flowgraph analysis of clustered data. We consider correlated random effects across multiple transitions when individuals are clustered by group membership. Then, we consider a second level of random effects when specific transitions may be repeated within individuals. We compare the performance of flowgraph models with random effects to naïve flowgraph models across various strengths of positive and negative correlation, various magnitudes of between-cluster variation and various sample sizes.

Our proposed approach enables broader and more complete evaluations of multistate time to event data. We provide both Frequentist and Bayesian perspectives on estimation and demonstrate the methodology with simulated data and meaningful real data applications. Lastly, we discuss the implications for future research. The flexibility of the flowgraph model and the ability to accommodate clustered data structures makes it an ideal choice for many applications in healthcare.

Included in

Biostatistics Commons