Physical Sciences and Mathematics Commons^™

The Strong Law Of Large Numbers For U-Statistics Under Random Censorship, Jan Höft

Theses and Dissertations

We introduce a semi-parametric U-statistics estimator for randomly right censored data. We will study the strong law of large numbers for this estimator under proper assumptions about the conditional expectation of the censoring indicator with re- spect to the observed life times. Moreover we will conduct simulation studies, where the semi-parametric estimator is compared to a U-statistic based on the Kaplan- Meier product limit estimator in terms of bias, variance and mean squared error, under different censoring models.

Flowgraph Models For Clustered Multistate Time To Event Data, Kristin Hall

USF Tampa Graduate Theses and Dissertations

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. …