This dissertation looks at two different problems essentially. In recent years, pseudo observations have found application in multi-state survival models, models for mean lifetime and competing risks to name a few. We have investigated the performance of estimates and confidence
intervals based on pseudo observations in the context of a multi-state model with independent right censoring. This has been compared to estimates from a Cox proportional hazards model with confidence intervals obtained from the bootstrap. While simulations show that the bootstrap is doing well,
it becomes evident from simulations and some theory that the pseudo observations method presents difficulty with implementation and may lead to inconsistent estimates, particularly with covariate-dependent censoring.
The cumulative sum (CUSUM) procedure has been used for quite some time as a graphical sequential monitoring scheme for detecting small persistent shifts in the mean of observations generated from a manufacturing process. In recent years, it has also found application in the medical
literature in the context of monitoring performances of participating centers for quality improvement in a multi-center study involving an ongoing intervention. In this dissertation, we develop and implement risk-adjusted CUSUM charts defined as a process in continuous time when the reports of outcomes are immediate as well as when there is a random delay or lag involved. Approximate theoretical results on the Average Run Length (ARL) of the CUSUM are also provided. A discussion on how to choose a control limit for the CUSUM and some relevant issues that come into play in doing so are also discussed in some detail. Simulation studies show that the new proposal is able to detect changes quicker than other methods in practice. The method is also illustrated on kidney transplant data from the Scientific Registry of Transplant Recipients (SRTR).Ph.D.BiostatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/57629/2/pbiswas_1.pd
