#### Defense Date

2013

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy

#### Department

Biostatistics

#### First Advisor

Leory Thacker

#### Abstract

Survival Analysis generally uses the median survival time as a common summary statistic. While the median possesses the desirable characteristic of being unbiased, there are times when it is not the best statistic to describe the data at hand. Royston and Parmar (2011) provide an argument that the restricted mean survival time should be the summary statistic used when the proportional hazards assumption is in doubt. Work in Restricted Means dates back to 1949 when J.O. Irwin developed a calculation for the standard error of the restricted mean using Greenwood’s formula. Since then the development of the restricted mean has been thorough in the literature, but its use in practical analyses is still limited. One area that is not well developed in the literature is the choice of the time point to which the mean is restricted. The aim of this dissertation is to develop a data driven method that allows the user to find a cut-point to use to restrict the mean. Three methods are developed. The first is a simple method that locates the time at which the maximum distance between two curves exists. The second is a method adapted from a Renyi-type test, typically used when proportional hazards assumptions are not met, where the Renyi statistics are plotted and piecewise regression model is fit. The join point of the two pieces is where the meant will be restricted. Third is a method that applies a nonlinear model fit to the hazard estimates at each event time, the model allows for the hazards between the two groups to be different up until a certain time, after which the groups hazards are the same. The time point where the two groups’ hazards become the same is the time to which the mean is restricted. The methods are evaluated using MSE and bias calculations, and bootstrap techniques to estimate the variance.

#### Rights

© The Author

#### Is Part Of

VCU University Archives

#### Is Part Of

VCU Theses and Dissertations

#### Date of Submission

May 2013