Modelling a time-dependant hazard ratio with regression splines

by Todd Mackenzie

Institution: McGill University
Department: Department of Mathematics and Statistics.
Degree: MS
Year: 1993
Keywords: Mathematics.
Record ID: 1659806
Full text PDF: http://digitool.library.mcgill.ca/thesisfile69720.pdf


The proportional hazards model proposed by Cox (1972) is by far the most popular method of regressing survival data. This model is attractive becuase: (i) It has a simple interpretation; the impact of a variable upon survival is a constant and multiplicative effect on the hazard function. (ii) It facilitates the employment of the partial likelihood inference technique so that it requires no assumptions about the baseline distribution of survival times. Many numerical tests as well as graphical approaches have been proposed for assessing the adequacy of the proportional hazards model. However only a few authors have discussed strategies for modelling data for which the hazard ratio varies over time. In this thesis the topic of survival analysis is overviewed, and methods for assessing the validity of the proportional hazards assumption are reviewed. Finally a method of estimating the hazard ratio as a flexible function of time using the method of regression splines and the AIC model selection criterion is proposed. We report the results of a simulation meant to examine the small sample properties of this technique.