A comparison between the additive and multiplicative risk models

Survival analysis examines and models the time it takes for events to occur. It focuses on the distribution of survival times. Survival data is time-to-event data, such as time to death, appearance of a tumor, or recurrence of a disease. Regression models for survival data have traditionally been based on the proportional hazards model, proposed by Cox, that has become the workhorse of regression analysis for censored data. The effect of the covariates on survival is to act multiplicatively on some unknown baseline hazard rate, which makes it difficult to model covariate effects that change over time. Secondly, if covariates are deleted from a model or measured with a different level of precision, the proportional hazards assumption is no longer valid. These weaknesses in the Cox model have generated interest in alternative models. One such alternative model is Aalen's (1989) additive model. This model assumes that covariates act in an additive manner on an unknown baseline hazard rate. The unknown risk coefficients are allowed to be functions of time, so that the effect of a covariate may vary over time. Aalen's additive model is not yet widely used. One reason for this is that the model is not available in any commonly used computer package, such as SAS or S-plus. In this thesis we use a SAS macro that performs the additive hazards regression. The aim of this thesis is to compare the proportional and additive hazards models through theory, application and simulation. We also highlight their respective advantages and disadvantages, and give guidelines as to which model to choose to fit given survival data.