Essays on the Assumption of Proportional Hazards in Cox Regression

This thesis consists of four papers about the assumption of proportional hazards for the Cox model in survival analysis. The first paper compares the hazard ratio estimated from the Cox model to an exact calculation of the geometric average of the hazard ratio when the underlying assumption of proportional hazards is false, i.e. when the hazards are not proportional. The estimates are evaluated in a simulation study. The second paper describes and compares six of the most common numerical procedures to check the assumption of proportional hazards for the Cox model. The tests are evaluated in a simulation study. Six graphical procedures to check the same assumption of proportional hazards for the Cox model are described and compared in the third paper. A criterion for rejection is derived for each procedure, to make it possible to compare the results of the different methods. The procedures are evaluated in a simulation study. In the fourth paper the effects of covariate measurement error on testing the assumption of proportional hazards is investigated. Three of the most common numerical procedures to check the assumption of proportional hazards for the Cox model are evaluated in a simulation study