In this thesis, two methods for assessing the functional form of covariates in the Cox proportional hazards model are evaluated. The methods include one graphical check based on martingale residuals and one graphical check, together with a Kolmogorov-type supremum test, based on cumulative sums of martingale residuals. The methods are evaluated in a simulation study under five different covariate misspecifications with varying sample sizes and censoring degrees. The results from both methods indicate that the type of covariate misspecification, sample size and censoring degree affect the ability to detect and identify the misspecification. The procedure based on smoothed scatterplots of martingale residuals reveals difficulties with assessing whether the behaviour of the smoothed curve in the plot is an indication of a misspecification or a phenomenon that can occur in a correctly specified model. The graphical check together with the test procedure based on cumulative sums of martingale residuals is shown to successfully detect and identify three out of five covariate misspecifications for large sample sizes. For small sample sizes, especially combined with a high censoring degree, the power of the supremum test is low for all covariate misspecifications.

In many clinical studies, continuous variables such as age, blood pressure and cholesterol are measured and analyzed. Often clinicians prefer to categorize these continuous variables into different groups, such as low and high risk groups. The goal of this work is to find the cutpoint of a continuous variable where the transition occurs from low to high risk group. Different methods have been published in literature to find such a cutpoint. We extended the methods of Contal and O’Quigley (1999) which was based on the log-rank test and the methods of Klein and Wu (2004) which was based on the Score test to find the cutpoint of a continuous covariate. Since the log-rank test is a nonparametric method and the Score test is a parametric method, we are interested to see if an extension of the parametric procedure performs better when the distribution of a population is known. We have developed a method that uses the parametric score residuals to find the cutpoint. The performance of the proposed method will be compared with the existing methods developed by Contal and O’Quigley and Klein and Wu by estimating the bias and mean square error of the estimated cutpoints for different scenarios in simulated data.

It is common practice to use Cox-Snell residuals to check for overall goodness of tin survival models. We evaluate the presumed relation of unit exponentially dis-tributed residuals for a good model t and evaluate under some violations of themodel. This is done graphically with the usual graphs of Cox-Snell residual andformally using Kolmogorov-Smirnov goodness of t test. It is observed that residu-als from a correctly tted model follow unit exponential distribution. However, theCox-Snell residuals do not seem to be sensitive to the violations of the model.