Date of Award


Degree Name

Doctor of Philosophy



First Advisor

Dr. Joshua D. Naranjo

Second Advisor

Dr. Michael R. Stoline

Third Advisor

Dr. Magdalena Niewiadomska-Bugaj

Fourth Advisor

Dr. Douglas N. Homnick


Two commonly used tests for comparison of survival curves are the generalized Wilcoxon procedure of Gehan (1965) and Breslow (1970) and the Log-rank test proposed by Mantel (1966) and Cox (1972). In applications, the Log-rank test is used after checking for validity of the proportional hazards (PH) assumption, with Wilcoxon being the fallback method when the PH assumption fails.

However, the relative performance of the two procedures depend not just on the PH assumption but also on the pattern of differences between the two curves. We will show that the crucial factor is whether the differences tend to occur early or late in time. We propose diagnostics to measure early-or-late differences between two survival curves. A pretest based on either diagnostic will help the user choose the more efficient test under various patterns of treatment differences.

Access Setting

Dissertation-Open Access