Comparison of Methods for Two Crossing Survival Curves Público

Abstract

In clinical research, it is not uncommon to see that the proportional hazard assumption is violated, particularly when survival curves cross. The log-rank test which is widely used in comparing survival curves is known to have less power under such circumstance. In this thesis, we introduce three methods to test the difference between two survival curves which are (1) Gehan’s weighted log-rank test, (2) Renyi type test, and (3) Lin and Xu’s test. We give a brief background of the statistical theory underpinning these methods. Then, we conduct a simulation study to compare the three tests with log-rank test under different situations and censor rates. We also apply all three methods to a real data example from a kidney dialysis trial. In our comparison of the three methods, we found that Gehan’s test does not perform well in the setting situations. The weight function of the weighted log-rank test must be specified prior to the analysis, and an inappropriate weight function may result in a misleading conclusion. Renyi test is suitable to use when two survival curves separate largely and cross, because its power stays above 90% even under a high censor rate. Lin and Xu’s test is appropriate when two survival curves do not separate largely, and its power is influenced by the censor rate.

Table of Contents

Table of Contents 1. Introduction........................................................................................................ 1 2. Weighted Log-rank Test ...................................................................................... 3 3. Renyi Type Test ................................................................................................... 6 4. Lin & Xu’s Test .................................................................................................... 8 5. Simulation Study ............................................................................................... 11 5.1 Estimation of Type I Error ........................................................................................... 11 5.2 Estimation of Power ................................................................................................... 11 5.2.1 Situation 1 .................................................................................................................... 12 5.2.2 Situation 2 .................................................................................................................... 13 5.2.3 Situation 3 .................................................................................................................... 14 6. Real Data Example from a Kidney Dialysis Trial .................................................. 16 7. Discussion and Conclusion ................................................................................ 18 8. Reference ......................................................................................................... 20 9. Appendix .......................................................................................................... 21

About this Master's Thesis

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School	Rollins School of Public Health
Department	Biostatistics
Degree	M.S.P.H.
Submission	Master's Thesis
Language	English
Research Field	Biology, Biostatistics
Palavra-chave	Renyi Type Test Weighted Log-rank Test Lin and Xu's test Survival Analysis
Committee Chair / Thesis Advisor	Binongo, Jose, Emory University
Committee Members	Ko, Yi-An, Emory University
Partnering Agencies	Does not apply (no collaborating organization)

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