Statistical Inference Methods for Two Crossing Survival Curves: A Comparison of Methods

A common problem that is encountered in medical applications is the overall homogeneity of survival distributions when two survival curves cross each other. A survey demonstrated that under this condition, which was an obvious violation of the assumption of proportional hazard rates, the log-rank te...

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Main Authors:	Li, Huimin, Han, Dong, Hou, Yawen, Chen, Huilin, Chen, Zheng
Format:	Online
Language:	English
Published:	Public Library of Science 2015
Online Access:	https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4304842/

id	pubmed-4304842
recordtype	oai_dc
spelling	pubmed-43048422015-01-30 Statistical Inference Methods for Two Crossing Survival Curves: A Comparison of Methods Li, Huimin Han, Dong Hou, Yawen Chen, Huilin Chen, Zheng Research Article A common problem that is encountered in medical applications is the overall homogeneity of survival distributions when two survival curves cross each other. A survey demonstrated that under this condition, which was an obvious violation of the assumption of proportional hazard rates, the log-rank test was still used in 70% of studies. Several statistical methods have been proposed to solve this problem. However, in many applications, it is difficult to specify the types of survival differences and choose an appropriate method prior to analysis. Thus, we conducted an extensive series of Monte Carlo simulations to investigate the power and type I error rate of these procedures under various patterns of crossing survival curves with different censoring rates and distribution parameters. Our objective was to evaluate the strengths and weaknesses of tests in different situations and for various censoring rates and to recommend an appropriate test that will not fail for a wide range of applications. Simulation studies demonstrated that adaptive Neyman’s smooth tests and the two-stage procedure offer higher power and greater stability than other methods when the survival distributions cross at early, middle or late times. Even for proportional hazards, both methods maintain acceptable power compared with the log-rank test. In terms of the type I error rate, Renyi and Cramér—von Mises tests are relatively conservative, whereas the statistics of the Lin-Xu test exhibit apparent inflation as the censoring rate increases. Other tests produce results close to the nominal 0.05 level. In conclusion, adaptive Neyman’s smooth tests and the two-stage procedure are found to be the most stable and feasible approaches for a variety of situations and censoring rates. Therefore, they are applicable to a wider spectrum of alternatives compared with other tests. Public Library of Science 2015-01-23 /pmc/articles/PMC4304842/ /pubmed/25615624 http://dx.doi.org/10.1371/journal.pone.0116774 Text en © 2015 Li et al http://creativecommons.org/licenses/by/4.0/ This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.
repository_type	Open Access Journal
institution_category	Foreign Institution
institution	US National Center for Biotechnology Information
building	NCBI PubMed
collection	Online Access
language	English
format	Online
author	Li, Huimin Han, Dong Hou, Yawen Chen, Huilin Chen, Zheng
spellingShingle	Li, Huimin Han, Dong Hou, Yawen Chen, Huilin Chen, Zheng Statistical Inference Methods for Two Crossing Survival Curves: A Comparison of Methods
author_facet	Li, Huimin Han, Dong Hou, Yawen Chen, Huilin Chen, Zheng
author_sort	Li, Huimin
title	Statistical Inference Methods for Two Crossing Survival Curves: A Comparison of Methods
title_short	Statistical Inference Methods for Two Crossing Survival Curves: A Comparison of Methods
title_full	Statistical Inference Methods for Two Crossing Survival Curves: A Comparison of Methods
title_fullStr	Statistical Inference Methods for Two Crossing Survival Curves: A Comparison of Methods
title_full_unstemmed	Statistical Inference Methods for Two Crossing Survival Curves: A Comparison of Methods
title_sort	statistical inference methods for two crossing survival curves: a comparison of methods
description	A common problem that is encountered in medical applications is the overall homogeneity of survival distributions when two survival curves cross each other. A survey demonstrated that under this condition, which was an obvious violation of the assumption of proportional hazard rates, the log-rank test was still used in 70% of studies. Several statistical methods have been proposed to solve this problem. However, in many applications, it is difficult to specify the types of survival differences and choose an appropriate method prior to analysis. Thus, we conducted an extensive series of Monte Carlo simulations to investigate the power and type I error rate of these procedures under various patterns of crossing survival curves with different censoring rates and distribution parameters. Our objective was to evaluate the strengths and weaknesses of tests in different situations and for various censoring rates and to recommend an appropriate test that will not fail for a wide range of applications. Simulation studies demonstrated that adaptive Neyman’s smooth tests and the two-stage procedure offer higher power and greater stability than other methods when the survival distributions cross at early, middle or late times. Even for proportional hazards, both methods maintain acceptable power compared with the log-rank test. In terms of the type I error rate, Renyi and Cramér—von Mises tests are relatively conservative, whereas the statistics of the Lin-Xu test exhibit apparent inflation as the censoring rate increases. Other tests produce results close to the nominal 0.05 level. In conclusion, adaptive Neyman’s smooth tests and the two-stage procedure are found to be the most stable and feasible approaches for a variety of situations and censoring rates. Therefore, they are applicable to a wider spectrum of alternatives compared with other tests.
publisher	Public Library of Science
publishDate	2015
url	https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4304842/
_version_	1613180331053023232

Statistical Inference Methods for Two Crossing Survival Curves: A Comparison of Methods

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