Testing proportional hazards for specified covariates
Volume 6, Issue 2 (2019), pp. 209–225
Pub. online: 15 February 2019
Type: Research Article
Open Access
Open Access
Received
2 October 2018
2 October 2018
Revised
9 January 2019
9 January 2019
Accepted
9 January 2019
9 January 2019
Published
15 February 2019
15 February 2019
Abstract
Tests for proportional hazards assumption concerning specified covariates or groups of covariates are proposed. The class of alternatives is wide: log-hazard rates under different values of covariates may cross, approach, go away. The data may be right censored. The limit distribution of the test statistic is derived. Power of the test against approaching alternatives is given. Real data examples are considered.
References
Andersen, P., Borgan, O., Gill, R., Keiding, N.: Statistical Models Based on Counting Processes. Springer, New York (1993) MR1198884. https://doi.org/10.1007/978-1-4612-4348-9
Andersen, P.K., Gill, R.D.: Cox’s regression model for counting processes: A large sample study. Ann. Stat. 10, 1100–1120 (1982) MR0673646
Bagdonavičius, V., Hafdi, M., Nikulin, M.: Analysis of survival data with cross-effects of survival functions. Biostatistics 5, 415–425 (2004) MR2127114. https://doi.org/10.1016/j.crma.2005.01.019
Cox, D.R.: Regression models and life tables (with discussion). J. R. Stat. Soc. B 34, 187–220 (1972) MR0341758
Grambsch, P., Therneau, T.M.: Proportional hazards tests and diagnostics based on weighted residuals. Biometrika 81, 515–526 (1994) MR1311094. https://doi.org/10.1093/biomet/81.3.515
Hosmer, D., Lemeshow, S., May, S.: Applied Survival Analysis: Regression Modeling of Time-to-Event Data. Wiley, Stowe (2008) MR2383788. https://doi.org/10.1002/9780470258019
Kraus, D.: Identifying nonproportional covariates in the cox model. Commun. Stat., Theory Methods 37, 617–625 (2008) MR2432302. https://doi.org/10.1080/03610920701669744
Kvaløy, J.T., Neef, L.R.: Tests for the proportional intensity assumption based on the score process. Lifetime Data Anal. 10, 139–157 (2004) MR2081718. https://doi.org/10.1023/B:LIDA.0000030200.61020.85
Lin, D.Y.: Goodness of fit analysis for the cox regression model based on a class of parameter estimators. J. Am. Stat. Assoc. 86, 725–728 (1991) MR1147097
Moreau, T., O’Quigley, J., Mesbah, M.: A global goodness-of-fit statistic for the proportional hazards model. Biometrics 34, 212–218 (1985) MR0827669. https://doi.org/10.2307/2347465
Quantin, C., Moreau, T., Asselain, B., Lellouch, J.: A regression model for testing the proportional hazards hypothesis. Biometrics 52, 874–885 (1996) MR1411737. https://doi.org/10.2307/2533049
Stablein, D.M., Koutrouvelis, I.A.: A two sample test sensitive to crossing hazards in uncensored and singly censored data. Biometrics 41, 643–652 (1985) MR0816008. https://doi.org/10.2307/2531284
