Group sequential checking of the proportional hazards assumption based on a time-dependent covariate. (English) Zbl 0942.62090
Summary: In a comparative trial comparing two survival curves, the Cox regression model assumes that the hazard ratios for the two treatments are constant over time. Many advantages of using the Cox model depend on this assumption. In a group sequentially monitored survival trial, we also wish to test the proportional hazards assumption in addition to monitoring the treatment effect. This allows early detection of inappropriateness of the model. As for testing the treatment effect, simply repeating the tests in the fixed sample size case will increase false rejections.
We develop a group sequential method to check the proportional hazards assumption based on the well-known time-dependent covariates by D.R. Cox [J. R. Stat. Soc., Ser. B 34, 187-220 (1972; Zbl 0243.62041)]. The test statistics proposed have an independent increments structure. This allows the use of the standard group sequential methods such as the alpha-spending approach by K.K.G. Lan and D.L. DeMets [Biometrika 70, 659-663 (1983; Zbl 0543.62059)]. The operating characteristics are studied by a simulation.
We develop a group sequential method to check the proportional hazards assumption based on the well-known time-dependent covariates by D.R. Cox [J. R. Stat. Soc., Ser. B 34, 187-220 (1972; Zbl 0243.62041)]. The test statistics proposed have an independent increments structure. This allows the use of the standard group sequential methods such as the alpha-spending approach by K.K.G. Lan and D.L. DeMets [Biometrika 70, 659-663 (1983; Zbl 0543.62059)]. The operating characteristics are studied by a simulation.
MSC:
| 62L10 | Sequential statistical analysis |
| 62N03 | Testing in survival analysis and censored data |
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
Keywords:
alpha spending; Cox regression; independent increments; martingales; score tests; survival dataReferences:
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