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Biometrika 1998 85(3):593-603; doi:10.1093/biomet/85.3.593
© 1998 by Biometrika Trust
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Two-sample goodness-of-fit tests for additive risk models with censored observations

JINHEUM KIM and SEUNG-YEOUN LEE

Department of Applied Statistics, University of Suwon Kyonggido, 445-743, South Koreajinhkim{at}stat.suwon.ac.kr
Department of Applied Statistics, Sejong University Seoul, 143-747, South Korealeesy{at}cs.sejong.ac.kr

The additive risk model assumes that the hazard function associated with a set of covariates is the sum of the baseline hazard function and the regression function of covariates. We propose two different test procedures for checking the adequacy of two-sample additive risk models for randomly censored observations. One is based on the martingale residuals and the other on the difference between weighted estimators of the excess risk. The test statistics are shown to be asymptotically normal under appropriate regularity conditions and consistent under any model misspecifications. Finally, two real examples are provided, along with results of a simulation study.

Key Words: Additive risk model • Consistency • Excess risk • Goodness-of-fit test • Martingale residual • Proportional hazards model • Weighted estimator


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