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Biometrika 1997 84(3):631-639; doi:10.1093/biomet/84.3.631
© 1997 by Biometrika Trust
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A test of fit for a semiparametric additive risk model

K. C. YUEN and M. D. BURKE

Department of Statistics, The University of Hong Kong Hong Kong e-mail: kcyuen{at}hkuce.hku.hk
Department of Mathematics and Statistics, University of Calgary Calgary, Alberta T2N 1N4, Canada e-mail: mdburke{at}acs.ucalgary.ca

Kolmogorov-Smirnov and Cramér-von Mises type test statistics based on the standardised cumulative hazard process are proposed. It is very difficult to evaluate their asymptotic distributions, but they can be approximated by the use of the bootstrap. The advantages of the goodness-of-fit test are that arbitrary partitions of the time axis and covariate spaces are not needed for evaluating test statistics and that it has excellent consistency properties. The test is applied to data from the Mayo Clime trial in primary biliary cirrhosis of the liver. A simulation study indicates that the proposed test is suitable for practical use.

Key Words: Additive risk • Baseline hazard function • Bootstrap • Cumulative hazard • Empirical process • Gaussian process • Goodness of fit • Random censorship • Survival times


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