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Biometrika 2002 89(2):283-298; doi:10.1093/biomet/89.2.283
© 2002 by Biometrika Trust
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A flexible additive multiplicative hazard model

Torben Martinussen1 and Thomas H.Scheike2

1 Department of Mathematics and Physics, The Royal Veterinary and Agricultural University, Thorvaldsensvej 40, DK-1871 Frederiksberg C, Denmark torbenm@dina.kvl.dk 2 Department of Biostatistics, University of Copenhagen, Blegdamsvej 3, DK-2200 Copenhagen N, Denmark ts@biostat.ku.dk

We present a new additive-multiplicative hazard model which consists of two components.The first component contains additive covariate effects through an additive Aalen model while the second component contains multiplicative covariate effects through a Cox regression model. The Aalen model allows for time-varying covariate effects, while the Cox model allows only a common time-dependence through the baseline. Approximate maximum likelihood estimators are derived by solving the simultaneous score equations for the nonparametric and parametric components of the model. The suggested estimators are provided with large-sample properties and are shown to be efficient. The efficient estimators depend, however, on some estimated weights. We therefore also consider unweighted estimators and describe their large-sample properties. We finally extend the model to allow for time-varying covariate effects in the multiplicative part of the model as well.

Key Words: Aalen's additive model; Counting process; Cox regression; Hazard model; Proportional excess hazard model; Time-varying effect

Received April 2000. Revised September 2001


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