Journal
BIOMETRIKA
Volume 89, Issue 2, Pages 283-298Publisher
OXFORD UNIV PRESS
DOI: 10.1093/biomet/89.2.283
Keywords
Aalen's additive model; counting process; Cox regression; hazard model; proportional excess hazard model; time-varying effect
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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.
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