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Biometrika 1994 81(1):61-71; doi:10.1093/biomet/81.1.61
© 1994 by Biometrika Trust
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Semiparametric analysis of the additive risk model

D. Y. LIN1 and ZHILIANG YING2

1Department of Biostatistics, SC-32, University of Washington, Seattle Washington 98195, U.S.A.
2Department of Statistics, University of Illinois, Champaign Illinois 61820, U.S.A.

In contrast to the proportional hazards model, the additive risk model specifies that the hazard function associated with a set of possibly time-varying covariates is the sum of, rather than the product of, the baseline hazard function and the regression function of covariates. This formulation describes a different aspect of the association between covariates and the failure time than the proportional hazards model, and is more plausible than the latter for many applications. In the present paper, simple procedures with high efficiencies are developed for making inference about the regression parameters under the additive risk model with an unspecified baseline hazard function. The subject-specific survival estimation is also studied. The proposed techniques resemble the partial-likelihood-based methods for the proportional hazards model. A real example is provided.

Key Words: Adaptive estimation • Censoring • Counting process • Excess risk • Failure time • Information bound • Martingale • Partial likelihood • Proportional hazards • Regression • Survival data • Time-dependent covariate • Truncation


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