Additive and multiplicative hazards modeling for recurrent event data analysis

Hyun J Lim,Xu Zhang

doi:10.1186/1471-2288-11-101

Abstract

BackgroundSequentially ordered multivariate failure time or recurrent event duration data are commonly observed in biomedical longitudinal studies. In general, standard hazard regression methods cannot be applied because of correlation between recurrent failure times within a subject and induced dependent censoring. Multiplicative and additive hazards models provide the two principal frameworks for studying the association between risk factors and recurrent event durations for the analysis of multivariate failure time data.MethodsUsing emergency department visits data, we illustrated and compared the additive and multiplicative hazards models for analysis of recurrent event durations under (i) a varying baseline with a common coefficient effect and (ii) a varying baseline with an order-specific coefficient effect.ResultsThe analysis showed that both additive and multiplicative hazards models, with varying baseline and common coefficient effects, gave similar results with regard to covariates selected to remain in the model of our real dataset. The confidence intervals of the multiplicative hazards model were wider than the additive hazards model for each of the recurrent events. In addition, in both models, the confidence interval gets wider as the revisit order increased because the risk set decreased as the order of visit increased.ConclusionsDue to the frequency of multiple failure times or recurrent event duration data in clinical and epidemiologic studies, the multiplicative and additive hazards models are widely applicable and present different information. Hence, it seems desirable to use them, not as alternatives to each other, but together as complementary methods, to provide a more comprehensive understanding of data.

Highlights

Ordered multivariate failure time or recurrent event duration data are commonly observed in biomedical longitudinal studies
Data consisted of medical record reviews of follow-ups of firearm victims younger than 19-years-old who were presenting to the Pediatric Emergency Department/Trauma Center at the Children’s Hospital of Wisconsin and all other hospitals in the Milwaukee metropolitan area between 1990 and 1997
A total of 511 subjects were eligible for this study; this sample was taken from the pediatric firearm emergency department (ED) visit database

Summary

Introduction

Ordered multivariate failure time or recurrent event duration data are commonly observed in biomedical longitudinal studies. The majority of existing regression methods for analyzing multivariate failure or recurrent event time data assumes multiplicative covariate effects. Others used the random effect frailty model or the conditional frailty model for such recurrent event data analysis [6,7] The popularity of these multiplicative models derives from their utility and wide applicability, and from convention and the availability of statistical software. The semiparametric additive hazards model proposed by Lin and Ying [8] is the most closely connected analogue of the multiplicative Cox hazards model. Their additive hazards model assumes that covariates act in an additive manner on an unknown baseline hazard rate and that the effect of a covariate is time-invariant. Numerous authors advocated and utilized the additive hazards models for multivariate failure time data [9,10,11,12,13,14]

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Conclusion