Additive Hazard Regression Models: An Application to the Natural History of Human Papillomavirus

Xianhong Xie,Xiaonan Xue,Howard D. Strickler

doi:10.1155/2013/796270

Abstract

There are several statistical methods for time-to-event analysis, among which is the Cox proportional hazards model that is most commonly used. However, when the absolute change in risk, instead of the risk ratio, is of primary interest or when the proportional hazard assumption for the Cox proportional hazards model is violated, an additive hazard regression model may be more appropriate. In this paper, we give an overview of this approach and then apply a semiparametric as well as a nonparametric additive model to a data set from a study of the natural history of human papillomavirus (HPV) in HIV-positive and HIV-negative women. The results from the semiparametric model indicated on average an additional 14 oncogenic HPV infections per 100 woman-years related to CD4 count < 200 relative to HIV-negative women, and those from the nonparametric additive model showed an additional 40 oncogenic HPV infections per 100 women over 5 years of followup, while the estimated hazard ratio in the Cox model was 3.82. Although the Cox model can provide a better understanding of the exposure disease association, the additive model is often more useful for public health planning and intervention.

Highlights

Time-to-event analysis is commonly used to study the risk factors associated with the incidence of clinical events [1]
The Cox proportional hazard model for the incident detection of oncogenic human papillomavirus (HPV) showed that HIV-positive women with CD4 > 500 had a hazard ratio (HR) 1.62 with 95% confidence interval (CI) 1.31 to 2.00 relative to HIV-negative women
Similar significant factors as in the incident oncogenic HPV were found with the additional findings that African American women had higher incidence of any HPV than Caucasian women, and the number of male sexual partners in the past 6 months was positively associated with the incident detection of any HPV

Summary

Introduction

Time-to-event analysis is commonly used to study the risk factors associated with the incidence of clinical events [1]. There are several different models for measuring the relation of time-to-event data with risk factors, including parametric, semiparametric, and nonparametric models. The strength of association is estimated using the maximum likelihood approach. Most notably Cox proportional hazard regression models [2], the hazard function is assumed to be multiplicatively related to the covariates, with an unspecified baseline hazard function, and the maximum partial likelihood method is used to estimate the parameters. Most notably the Kaplan-Meier approach, no assumptions are made regarding the relationship between the disease risk and the covariates. The survival function for each stratum of the covariates is estimated with empirical methods, and the log-rank test and other nonparametric tests are typically used to test the effects of these covariates

Methods

Results

Conclusion