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Additive hazard regression models: an application to the natural history of human papillomavirus.

Xie X, Strickler HD, Xue X - Comput Math Methods Med (2013)

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

Affiliation: Department of Epidemiology and Population Health, Albert Einstein College of Medicine, Bronx, NY 10461, USA. xianhong.xie@einstein.yu.edu

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.

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Cox-Snell residual plots for oncogenic HPV models with diagonal reference lines: (a) semiparametric additive model; (b) nonparametric additive model.
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fig2: Cox-Snell residual plots for oncogenic HPV models with diagonal reference lines: (a) semiparametric additive model; (b) nonparametric additive model.

Mentions: In this analysis based on model (2), the estimated survival probability of oncogenic HPV over 5 years of followup among HIV-negative women with an age < 30, of Caucasian race, who were nonsmokers, and had only one male sexual partner in the past 6 months, was 0.80. The corresponding cumulative incidence was 1 − 0.80 = 0.20, which implies that over 5 years of followup 20% of HIV-negative women with the previously mentioned characteristics had at least one positive test for oncogenic HPV; the cumulative incidence rates by 5 years of followup were 0.33, 0.47, and 0.60 for CD4 > 500, CD4 200–500, and CD4 < 200 groups, respectively. Thus, for every 100 women with CD4 < 200, there were 40 more oncogenic HPV infections by year 5 compared to every 100 HIV-negative women, which is a significant increase in number of infections. Both the semiparametric and nonparametric additive hazard models fit the data well based on the Cox-Snell residual plots (Figure 2): the estimated cumulative hazard curves approximately follow the 45 degree lines.


Additive hazard regression models: an application to the natural history of human papillomavirus.

Xie X, Strickler HD, Xue X - Comput Math Methods Med (2013)

Cox-Snell residual plots for oncogenic HPV models with diagonal reference lines: (a) semiparametric additive model; (b) nonparametric additive model.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3569891&req=5

fig2: Cox-Snell residual plots for oncogenic HPV models with diagonal reference lines: (a) semiparametric additive model; (b) nonparametric additive model.
Mentions: In this analysis based on model (2), the estimated survival probability of oncogenic HPV over 5 years of followup among HIV-negative women with an age < 30, of Caucasian race, who were nonsmokers, and had only one male sexual partner in the past 6 months, was 0.80. The corresponding cumulative incidence was 1 − 0.80 = 0.20, which implies that over 5 years of followup 20% of HIV-negative women with the previously mentioned characteristics had at least one positive test for oncogenic HPV; the cumulative incidence rates by 5 years of followup were 0.33, 0.47, and 0.60 for CD4 > 500, CD4 200–500, and CD4 < 200 groups, respectively. Thus, for every 100 women with CD4 < 200, there were 40 more oncogenic HPV infections by year 5 compared to every 100 HIV-negative women, which is a significant increase in number of infections. Both the semiparametric and nonparametric additive hazard models fit the data well based on the Cox-Snell residual plots (Figure 2): the estimated cumulative hazard curves approximately follow the 45 degree lines.

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

Affiliation: Department of Epidemiology and Population Health, Albert Einstein College of Medicine, Bronx, NY 10461, USA. xianhong.xie@einstein.yu.edu

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.

Show MeSH
Related in: MedlinePlus