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Biostatistics. 2011 Apr;12(2):354-68. doi: 10.1093/biostatistics/kxq061. Epub 2010 Sep 21.

Estimation of the 2-sample hazard ratio function using a semiparametric model.

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  • 1Office of Biostatistics Research, National Heart, Lung, and Blood Institute, Bethesda, MD 20892, USA.


The hazard ratio provides a natural target for assessing a treatment effect with survival data, with the Cox proportional hazards model providing a widely used special case. In general, the hazard ratio is a function of time and provides a visual display of the temporal pattern of the treatment effect. A variety of nonproportional hazards models have been proposed in the literature. However, available methods for flexibly estimating a possibly time-dependent hazard ratio are limited. Here, we investigate a semiparametric model that allows a wide range of time-varying hazard ratio shapes. Point estimates as well as pointwise confidence intervals and simultaneous confidence bands of the hazard ratio function are established under this model. The average hazard ratio function is also studied to assess the cumulative treatment effect. We illustrate corresponding inference procedures using coronary heart disease data from the Women's Health Initiative estrogen plus progestin clinical trial.

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