Modelling and inference on time-varying hazard ratios for survival data

Song Yang
Office of Biosatistics Research, Office of the Director
National Heart, Lung, and Blood Institute

Wednesday, October 17, 2007
3:30pm
MoosT 1-450G
Minneapolis Campus

Abstract:

The hazard ratio is arguably the standard measure for assessing the treatment effect with survival data. In clinical applications, often the hazard ratio is given as a single value. When there is evidence of varying hazard ratio over time, a common approach to assess the treatment effect is to give a hazard ratio over each of a few time intervals. From the modelling point of view, these practices correspond to assuming the Cox model, for the entire range or separately for each time period. In general, the hazard ratio is a function of time, and provides a visual display of the temporal pattern of the treatment effect. In the literature, a variety of non-proportional hazards alternatives to the Cox model have been proposed, and some of them have been investigated more thoroughly in recent years. However, these alternative models have not been widely used in clinical practice, and results on time-varying hazard ratio are almost nonexistent. A review of the common non-proportional hazards models reveals their restrictions on the of variation pattern of the hazard ratio. We investigate a model that allows a wider range of time-varying hazard ratios. The point estimates, point-wise confidence intervals, and confidence bands of the hazard ratio are proposed under this model. We demonstrate the inference procedures in several data sets, with mild to severe time-dependent hazard ratios. These examples show that the hazard ratio and its confidence bands can be very useful as part of a visual display tool kit for assessing the treatment effect with survival data.

A social tea will be held at 3:00 P.M. in A434 Mayo. All are Welcome.
For more details contact 612-624-4655 or see http://www.biostat.umn.edu/seminar_academic.html