A1388
Title: Bounded hazard ratio Cox model for the effect of time to treatment on mortality
Authors: Krithika Suresh - University of Michigan (United States) [presenting]
John Rice - University of Michigan (United States)
Abstract: In resource-limited settings, there is often interest in assessing the effect of time to treatment (TTT) on subsequent mortality. It is demonstrated that the traditional Cox proportional hazards model specifying the effect of TTT as an unrestricted term in the log hazard ratio results in a mathematical anomaly that violates the expected monotonic TTT effect on survival (i.e., as TTT increases, survival probability should decrease). A class of bounded hazard ratio (BHR) Cox models is proposed that attenuate the hazard ratio for TTT towards the null with increasing treatment time, such that hazard for death after treatment does not exceed the hazard without treatment. Estimation is performed using direct optimization of the partial log-likelihood, and a linearized approximation is proposed to fit the model in standard software for large sample sizes. From BHR models, the estimated hazard ratio curve describes how the treatment effect diminishes with delays in treatment. Additionally, the marginal survival probability difference comparing immediate treatment to a treatment time in the future is presented. The performance of model estimation is evaluated in a simulation study and the use of the approach is demonstrated in an application to treatment for colon cancer using NCDB data.
