Mark-specific additive hazards regression with continuous marks

For survival data, mark variables are only observed at uncensored failure times, and it is of interest to investigate whether there is any relationship between the failure time and the mark variable. The additive hazards model, focusing on hazard differences rather than hazard ratios, has been widely used in practice. In this article, we propose a mark-specific additive hazards model in which both the regression coefficient functions and the baseline hazard function depend nonparametrically on a continuous mark. An estimating equation approach is developed to estimate the regression functions, and the asymptotic properties of the resulting estimators are established. In addition, some formal hypothesis tests are constructed for various hypotheses concerning the mark-specific treatment effects. The finite sample behavior of the proposed estimators is evaluated through simulation studies, and an application to a data set from the first HIV vaccine efficacy trial is provided.