Additive hazards model with multivariate failure time data

Marginal additive hazards models are considered for multivariate survival data in which individuals may experience events of several types and there may also be correlation between individuals. Estimators are proposed for the parameters of such models and for the baseline hazard functions. The estimators of the regression coefficients are shown asymptotically to follow a multivariate normal distribution with a sandwich-type covariance matrix that can be consistently estimated. The estimated baseline and subject-specific cumulative hazard processes are shown to converge weakly to a zero-mean Gaussian random field. The weak convergence properties for the corresponding survival processes are established. A resampling technique is proposed for constructing simultaneous confidence bands for the survival curve of a specific subject. The methodology is extended to a multivariate version of a class of partly parametric additive hazards model. Simulation studies are conducted to assess finite sample properties, and the method is illustrated with an application to development of coronary heart diseases and cardiovascular accidents in the Framingham Heart Study.