A kernel method for incorporating information on disease progression in the analysis of survival

This paper considers incorporating information on disease progression in the analysis of survival. A three-state model is assumed, with the distribution of each transition estimated separately. The distribution of survival following progression can depend on the time of progression. Kernel methods are used to give consistent estimators under general forms of dependence. The estimators for the individual transitions are then combined into an overall estimator of the survival distribution. A test statistic for equality of survival between treatment groups is proposed based on the tests of Pepe & Fleming (1989, 1991). In simulations the kernel method successfully incorporated dependence on the time of progression in some reasonable settings, but under extreme forms of dependence the tests had substantial bias. If survival beyond progression can be predicted fairly accurately, then gains in power over standard methods that ignore progression can be substantial, but the gains are smaller when survival beyond progression is more variable. The methodology is illustrated with an application to a breast cancer clinical trial.