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

This paper considers incorporating information on disease progressionin 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 dependon the time of progression. Kernel methods are used to giveconsistent estimators under general forms of dependence. Theestimators for the individual transitions are then combinedinto an overall estimator of the survival distribution. A teststatistic for equality of survival between treatment groupsis proposed based on the tests of Pepe & Fleming (1989,1991). In simulations the kernel method successfully incorporateddependence on the time of progression in some reasonable settings,but under extreme forms of dependence the tests had substantialbias. If survival beyond progression can be predicted fairlyaccurately, then gains in power over standard methods that ignoreprogression can be substantial, but the gains are smaller whensurvival beyond progression is more variable. The methodologyis illustrated with an application to a breast cancer clinicaltrial.