NONPARAMETRIC ESTIMATION OF SURVIVAL FUNCTION FROM INCOMPLETE OBSERVATIONS

Tsai, Ferguson, Susarla and van Ryzin studied the generalized self-consistent estimator and nonparametric Bayesian estimator of survival function from incomplete observations. In this paper we generalized the results to dependent competing risks model and show that these estimators have similar large sample properties. We derive a integral equation which relates the survival functions of X⁰, L, R to the joint distribution functions of Y and δ under the dependent doubly censorship model. The solution \hatS^0(t) can be calculated numerically by using the EM algorithm or by the Newton-Raphson method.