Nonparametric estimation of lifetime and disease onset distributions from incomplete observations

In this paper we derive and investigate nonparametric estimators of the distributions of lifetime and time until onset associated with an irreversible disease that is detectable only at death. The nonparametric maximum likelihood solution requires an iterative algorithm. An alternative though closely related pair of estimators for the lifetime and onset distributions exists in closed form. These estimators are the familiar Kaplan-Meier estimator and an isotonic regression estimator, respectively. First-order approximations provide variance estimators. The proposed methods generalize and shed additional light on the constrained estimators presented by Kodell, Shaw and Johnson (1982, Biometrics 38, 43-58). Data from an animal experiment illustrate the techniques.