On the small-sample performance of Efron's and of Gill's version of the product limit estimator under nonproportional hazards

Various proposals have been made to extend the product limit estimator to survival times beyond the largest observation in case that observation is censored. Two extreme extensions are examined with respect to bias and mean squared error (MSE). Their quality depends considerably on the "censoring constellation." The MSE of one extension appears to be robust against a wide variety of nonproportionalities of the hazard rates of the distributions of lifelength and time to censoring.