Efficient and Ad Hoc Estimation in the Bivariate Censoring Model

A large number of proposals for estimating the bivariate survival function under random censoring has been made. In this paper we discuss nonparametric maximum likelihood estimation and the bivariate Kaplan-Meier estimator of Dabrowska. We show how these estimators are computed, present their intuitive background and compare their practical performance under different levels of dependence and censoring, based on extensive simulation results, which leads to a practical advise.

A Note on the Asymptotic Variance of Survival Function in the Semi-Markov Model

In Malani and Neilsen (1992) we have proposed alternative estimates of survival function (for time to disease) using a simple marker that describes time to some intermediate stage in a disease process. In this paper we derive the asymptotic variance of one such proposed estimator using two different methods and compare terms of order 1/n when there is no censoring. In the absence of censoring the asymptotic variance obtained using the Greenwood type approach converges to exact variance up to terms involving 1/n. But the asymptotic variance obtained using the theory of the counting process and results from Voelkel and Crowley (1984) on semi-Markov processes has a different term of order 1/n. It is not clear to us at this point why the variance formulae using the latter approach give different results.