© 1997 by Biometrika Trust
Efficient estimation of the lifetime and disease onset distribution
Division of Biostatistics, University of California Berkeley, California, U.S.A. e-mail: laan{at}stat.berkeley.edu jewell{at}stat.berkeley.edu derick{at}stat.berkeley.edu
We study efficient nonparametric maximum likelihood estimation of the distribution of onset and lifetime associated with an irreversible disease that is only detectable at sacrifice or death. We show that, if the onset distribution is continuous, then estimation of the lifetime distribution cannot be improved by using current status information on the time till onset. In this case the Kaplan-Meier estimator of the lifetime distribution is asymptotically efficient. The nonparametric maximum likelihood estimator tries to use current status information on the time till onset, but it is asymptotically equivalent to the Kaplan-Meier estimator, and it is outperformed by the latter in simulations. The nonparametric maximum likelihood estimator of the onset distribution is shown to be an iteratively reweighted least squares estimator which can be computed with the weighted pool-adjacent-violators algorithm. We show that it is unnecessary to estimate the weights iteratively since an initial estimate cannot be improved. This insight leads to a simple, explicit estimator which improves on the nonparametric maximum likelihood estimator of the onset distribution. The results are verified with simulations, and a data analysis example is provided.
Key Words: Current status data • Kaplan-Meier estimator • Nonparametric maximum likelihood estimation