Choice of Monitoring Mechanism for Optimal Nonparametric Functional Estimation for Binary Data

Nicholas P. Jewell, Division of Biostatistics, School of Public Health, University of California, Berkeley
Mark J. van der Laan, Division of Biostatistics, School of Public Health, University of California, Berkeley
Stephen Shiboski, Department of Epidemiology and Biostatistics, University of California, San Francisco

Abstract

Optimal designs of dose levels in order to estimate parameters from a model for binary response data have a long and rich history. These designs are based on parametric models. Here we consider fully nonparametric models with interest focused on estimation of smooth functionals using plug-in estimators based on the nonparametric maximum likelihood estimator. An important application of the results is the derivation of the optimal choice of the monitoring time distribution function for current status observation of a survival distribution. The optimal choice depends in a simple way on the dose response function and the form of the functional. The results can be extended to allow dependence of the monitoring mechanism on covariates.