Local Polynomial Density Estimation with Interval Censored Data

• Activity Number: 295
• Type: Topic Contributed
• Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Derick Peterson*+ and Mark J van der Laan
• Companies: University of Rochester and University of California-Berkeley
• Keywords: interval censored data ; local polynomial regression ; bandwidth selection ; survival analysis ; smoothing ; density estimation

Abstract

A survival time T is interval censored if only its current status is observed at several monitoring times. We provide an estimator with pointwise confidence limits for any derivative of the distribution of T, assuming that the observed monitoring times are independent of T. Our estimator is a standard local polynomial regression smoother applied to the pooled sample of N dependent current status observations. We show that the proposed estimator has a normal limiting distribution identical to that of a smoother applied to N i.i.d. current status observations. Thus local bandwidth selection techniques and pointwise confidence limit procedures for standard nonparametric regression perform properly despite the dependence in the pooled sample. Our results also imply that, for a large number of subjects, each additional monitoring time for subjects already monitored actually carries as much information for estimation of the survival function as a monitoring time for a new, independent subject. We investigate the practical performance of our proposed data-driven density estimator in a simulation study.