The NPMLE in the Uniform Doubly Censored Current Status Data Model

In biostatistical applications interest often focuses on the estimation of the distribution of time T between two consecutive events. If the initial event time is observed and the subsequent event time is only known to be larger or smaller than an observed point in time, then the data is described by the well understood singly censored current status model, also known as interval censored data, case I. Jewell, Malani and Vittinghoff (1994) extended this current status model by allowing the initial time to be unobserved, but with its distribution over an observed interval [A,B] known to be uniformly distributed; the data is referred to as doubly censored current status data. These authors used this model to handle applications in AIDS partner studies focusing on the nonparametirc maximum likelihood estimate (NPMLE) of the distribution function, G, of T. The model is a submodel of the current status model, but G is essentially the derivative of the distribution function of interest, F, in the current status model. In this paper we establish that the NPMLE of G is uniformly consistent and that the resulting estimators for square root n estimable parameters are efficient. We propose an iterative weighted Pool-Adjacent-Violator-Algorithm to compute the NPMLE of G. The rate of convergence of the NPMLE of F is also established