SEMINAR DETAILS

Time:

2:00 PM - 3:00 PM

Place:

133 Rosenau Hall Auditorium

Speaker:

Moulinath Banerjee, PhD

Affiliation

Department of Statistics and Biostatistics
University of Michigan

Title & Abstract:

Asymptotics of Interval Censored Data under Various Observation Time Schemes

We investigate the pointwise asymptotic distribution of the MLE of the survival time distribution in the setting of interval censored (current status) data under a variety of observation time schemes. Current status data arises when the time to death/infection of an individual, X, cannot be determined exactly; what is known is whether the individual was infected/failed by the observation time T. Thus, the observed data on an individual are (Δ; T) where Δ = 1(X ≤ T). Usually T is taken to be independent of X (conditionally independent in the presence of covariates). A standard assumption when doing inference for F, the distribution of X, is that the observation time T comes from a Lebesgue density on an interval. Inference in this scenario has been studied extensively. However, in many applications, it is more realistic to think of the observation times as coming from a grid on a time interval, with the distinct ones assumed to grow with the sample size but at a slower rate. We investigate inference under such settings and show that for sufficiently sparse grids, the limit distribution of F at a fixed point is normal, while for dense grids the limit transitions to the non-Gaussian Chernoff's distribution. There is a particular grid resolution  at which this transition happens and the limit at this particular resolution is different from either of the previous limits. We discuss this problem in the general setting of an isotonic regression problem and indicate extensions and other related problems of interest. In particular, our work shows that the likelihood ratio based inference strategy using Banerjee and Wellner (2001)'s limit distribution is fairly robust to departures from the Lebesgue density assumption on the observation times.  

This is joint work with Michael Kosorok and Runlong Tang.

Contact :

Tania Osborn (919) 966-7268

Notes:

n/a