Yale University
Department of Statistics
"Local EM Estimation of the Hazard Function for Interval Censored
Data"
Monday, November 25, 1996
Rebecca Betensky
School of Public Health
Harvard University
Seminar to be held in Room 309, LEPH, 60 College
I will discuss a
smooth hazard estimator for interval censored survival data, using the
local likelihood method of Tibshirani and Hastie (1987). To fit the model,
a local EM algorithm is used
in which the current estimate of the hazard function is updated within
overlapping neighborhoods conditional on the observed data and the current
estimate. This local hazard
estimate is then mapped to a global piecewise exponential survivorship
function. The entire procedure is iterated until convergence. The resulting
estimate is ``loosely'' parametric in that it is derived assuming a
``running exponential'' model for the survivorship function. As such, it is
more descriptive than purely non-parametric estimates in regions of
concentrated information and takes on a parametric flavor in regions of
sparse information. Two different pointwise confidence intervals are
derived for the smooth curve, one based on asymptotic theory
and the other on the
bootstrap. I will illustrate
the local EM method for the breast cosmesis data of Finkelstein ({\em
Biometrics}, 1986)
and the AIDS data of Richman, Grimes and Lagakos ({\em J. AIDS}, 1990). The
local likelihood
estimates are compared to the non-parametric estimate of Turnbull ({\em
JRSS-B}, 1976)
and to the
logspline estimate of Kooperberg and Stone ({\em JCGS}, 1992).
This is joint work with Jane Lindsey and Louise Ryan.