Year: 2009
Type: article
Abstract: Regression analysis of censored clustered-correlated time-to-event data is ofinterest in family studies, litter-matched tumorigenesis studies, and
other settings where the survival times may be thought of as arising
in groups or ``clusters, and the correlation among survival times in
each cluster must be taken into account. A natural way to address
such dependence is through incorporation of subject-specific random
effects. In the first part of this disseration, we propose an accelerated failure time (AFT) model for such data
that involves normally-distributed, mean zero random effects and a
within-cluster ``error term that is assumed to have distribution with
a density satisfying mild ``smoothness conditions. We approximate the
smooth density by the ``seminonparametric (SNP) representation of
Gallant and Nychka (1987), which admits a ``parametric form for the
density depending on a known ``kernel density and a tuning parameter
that determines the degree of flexibility for capturing the true
density. This representation facilitates likelihood-based inference
on the regression parameter, random effects variance components, and
the density, which we implement by a Monte Carlo
expectation-maximization (MCEM) algorithm; and we choose the tuning parameter
and ``kernel using standard information criteria. Moreover, arbitrary
censoring patterns may be accommodated straightforwardly. We
illustrate the approach via simulations and by applications to data
from Diabetic Retinopathy Study (DRS, Diabetic Retinopathy Study Research Group, 1981),
from a litter-matched tumorigenesis study (Mantel, Bohidar, and Ciminera, 1977),
and from western Kenya parasitaemia study (McElroy et al., 1997).
The second part of this dissertation focuses on estimation of a bivariate survival function.
In many situations, such as twin studies, matched pair studies, and
studies of organ such as the eyes and kidneys, correlated, bivariate
failure times are recorded. Based on a sample of possibly censored
such failure times, an objective of analysis is to estimate the joint
survival distribution. We extend the use of SNP in the first part of the dissertation to
the two dimensional case and represent the joint density of the failure time using SNP. We illustrate the approach via
simulations and by application to data from the DRS.
Author: Lihua Tang
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2527422982