Journal of Applied Mathematics and Decision Sciences
Volume 2007 (2007), Article ID 56372, 12 pages
doi:10.1155/2007/56372
Abstract
We look at fitting regression models using data from stratified cluster samples when the
strata may depend in some way on the observed responses within clusters. One important
subclass of examples is that of family studies in genetic epidemiology, where the probability
of selecting a family into the study depends on the incidence of disease within the family.
We develop the survey-weighted estimating equation approach for this problem,
with particular emphasis on the estimation of superpopulation parameters. Full maximum
likelihood for this class of problems involves modelling the population distribution of the
covariates which is simply not feasible when there are a large number of potential covariates.
We discuss efficient semiparametric maximum likelihood methods in which the covariate
distribution is left completely unspecified. We further discuss the relative efficiencies of these
two approaches.