Journal of Applied Mathematics and Decision Sciences
Volume 2007 (2007), Article ID 56372, 12 pages
Methods for Stratified Cluster Sampling with Informative Stratification
Department of Statistics, University of Auckland, Private Bag, Auckland 92019, New Zealand
Received 24 April 2007; Accepted 8 August 2007
Academic Editor: Paul Cowpertwait
Copyright © 2007 Alastair Scott and Chris Wild. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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