# Efficiency of the semi-parametric maximum likelihood estimator in generalized case-control studies

Abstract (Summary)

In this thesis, we investigate the efficiency of the semi-parametric maximum likelihood
estimator in the context of generalized case-control studies. We introduce the
idea of a multi-sample model and show that it enables us to treat a number of variations
of the basic case-control study under the same framework in a natural way.
For example, data from a case-control study are a multi-sample, since they consist
of two independent samples, one from the case population and one from the control
population. Some missing data can also be treated as a multi-sample. We select
full data from the full data population and partial data from the other population.
Moreover, data gathered using an outcome-dependent two-phase sampling design
can also be regarded as a multi-sample.
We show that the theory of M-estimation for an i.i.d. model can be extended
naturally to multi-sample models, and treat maximum likelihood in these models as
a special case of M-estimation. The efficiency of the maximum likelihood estimator
can then be studied using the theory of M-estimators in a multi-sample model.
Scott & Wild (1997, 2001) use a profile likelihood approach to calculate the semiparametric
maximum likelihood estimator in generalized case-control studies. The
resulting estimating equations cannot be treated using standard M-estimator theory,
since the estimating functions depend on the sample size. We extend the
standard treatment of estimating functions to include the derivative of the profile
log-likelihood so that the maximum likelihood estimator, the solution to its
corresponding estimating equation, is a special case of an M-estimator. We then
demonstrate that the semi-parametric MLE is the most efficient among the class of
extended M-estimators.
Bibliographical Information:

Advisor:

School:The University of Auckland / Te Whare Wananga o Tamaki Makaurau

School Location:New Zealand

Source Type:Master's Thesis

Keywords:

ISBN:

Date of Publication:01/01/2005