There has been considerable interest recently in quantifying
uncertainty beyond that due to random error in meta-analyses.
This is particularly relevant to meta-analyses of observational studies,
since error in estimates from these studies cannot be attributed
to a randomization mechanism. Typically, observational studies are
also subject to error due to measurement error, non-participation,
and incomplete adjustment for confounding. Errors due to these
sources are often referred to as bias. To quantify uncertainty due
to bias, researchers have proposed using "bias models" and giving
subjectively elicited probability distributions to parameters that
are not identifiable in the models.
In a typical meta-analysis, probability distributions involving
tens of parameters will have to be elicited. At the same time, the
resulting estimate and uncertainty interval of the overall (meta-analytic) effect measure will generally be very sensitive to this
multi-dimensional subjectively-elicited distribution. To overcome
some of the problems associated with the use of such a distribution,
I propose an alternative method for eliciting and quantifying
uncertainty due to bias. In the method of this thesis, the lower and
upper bounds of bias parameters are elicited instead of probability
distributions. The most extreme Bayesian posterior inference
for the target parameter of interest within the specified bounds
is sought through an algorithm. The resulting lower and upper
bounds for the target parameter of interest have interpretation of
a Robust Bayes analysis.
In this thesis, the method is applied to a meta-analysis of
childhood leukaemia and exposure to electromagnetic fields. The
method of this thesis was found to produce uncertainty intervals
that are generally more conservative in comparison with the standard
approach. It is also proposed that the method be used as a
tool for sensitivity analysis, and some interesting insight is gained
from the childhood leukaemia data. [For supplementary files please contact author].