Faecal occult blood testing for population health screening May 2004

3. The positive predictive value (PPV) for each FOBT was also determined; these data
are reported in Appendix F, for completeness.
The PPV is the probability that if a person tests positive that they actually have the
condition:
True positive/(True positive + False positive).
Meta-analyses
This project required separate meta-analyses of various outcomes measuring the
efficacy of the test being examined. The analyses were also carried out for various
populations.
Typically, each set of trial results consisted of two or more observed proportions, one for
each test used. For each trial, the tests were usually repeated on the same set of patients.
These circumstances, in general, preclude the use of classical meta-analyses methods for
summary data, as these methods were developed for two-arm trials with independent sets
of subjects in each arm.
In addition, there was usually a small number of trials involved in each meta-analysis.
Classical random-effects meta-analysis (Der Simonian and Laird 1986) implicitly assumes
that a between-studies variance estimate used in the calculation of the weights for the
method is known with precision, and this is not likely to be true for a small number of
trials.
A further source of variability may be that diagnostic test results are sensitive to the
threshold set for the test, which may vary between studies (see Lijmer et al 2002 for
details).
The circumstances outlined above suggest that a more sophisticated random-effects
analysis is required, and a Bayesian approach was deemed to provide a more appropriate,
conservative approach (Higgins and Whitehead 1996; Smith et al 1995). The analyses
were carried out using Markov Chain Monte Carlo (MCMC) simulation as implemented
in the statistical package WinBUGS (version 1.3, Spiegelhalter et al 2000).
The method is based on fitting logistic regression models incorporating random effects.
A random intercept model of the form was adopted:
logit(p ij) = α + b i + β j × x ij,
where,
• p ij = prob(Y ij = 1) is the probability that the event occurs
• α is an intercept, interpreted as the log-odds for the event occurring in a
reference category, in this case the guaiac test group
• b i is a random effect for the i th study, which is common across all categories of
interest
24 Faecal occult blood testing