A systematic review and economic model of the effectiveness and ...

economic model rests on the assumption that the
relative treatment effects will be the same across
trials. This is a common assumption used in any
routine meta-analysis. As Table 86 shows, there is
not a common comparator between all the trials.
Therefore, in order to pool the data, a mixed
treatment comparison (MTC) model was
used. 150,151 An MTC provides an explicit analytical
framework to combine all the evidence
simultaneously in order to estimate a set of
response rates for the economic model. The
framework requires few additional assumptions
over those routinely made in simple meta-analyses.
Mixed treatment comparison
This section provides a brief overview of the
principles underlying an MTC. Suppose there are
three clinical trials comparing three treatments of
interest, A, B and C. Each clinical trial assesses a
different pair-wise comparison, AB, AC and BC. A
simplistic method might be to compare direct
treatment effects against a common baseline, for
example A, and merely discard the information
provided by the BC comparison. This is in
accordance with the view that indirect comparisons
of A and C based on comparisons of AB and BC
represent a lower level of evidence. However, it is
evident that, based on the principle of transitivity,
if the true differences between AB, AC and BC are
(on the appropriate scale) AB, AC and BC, then
we expect
AC = AB + BC
Hence the information provided by the BC
comparison need not be discarded and can be
used to update the direct comparisons of AB and
AC. Higgins and Whitehead 150 have shown how
the use of ‘external’ AB and BC evidence can
substantially reduce uncertainty about an AC
comparison of primary interest. For example, with
reference to this report, the estimate of the effect
of ER-MPH12 compared with IR-MPH from Steele
and colleagues 90 can be combined with an
estimate of the effect of IR-MPH relative to
placebo in order to obtain an estimated relative
treatment effect for ER-MPH12 compared with
placebo. This estimate would be otherwise
unavailable in this dataset.
Based on these general principles, a Bayesian
meta-analysis of the proportion of responders
assuming random treatment effects was conducted
using Markov Chain Monte Carlo (MCMC)
implemented in WinBUGS. 147 The WinBUGS
model used to estimate the proportions of
responders assumes a regression-like structure,
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Health Technology Assessment 2006; Vol. 10: No. 23
with the logit of the proportion of responders for
any treatment k, depending on a ‘baseline’ term i
in trial i, i = 1, 2, …, 6, and a treatment effect i k .
The trial-specific baselines are drawn from a
common random normal distribution, whose
parameters must be estimated from the data, given
vague priors. Formally, this can be expressed as
logit( i k ) = i + i k
i ~ N(,a) ~ N(0,0.0001),
sa 2 ~ uniform(0,10)
a = 1/sa 2
The trial-specific treatment effects i k are assumed
to be drawn from a common random normal
distribution around the ‘true’ treatment effect k .
A binomial likelihood is assumed from the
available data points:
i k ~ N( k ,b) k ~ N(0,0.0001),
sb 2 ~ uniform(0,10)
b = 1/sb 2
r i k ~ Bin(pi k , ni k ),
where k denotes all treatment indices in study i, r i
denotes the observed number of responses and n i
denotes the total number in the group.
The WinBUGS code for the model is reported in
Appendix 9. The code represents an extension of
the Higgins and Whitehead 1996 model 150 to
more general MTC structures. The output from
the model incorporates the uncertainty around the
estimated response rates and also any correlation
between treatments. However, for simplicity, threearm
trials were treated as two two-arm trials with a
common comparator.
Combination therapy
As noted in the clinical effectiveness review in
Chapter 4, where behavioural therapies are used
in combination with pharmacotherapy, they vary
between trials. As such, there is no one ADHD
combination therapy that we could assess in
comparison with drug monotherapy. However,
some of the trials did show a (non-statistically
significant) favourable effect of combination
therapy compared with drug monotherapy. The
data do not allow us to compare a single consistent
behavioural therapy component in combination
with all of the relevant treatment comparators.
Instead, we can only estimate the relative increase
in response rate associated with IR-MPH and BT
compared with IR-MPH alone. 65,133 Hence
combination therapy was considered in a
secondary analysis, where the relative increase in
response rate for IR-MPH with BT compared with
105