**Realistic priors for related
parameters**

In certain statistical applications the inference regarding a parameter
of principle interest is

strongly dependent on the value of a
nuisance parameter. For example, in cross-over trials the

inference regarding the direct effect
of treatment will be strongly dependent on assumptions

regarding the carry-over effect. In a
random effects meta-analysis the inferences about the overall

effect of treatment may be strongly dependent on
assumptions about the random-effects variance,

in particular if the number of trials is small.
In many such cases, however, putting uninformative

priors on the nuisance parameter can be dangerous.
For instance, if an uninformative prior is put

on the carry-over effect for an AB/BA cross-over,
then inference about the treatment is reduced to

a comparison of the first period values only.
Furthermore, such independent specification of priors

for main and nuisance parameters can exhibit
incoherence. As a concrete example consider the

trial by Martin and Browning (1985). The ratio of
the interval of measurement between the last dose

of the previous treatment and the last dose of
the current treatment was at least 125. Thus to use

the same prior for carry-over and direct effect is
to say that it is just as likely that the former will be

greater than the latter as vice-versa
despite the fact that the duration of action would have to be

125 times as great. Similarly for random effects
meta-analysis it is much more plausible that the

random effect variance can be large if the treatment
effect is large than if it is small.

This project will look at possible Bayesian approaches to analysis using
linked (joint)
priors to

see whether any practical contribution can be made
to modelling in
such cases. It is likely to include an

empirical investigation of published
meta-analyses to compare estimated random effect variances to treatment

estimates.

**References**

Martin A, Browning RC. Metoprolol in the aged
hypertensive: a comparison
of two dosage

schedules. Postgrad
Med J 1985;**61**(713):225-7.

Senn SJ. Consensus and controversy in
pharmaceutical statistics (with discussion). The

Statistician 2000;**49**:135-176.

Senn SJ. Cross-over Trials in Clinical Research.
Second ed.

Senn, SJ. Trying to be precise about
vagueness *Statistics in Medicine*, 2007: **26**, 1417-1430.

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