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
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
Senn SJ. Cross-over Trials in Clinical Research.
Senn, SJ. Trying to be precise about vagueness Statistics in Medicine, 2007: 26, 1417-1430.
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