Dear BUGS-users,
I am relatively new to Bayesian statistics, and I am having a problem for which
someone may know the appropriate solution (or a way to it).
I have implemented a survival model for treatment effect which has three
parameters, including a cured fraction. I estimate the treatment effect by
computing the posterior distribution of difference of the cure-rate fractions
between treatments. From this distribution, I compute a ‘Bayesian p’ with a
step function (i.e. if the samples are most positive or negative (>97.5%) there
is a highly significant treatment effect).
Based on this model, I would like to investigate the impact of inclusion of
additional data on the stability and accuracy of the parameter estimates.
In principle, one can expect the credible interval to provide some of that
information, but the data in this analysis is not homogeneous. In fact, upon
stepwise inclusion of new data one observes a marginal decrease in credible
intervals whilst the point estimate (‘Bayesian p’) changes considerably. This
behaviour suggests that parameter estimation has not stabilised yet and new
data still contributes to its estimation.
Can anybody suggest an objective procedure or criterion to evaluate stability
of estimates as new data is added to the analysis ? In other words, I would
like to identify the moment at which additional data does not effectively
contribute to the final estimation of the posterior distribution.
In addition, I would like to understand whether it is necessary to evaluate
individual treatment parameters (ie. posterior distribution of the parameter in
each treament arm) rather than the posterior distribution of the difference
between treatments.
Thanks a lot for your time,
Gijs Santen,
PhD-student Leiden University.
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