Berry D

#Berry, D 2005 Bayesian Clinical Trials. Nature Reviews

Very helpful overview of current status of bayesian methodology in clinical trials. Need to chase a number of references (including Berry’s Bayesian Biostatistics) Short notes: (1) focus appears to be bayesian techniques to improve frequentist trials (reduction of sample size, review of stopping rules..) the final data analysis still appears to be frequentist (though there is some perhaps ambiguous comment that this is a relic of current regulatory requirements - ambiguous because Berry is not absolutely explicit that this is bad). If frequentist methods make the wrong inference (p-values) then they always make the wrong inference - whether the trial is streamlined by bayesian methods or not. Follow-up, post meeting 8/12/05 - Two issues need to be separated; (i) the use of bayesian methodology to assist the design of a frequentist trial - i.e. deciding sample size and type of trial design etc - this use of bayesian methodology makes some sense, it is external from the actual trial once it starts and it provides a rational approach to things such as sample size on which the frequentist methods can not approach as directly; and (ii) the use of a bayesian stopping rule within a frequentist trial, although this appears to happen (in some - perhaps rare - situations) this does not make sense - from the bayesian perspective the final frequentist analysis of the trial in terms of p-values is meaningless and from the frequentist perspective it is not possible for them to calculate a p-value in any real sense becuase it requires the false assumption that no interim analysis had taken place - if it accepts interim analysis has taken place then this interim analysis needs to be frequentist in order to calculate an overall significance level for the trial. (2) p2 states that " (frequentist) parameters are regarded as fixed and not subject to probability distributions" I need to ensure I understand this and its relevance for estimation of magnitude of effect within frequentist methods (3) use of bayesian techniques to allow trials to stop early are interesting - need to investigate examples - e.g. Herceptin v control; aiming for 164 patients but ceasing at 34 (16 on control and 18 on Herceptin; 25% and 67% respective response rate); trial was permitted to stop due to the fact that based on current data the probability of finding a significant difference between the two treatments at study end was 95%. Obvious benefits here if we accept bayesian posterior - but assuming that we started with a flat prior probability distribution with such small numbers should be hold much weight (?second order probability) for our bayesian posterior. I think this problem will come up again and again - need to get my head around it. [YES, CAN QUANTIFY THIS WITH SECOND-ORDER PROBABILITY. BERGER’S WRITTEN A LOT ABOUT THIS. JASON] (4) the link between the science story and the statistical inference is also raised again - are there as many challenges here as for the frequentist interpretation? - e.g. if i had an unconfirmed but plausible science story for why there may be a delayed harm for Herceptin - or delayed benefit for control - would my posterior look any different? Or would this just become a debate of priors. [IT WOULD BE A DEBATE ON PRIORS … POSSIBLY ON THE DIMENSIONS OF THE PRIOR AS WELL AS THE SHAPE, BUT TYPICALLY JUST THE SHAPE. JASON] (5) relatedly - is the Bayesian methodology always superior? Are there any clinical questions which are better answered via frequentist methodology ? (this is worded a little awkwardly given that i accept the arguments against frequentism - perhaps what i mean is that some of the components for the frequentist method - such a inflexibility of design etc should be kept for certain questions - but which components for which questions? - and does this return to the question of second order probability on bayesian posteriors?) A real example which might help explain this query is that of sub-group analysis. The benefits of the bayesian approach with respect to known hypotheses seems clear but what of hypothesis generation - subgroup analysis of current trial methodology permits much hypothesis generation and very little hypothesis confirmation - it seems that the bayesian approach might have the opposite effect. By permiting adaption of clinical trials as they progress to provide better answers of known questions do we risk generating less questions. If so, is it necessarily bad - at the least this seems a very backhanded compliment to frequentist methods. [GOOD QUESTIONS! JASON] As per meeting record 8/12/05 this is framing the question incorrectly. It is not a matter of bayesian v nonbayesian. The real point to note here is that if we use a bayesian methodolgy we do not always want to only hypothesis-confirm but also hypothesis-generate. This will require different methodology and different bayesian analysis. There appears a couple of philosophical questions here (i) an ethical question - can we ethically enrol more patients in trials than necessary in order to generate hypotheses on the drug; such as efficacy in sub-groups or safety; (ii) an epistemological question - what does a bayesian methodology with the ability to hypothesis generate in the necessary way look like?… ?more philosophical questions