### Bayesian methods and trials in rare and common diseases

One of the places that Bayesian methods have made some progress in the clinical trials world is in very rare diseases. And it’s true, traditional methods are hopeless in this situation, where you can never get enough recruits to get anywhere near the sample size that traditional methods demand for an “adequately powered” study, and it’s unlikely that a result will be “statistically significant”. Bayesian methods really help here, because they give you a result in terms of probability that a treatment is superior. This is good for two main reasons. First, it’s helpful to quantify the probability of benefit, and its size and uncertainty. This tells us a lot more than simply dichotomising it into “significant” and “non-significant”, with the unstated assumption that “significant” means clinically useful. Second, there isn’t a fixed probability of benefit that means an intervention should be used; it will vary from situation to situation. For example, if there is almost no cost to using a treatment, it might only need a small probability of being better to be worthwhile. If we don’t estimate this probability we can’t make this sort of judgement.

But (and this is something I have experienced several times now in a variety of places so I think it is real) – this seems to have had an unfortunate side effect. A perception seems to have grown that Bayesian methods are something to consider using when a “proper” trial (with all of the usual stuff: interpretation based on p < 0.05 in a null hypothesis test, fixed pre-planned sample size based on a significance test, 80% or 90% power and so on) isn’t feasible. In reality, the ability to quantify probability of benefit would be helpful in just about all situations, even (or especially) large Phase 3 trials that are looking for modest treatment benefits. How many of these trials don’t “achieve statistical significance” but have results that would show a 70% or 80% probability of benefit? They might still provide good enough evidence to make decisions about treatments (based on, for example, cost-effectiveness), but at the moment they tend to get labelled as “non-significant” or “negative trials.”

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