You're a Bayesian!
I've written a bit before about Bayesian statistics, here, here and here (that last one where I stole a line from Brad Efron, who said "We can all be Bayesians when we need to be," and also in a recently published book. I'm kind of sympathetic towards Bayesian analysis, but I very rarely do it. The basis for Bayesian analysis is that we incorporate the prior probability of a result into our analysis. Some people are positively antagonistic towards Bayesian thinking - denying that there is ever a use for it - the selection of the prior probability being something of a sticking point. (Actually, Bayesian analysis is lots more complex than that, and doesn't always require what are called 'informative priors', but we won't worry about that for a minute.
However, the most recent issue of Significance had a very interesting article by Stephen Senn, in which he wrote about the TeGenero tgn1412 drug trial catastrophe which occurred in March 2006, when 6 volunteers received the drug, and two received a placebo. The 6 volunteers almost immediately had massive immune system reactions - specifically a cytokine storm, and were hospitalised for at least a month.
What we have here, is the potential of a statistical analysis We've got a 2x2 table, so let's do the stats.
But that's got to be a silly thing to say. It's obvious that the drug did cause the cytokine storm. It's not just barely significant; it's really, really obvious. Why is it so obvious? It's obvious because people don't have cytokine storms every day. In fact, if you haven't got the Spanish Flu we're pretty safe saying that you will never have a cytokine storm. In other words, it's not just the data that we have obtained here that we need to take into account. We need to take into account the probability of having a cytokine storm ever is very low. In other words, we need to take into account the prior probability. And so we have just done a Bayesian analysis.
However, the most recent issue of Significance had a very interesting article by Stephen Senn, in which he wrote about the TeGenero tgn1412 drug trial catastrophe which occurred in March 2006, when 6 volunteers received the drug, and two received a placebo. The 6 volunteers almost immediately had massive immune system reactions - specifically a cytokine storm, and were hospitalised for at least a month.
What we have here, is the potential of a statistical analysis We've got a 2x2 table, so let's do the stats.
Placebo DrugA 2x2 table. We obviously can't do a chi-square test, as the sample is too small. But we can do a Fisher's exact test. If we do that we get a one-tailed p of 0.036. It's a one-tailed test, so our p-value cut off is 0.025, so we don't have evidence that the drug caused the cytokine storm, and all the subsequent ills.
Yes 0 6
Cytokine Storm
No 2 0
But that's got to be a silly thing to say. It's obvious that the drug did cause the cytokine storm. It's not just barely significant; it's really, really obvious. Why is it so obvious? It's obvious because people don't have cytokine storms every day. In fact, if you haven't got the Spanish Flu we're pretty safe saying that you will never have a cytokine storm. In other words, it's not just the data that we have obtained here that we need to take into account. We need to take into account the probability of having a cytokine storm ever is very low. In other words, we need to take into account the prior probability. And so we have just done a Bayesian analysis.
1 Comments:
Interesting post.
I'll play Devil's advocate: why not use the Binomial test? For example, if the Q. was 'what is the chance that on eight rolls of a six-sided die I'll get 6 sixes?' the same contingency table would get a highly significant result (assuming p(6) = 1/6). In this I think frequrntists stats can be sensitive to priors, but a less explicit when they do and don't model the distribution of the prior.
Even with the standard chi-square test one might argue that alpha should not be set at a level that weights Type I errors as worse than Type II in such a trial - or indeed that a statistical test is irrelevant if there is a single serious adverse effect that could be attributed to the drug.
Thom
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