"can a Bayesian approach give me a better number to use than saying we can likely reduce your chance from ~12% down to 10%?"
No. All Bayes does for you here (a high-statistics study) is give you a more meaningful quantification of "likely" than you can get from frequentism. The probability that the drug reduces the chance of the primary o…
"can a Bayesian approach give me a better number to use than saying we can likely reduce your chance from ~12% down to 10%?"
No. All Bayes does for you here (a high-statistics study) is give you a more meaningful quantification of "likely" than you can get from frequentism. The probability that the drug reduces the chance of the primary outcome (by some amount) is 97.8%. The most likely reduction is, as you say, from ~12% to ~10%.
I agree that the patient should make the decision.
All medical professionals have been trained in frequentist methods, and almost none in Bayesian methods, and this is not going to change any time soon. This is a real shame, because Bayesian methods, once learned, are so much more intuitive. But for now all of you have to learn frequentist methods, because that's what's used in every paper you read.
I became a Bayesian 40 years ago when a standard frequentist analysis of some low-quality data was giving me a nonsensical result, that some signal that could not possibly be negative was negative with some decent confidence. But I actually had 100% confidence that it was not negative! How could I put that into the analysis? The answer is a Bayesian prior. This is the sort of situation where Bayesian methods give better results. I would think that medicine has a lot of situations where there are no high-statistics studies at all, and yet doctors have patients who need advice. Bayesian methods would result in better advice in these cases, so I hope they eventually become more common.
Excellent - so it seems that a frequentist approach to looking at clinical trials is at least a reasonable approach when it comes to using clinical trial data and making decisions in patient care. Thanks.
"can a Bayesian approach give me a better number to use than saying we can likely reduce your chance from ~12% down to 10%?"
No. All Bayes does for you here (a high-statistics study) is give you a more meaningful quantification of "likely" than you can get from frequentism. The probability that the drug reduces the chance of the primary outcome (by some amount) is 97.8%. The most likely reduction is, as you say, from ~12% to ~10%.
I agree that the patient should make the decision.
All medical professionals have been trained in frequentist methods, and almost none in Bayesian methods, and this is not going to change any time soon. This is a real shame, because Bayesian methods, once learned, are so much more intuitive. But for now all of you have to learn frequentist methods, because that's what's used in every paper you read.
I became a Bayesian 40 years ago when a standard frequentist analysis of some low-quality data was giving me a nonsensical result, that some signal that could not possibly be negative was negative with some decent confidence. But I actually had 100% confidence that it was not negative! How could I put that into the analysis? The answer is a Bayesian prior. This is the sort of situation where Bayesian methods give better results. I would think that medicine has a lot of situations where there are no high-statistics studies at all, and yet doctors have patients who need advice. Bayesian methods would result in better advice in these cases, so I hope they eventually become more common.
Excellent - so it seems that a frequentist approach to looking at clinical trials is at least a reasonable approach when it comes to using clinical trial data and making decisions in patient care. Thanks.