I appreciate all that. So if my use of the CI doesn't cut it then can you, using the specific example of the trial I showed, tell me how a clinician and/or patient should interpret the specific findings from this trial. The only way for any individual to make a decision is to have an idea of the benefits and harms. So in this case if the…
I appreciate all that. So if my use of the CI doesn't cut it then can you, using the specific example of the trial I showed, tell me how a clinician and/or patient should interpret the specific findings from this trial. The only way for any individual to make a decision is to have an idea of the benefits and harms. So in this case if the person was similar to the people enrolled in the trial what could we tell them about the benefit of this medication on their risk of a CVD event. You say that Bayes can uncover the answer so could you tell me the answer that is better than what I have done with the CI. Thanks.
By not cutting it I wasn't referring to you but the general problem with CIs besides the almost impossibility of defining them. Clinicians have specific interests, e.g. what's the evidence that the effect > 0? > 15%? The intervals for those are [0, infinity], [15%, infinity]. To get the evidence for the unknown being in the interval you must use Bayes. Frequentist takes control of the interval endpoints after you define the compatibility probability. This is very non-clinical.
So am I correct in saying that you think my approach to using the CI to get information I can use clinically is not unreasonable? If it is not reasonable then can you show me how if I went to the "extra" work of taking a Bayesian approach that I would get more clinically useful information. I really do think a Bayesian approach is incredibly useful and I use it all the time when it comes to tests and estimating pre and then post-test probability. However I can't seem to get any good answers from anyone as to how it can help with interpretation of clinical trials - above and beyond a frequentists approach. Thanks.
I have a lot of material at https://hbiostat.org/bayes/bet . I think the CI gets you one piece of the puzzle and is helpful but it doesn't get you far enough. For example if the CI for a hazard ratio were [0.8, 1.01] I'd rather want to know Pr(HR < 1) ad Pr(HR < 0.9). For non-inferiority the Bayesian approach is especially appealing. Also if you were tempted to say that 2 treatments give the same results you'd need to back that up with e.g. a high P(7/8 < HR < 8/7).
Interesting - sounds like, and hopefully I don't get blasted for this - not by you but maybe others - a frequentist approach and a Bayesian approach can live in harmony with each other - it often just depends on what output you need from the experiment/clinical trial to help you make decisions. However IMO I think when it comes to tests the best approach is Bayesian.
Since the frequentist approach deals with complex sampling distributions, and even more so since it provides only indirect evidence against a hypothesis and never provides evidence in favor of anything, I'm not seeing the value added by a frequentist approach to what a Bayesian analysis can provide.
Then, can you, using your Bayesian approach with the real-life example below, calculate/estimate the numbers a clinician needs around risks, benefits and harms so that they could present these to a patient.
THE EXAMPLE
EMPA-REG trial https://pubmed.ncbi.nlm.nih.gov/26378978/. The abstract states "The primary outcome occurred in 490 of 4687 patients (10.5%) in the pooled empagliflozin group and in 282 of 2333 patients (12.1%) in the placebo group (hazard ratio in the empagliflozin group, 0.86; 95.02% confidence interval, 0.74 to 0.99; P=0.04"
MY SYNOPSIS OF THIS STUDY IS AS FOLLOWS
I believe the relative benefit is somewhere between a 26% relative benefit (0.74) and a 1% relative benefit (0.99) and the observed relative benefit was 14% (0.86). So the absolute benefit seen in this trial was 12.1% minus 10.5% = 1.6% - so a 1.6% benefit and therefore 98.4% get no benefit - or approximately 60 people need to take this drug for three years for 1 to benefit. However, because we don't know the true effect all I can say is that the effect is likely - sorry I know Bayesians don't really like that word - somewhere as large as a 26% relative benefit or as small as 1%. So the absolute benefit might be as large as ~3% or close to no benefit at all. Then I would add in that the cost of the medication is about CA $1000 a year and 5-10% of people will get a genital infection because of the drug.
Yes, given a little bit of time someone could do a complete Bayesian re-analysis. I would state the main results like this (capitalizing on Bayesian uncertainty intervals having simple interpretations; numbers are examples): The probability of any benefit is 0.94 and the probability of at least 5% benefit is 0.83. We are 0.95 certain that the true benefit is between 1.5% and 28%.
I appreciate all that. So if my use of the CI doesn't cut it then can you, using the specific example of the trial I showed, tell me how a clinician and/or patient should interpret the specific findings from this trial. The only way for any individual to make a decision is to have an idea of the benefits and harms. So in this case if the person was similar to the people enrolled in the trial what could we tell them about the benefit of this medication on their risk of a CVD event. You say that Bayes can uncover the answer so could you tell me the answer that is better than what I have done with the CI. Thanks.
By not cutting it I wasn't referring to you but the general problem with CIs besides the almost impossibility of defining them. Clinicians have specific interests, e.g. what's the evidence that the effect > 0? > 15%? The intervals for those are [0, infinity], [15%, infinity]. To get the evidence for the unknown being in the interval you must use Bayes. Frequentist takes control of the interval endpoints after you define the compatibility probability. This is very non-clinical.
So am I correct in saying that you think my approach to using the CI to get information I can use clinically is not unreasonable? If it is not reasonable then can you show me how if I went to the "extra" work of taking a Bayesian approach that I would get more clinically useful information. I really do think a Bayesian approach is incredibly useful and I use it all the time when it comes to tests and estimating pre and then post-test probability. However I can't seem to get any good answers from anyone as to how it can help with interpretation of clinical trials - above and beyond a frequentists approach. Thanks.
I have a lot of material at https://hbiostat.org/bayes/bet . I think the CI gets you one piece of the puzzle and is helpful but it doesn't get you far enough. For example if the CI for a hazard ratio were [0.8, 1.01] I'd rather want to know Pr(HR < 1) ad Pr(HR < 0.9). For non-inferiority the Bayesian approach is especially appealing. Also if you were tempted to say that 2 treatments give the same results you'd need to back that up with e.g. a high P(7/8 < HR < 8/7).
Interesting - sounds like, and hopefully I don't get blasted for this - not by you but maybe others - a frequentist approach and a Bayesian approach can live in harmony with each other - it often just depends on what output you need from the experiment/clinical trial to help you make decisions. However IMO I think when it comes to tests the best approach is Bayesian.
Since the frequentist approach deals with complex sampling distributions, and even more so since it provides only indirect evidence against a hypothesis and never provides evidence in favor of anything, I'm not seeing the value added by a frequentist approach to what a Bayesian analysis can provide.
Then, can you, using your Bayesian approach with the real-life example below, calculate/estimate the numbers a clinician needs around risks, benefits and harms so that they could present these to a patient.
THE EXAMPLE
EMPA-REG trial https://pubmed.ncbi.nlm.nih.gov/26378978/. The abstract states "The primary outcome occurred in 490 of 4687 patients (10.5%) in the pooled empagliflozin group and in 282 of 2333 patients (12.1%) in the placebo group (hazard ratio in the empagliflozin group, 0.86; 95.02% confidence interval, 0.74 to 0.99; P=0.04"
MY SYNOPSIS OF THIS STUDY IS AS FOLLOWS
I believe the relative benefit is somewhere between a 26% relative benefit (0.74) and a 1% relative benefit (0.99) and the observed relative benefit was 14% (0.86). So the absolute benefit seen in this trial was 12.1% minus 10.5% = 1.6% - so a 1.6% benefit and therefore 98.4% get no benefit - or approximately 60 people need to take this drug for three years for 1 to benefit. However, because we don't know the true effect all I can say is that the effect is likely - sorry I know Bayesians don't really like that word - somewhere as large as a 26% relative benefit or as small as 1%. So the absolute benefit might be as large as ~3% or close to no benefit at all. Then I would add in that the cost of the medication is about CA $1000 a year and 5-10% of people will get a genital infection because of the drug.
Yes, given a little bit of time someone could do a complete Bayesian re-analysis. I would state the main results like this (capitalizing on Bayesian uncertainty intervals having simple interpretations; numbers are examples): The probability of any benefit is 0.94 and the probability of at least 5% benefit is 0.83. We are 0.95 certain that the true benefit is between 1.5% and 28%.