Prostate Cancer Screening & Bayesian Dogma?
MR's short post "Risk Analysis using Roulette Wheels" reads:
A PSA test can reveal the presence of prostate cancer. But not all such cancers are fatal and treatment involves the risk of impotence. Do you really want the test? It's difficult for patients to evaluate these kinds of risks. Mahalanobis points us to an article advocating visual tools such as roulette wheels to help patients understand relative risks and chance. Even better than the diagrams is this impressive video; the video may be of independent interest to the older men in the audience.
The basic problem is that the screening doesn't distinguish non-fatal cancer (presumably harmless) from fatal cancer. They say that, in case of a positive test result, one "must" pursue treatment, since the probability of death and is pretty high without it. They don't mention that one could just as well refuse treatment, since with treatment the probability is also high that one will get bad side-effects unnecessarily (in the cases of non-fatal cancer).
But if the screening is free, shouldn't we *always* have it done? Isn't this an axiom of rationality?
A rationalist would argue that one should choose not to do the screening ONLY IF one's decision were going to be the same in either case, i.e. no treatment regardless of the result of the screening.
My interpretation:
They say that one could choose not to be screened because people who get screened have a higher probability of bad side-effects. This is true, but only because people who get screened have a higher probability of finding something, and therefore a higher probability of getting treatment. A rationalist (like me) would argue that if you have the balls to face a higher risk of death in exchange for a smaller chance of getting side-effects when these probabilities are small, then you should have the balls to make the same choice when the chances are high (e.g. tumor strikes). But in practice, one might not trust oneself to.
Graphviz code:
digraph prostate_cancer
{
/* graph [fontsize=8];
edge [fontsize=8]; */
node [fontsize=10];
"fatal-type \n cancer" -> "test positive";
"non-fatal-type \n cancer" -> "test positive";
"treatment" [shape=box];
"fatal-type \n cancer" -> "death";
"treatment" -> "death" [style=dashed];
"treatment" -> "side-effects: \n impotence or\n incontinence";
}
A PSA test can reveal the presence of prostate cancer. But not all such cancers are fatal and treatment involves the risk of impotence. Do you really want the test? It's difficult for patients to evaluate these kinds of risks. Mahalanobis points us to an article advocating visual tools such as roulette wheels to help patients understand relative risks and chance. Even better than the diagrams is this impressive video; the video may be of independent interest to the older men in the audience.
The basic problem is that the screening doesn't distinguish non-fatal cancer (presumably harmless) from fatal cancer. They say that, in case of a positive test result, one "must" pursue treatment, since the probability of death and is pretty high without it. They don't mention that one could just as well refuse treatment, since with treatment the probability is also high that one will get bad side-effects unnecessarily (in the cases of non-fatal cancer).
But if the screening is free, shouldn't we *always* have it done? Isn't this an axiom of rationality?
A rationalist would argue that one should choose not to do the screening ONLY IF one's decision were going to be the same in either case, i.e. no treatment regardless of the result of the screening.
My interpretation:
They say that one could choose not to be screened because people who get screened have a higher probability of bad side-effects. This is true, but only because people who get screened have a higher probability of finding something, and therefore a higher probability of getting treatment. A rationalist (like me) would argue that if you have the balls to face a higher risk of death in exchange for a smaller chance of getting side-effects when these probabilities are small, then you should have the balls to make the same choice when the chances are high (e.g. tumor strikes). But in practice, one might not trust oneself to.
Graphviz code:
digraph prostate_cancer
{
/* graph [fontsize=8];
edge [fontsize=8]; */
node [fontsize=10];
"fatal-type \n cancer" -> "test positive";
"non-fatal-type \n cancer" -> "test positive";
"treatment" [shape=box];
"fatal-type \n cancer" -> "death";
"treatment" -> "death" [style=dashed];
"treatment" -> "side-effects: \n impotence or\n incontinence";
}