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Re: MSTS RiskFrom: Richard M. Roberts (gene@vol.com)Wed Feb 14 10:39:11 2001
To Wayne and all, sorry, I did throw you a screwball. Due lateness of the hour (not to mention advancing age/degenerating cerebral function) I screwed up. The difference between odds and risk is straightforward, and NOT different from 1:1 being 1 in 2 (odds versus risk). And yes, the only clinical usefullness is in caclulating risk based on Bayesian analysis. Risk is based on the total different units. If a bookie says "I'll give you 10 to 1 odds that it's going to be Gluebag in the 4th", the person who holds the pot easily calculates the risk. If you took the bet, you have risked 1 out of a total of 11 dollars held by the 3rd party. The bookie is betting the risk of your loosing is 1 in 11 (the third party is holding 11 dollars). On the other hand, the Bookie may have other knowledge which may change the actual risk he has presented to you through Bayesian analysis, such as the fact that the Jockey of Gluebag has accepted $1000 from him to assure that the horse will not win. In that case the odds are altered considerably, nearing 1 chance in infinity that you will win. Then the risk that you will win is 1/near infinity plus 1. To change odds to risk, you add the two odds numbers together to get the total, then correct the fraction to risk, by stating the number risked to the total.. If the odds are 3 to 5, then the risk is 3/8. In caluclating Bayesean risk, you take the prior risk of an event (lets take a woman whose brother and uncle is affected with Duchenne), and you can modify her risk of being a carrier based on other risk informtation, such as CPK results, or, for example here, lets suppose that this woman has a male child who is 10 years old and shows no signs of Duchenne. Well, we know that he is unaffected with Duchenne, because at age 10, he would have shown signs already if he inherited the gene from his mother. We also know that his maternal grandmother is an obligate carrier, without doing any special testing, because her brother and son were both affected. So, the probability that the maternal grandmother is a carrier is 1. Now, here's where Bayesian analysis comes in. The boy's mother has a Prior probablility(risk) that she is a carrier of 1 in 2, or 50%. (She either inherited the gene from her mother or not. The prior probability that she is NOT a carrier is also, in this case, 1 in 2. Now comes conditional probablility. What is the risk, if she is a carrier, that she has had a normal boy? 1 in 2. (If male, the risk of being affected is 1 in 2). What is the conditional probablility that she would have a normal boy if she is not a carrier? The answer is very close to one (actually, 1 minus the chance that the normal risk that the gene would mutate to one which causes Duchenne in the fertilized egg.) The next step is to alter the prior probability by the conditional probablility, which is done by simply multiplying the two togeter. The combined risk that she is a carrier hand has had one normal male is 1/2 times 1/2, or 1/4. The combined risk that she is not a carrier and has had a normal son is 1/2 times 1, or 1/2. Because you can't compare fractions with different denominators, we change to the nearest common denominator, to find out the total number of options available: Carrier, 1/4, not a carrier, 2/4. NOW TRUST ME ON THIS, BECAUSE IT IS CORRECT; the ODDS that she is a carrer is 1 to 2 (a comparison of the numerators). The RISK that she is a carrier is no longer 1 in 2, it is 1 in 3 (there are a total of 3 outcomes, in carrier vs non-carrier, one of which is her risk of being a carrier.) This is how Bayesian analysis is done withought using complicated formulas. So you can see quite readily that the effect of having one male who is normal reduces that mother's risk from 1 in 2 to 1 in 3. This is not guesswork: that truly is her risk of being a carrier. That is the genious of Bayes' theorem. Now that cant be right, you say, from a conceptual standpoint. But it is, and you can convince yourself that it is correct by pretending that Mom has the reproductive capacity of a fruit fly, and has 1000 children, and of all these children, none of those who are male ever developed Duchenne. The probability of her being a carrier then approaches 0. Cheers.
>>> Gene you lost me here, "Odds are different from actual risk, with
>>> To: Multiple recipients of list ULTRASOUND
-- Richard M. Roberts, PhD, MD, FACMG
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