World Series MVP Mike Lowell is willing to give blood if that’s what it takes to be tested for human growth hormone. But only if the test is 100 percent accurate. Not 99 percent.

"If it’s 99 percent accurate, that’s going to be seven false positives," the Red Sox third baseman said Thursday before the annual dinner of the Boston chapter of the Baseball Writers’ Association of America. "Ninety-three percent is 70 guys. That’s almost three whole rosters.

"You’re destroying someone’s reputation. What if one of the false positives is Cal Ripken? Doesn’t it put a black mark on his career?"

Easy to forget now that Lowell was one of the prime steroid suspects after he crashed and burned in 2005. As always, his candor is refreshing. Truly one of the class acts in sports.

This reminds me of a class I took in probability theory.

I googled this up, as this is pretty textbook:

1% of women at age forty who participate in routine screening have breast cancer. 80% of women with breast cancer will get positive mammographies. 9.6% of women without breast cancer will also get positive mammographies. A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer?

Apparently, only 15% of doctors got it right. I kid you not.

I’ll return with the answer later. But this shows you that maybe Lowell does understand this after all..

It’s very admirable of Mike Lowell to make that statement, but it will be a cold day in hell before the Player’s Association agrees to blood testing.

Do we have to show our work?

For some reason, I suddenly imagined a future where the MLB takes blood samples for “testing” and makes clones of baseball’s greatest players, and then the contract demands of a dozen A-Rods cripple the American economy.

Lowell is making the case for why the PA won’t accept blood testing without a huge fight. No test is 100% accurate; if that’s where the bar is set, the test won’t clear it. The more pertinent demand, I think, is not about having an infallible test, but to have an agreed upon way to deal with the inevitability of false positives. If even seven FPs is too many (which it might be) then is there another way to discourage drug use?

The probability based on her positive mammograph or the probability based on the fact that she went into a screening? Or maybe it’s even trickier than that, and I haven’t understood it (I usually fall for this sort of math trap).

Probability based on screening: 1% = .01

Probability based on positive mammograph:

There are 4 outcomes…

breast cancer, negative mammograph (.01 * .2 = .002)

breast cancer, positive mammograph (.01 * .8 = .008)

no breast cancer, negative mammograph (.99 * .904 = .89496)

no breast cancer, positive mammograph (.99 * .096 = .09504)

Add the top two categories together and you get… .01 = 1%, so that adds up correctly.

Now, this woman falls into the positive mammograph category, 10.304% of the population (in this scenario). 0.8% actually have breast cancer…so the odds given the positive mammograph are .008/.10304 = .07764 (rounding up from .077639longstringofnumbers.).

So once you have a positive mammograph, your odds of having cancer are about 7.764%?

Did I screw up? Is it simply 1%?

Hey, I got 7.766..% I must have screwed something up. I’m pretty sure it isn’t just 1% though.

Nah, it’s entirely possible I punched a number in wrong somewhere, FSP.

BTW, much obliged on the Manni reply (RE: Lola and her propensity to run) in that other thread…and yeah, if any movie can replicate Manny’s strange frame of my mind, that one has a chance. (Now I’m imagining those freeze frame snapshot montages, but with Manny hitting home runs.)

The 7.something % is right. Which doesn’t feel right, but ya.

Which is why I agree with Lowell here..

I thought it was the opposite – once you have a positive mammograph, you have a 93.4% chance of having breast cancer (i.e. once you have the positive test, the only chance you don’;t have it is if you fall into the 9.6% of false positives).

The test wouldn’t be very valuable if only 7% of the positive testees actually had breast cancer.

The test has an extremely high rate of false positives. If nearly 10% of the non-cancer-having population (which is almost everybody–99%) is showing a positive, that’s just a lot, lot, lot of false positives. Which is why the success rate of the test is so low.

I wonder if this is at all comparable to real life, statistically. I mean, I know from life experience that when you get a positive, the next step is several other (generally more expensive) tests to verify that you do indeed have a problem, so this scenario might not be that inaccurate.

Even if you lower the false positive rate to 1% (from 9.6%), that’s still 1% of nearly the entire population, so that your chances of having cancer (once you have a positive result) are then about 44.7% (maybe this is more like real life). This is the danger of a test with practically any rate of false positives.

Quote Devine: <>

I alluded to this in my previous post, but I thnk you guys are looking at this wrong. If a test produces false positives in 1% of subjects, and you get a positive result, you have a 99% chance of having cancer, or being a juicer, or whatever the test is for. The other stats, like missed positives, the percentage of the total population with cancer, etc. are irrelevant when calculating the accuracy of a positive result.

Lowell’s point is valid, that a PED test with 99% accuracy is too low, since it will unfairly tarnish the name of a bunch of clean players.

But that’s what we’re doing: calculating the accuracy of a positive result. If there are 10,000 people and 100 of them have cancer, but you’re getting 1,000 positives, then the test just isn’t that accurate in measuring cancer.

Let’s go over it same as above, but with 10,000 people. I’ll call positive mammograph, PM, and negative, NM.

breast cancer, NM: 20

breast cancer, PM: 80

no breast cancer, NM: 8950

no breast cancer, PM: 950

So if you get a positive result, the chances are great that you got a false positive. There are 1,030 total positive results, but 950 of them are false positives.

If you’re calculating the probability of a poitive result, that’s one thing. But the problem originally posted by Lar reads, “A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer?”

So you’re actually supposed to solve for the probability of someone *who received a positive result* having cancer. The other information in the problem is a red herring, which is why I’d guess only 15% of doctors got it correct.

-Mark

Yes, but the probability of her having cancer based on her getting a positive result is that 7.7someodd%. She has a positive result, so she is one of these 1030 people (in a group of 10,000). But only 80 of those people ACTUALLY have cancer. You are trying to find out what the odds are that you actually have cancer, given that you got a positive test (as you say). Those odds are 80 divided by 1030, which is why Lar says that the true answer is 7.something%.

Wait, nevermind, I misread this part of that: “9.6% of women without breast cancer will also get positive mammographies.” Ignore me, please.

Back to the original story of Lowell’s statement, ESPN’s Rob Neyer has very different tak eon Lowell’s quote than Paul does:>

http://insider.espn.go.com/espn/blog/index?name=neyer_rob

Quote:

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Yes, I too think it is neither particularly positive nor negative for Lowell to say he would, under the proper circumstances, go for testing. Nice sentiment, no need to back it up.

That probability theory question is making my head spin. I have to take off my shoes and count my toes just to figure it out. ;)

If Mike Lowell understands this question, he is a mathematical genius–in addition to being a Gold-Glove caliber 3B man.

urine analysis is the easiest test to beat. followed by the saliva swab test. both blood and hair follicle test are harder but still beatable. given an hour notice prior to any drug screening, you can use a number of detoxifying agents to pass. i recommend a product called Stat Flush.

Nice post. Thanks for sharing.