William M. Briggs

Statistician to the Stars!

Page 146 of 547

Angelina Jolie’s Decisions Shouldn’t Necessarily Be Yours

Celebrities don’t always know what is best for YOU

Men ordinarily don’t like writing about women’s breasts, but I had so many emails asking me why Angelina Jolie decided to part with hers that I felt we had better take a look.

Where better to start than with her own words? In the New York Times (D—though they are so far in cahoots with that party we could easily write ‘DD’) in a piece called “My Medical Choice“, after informing us that her mother died from cancer, she said:

[T]he truth is I carry a “faulty” gene, BRCA1, which sharply increases my risk of developing breast cancer and ovarian cancer.

My doctors estimated that I had an 87 percent risk of breast cancer and a 50 percent risk of ovarian cancer, although the risk is different in the case of each woman.

Only a fraction of breast cancers result from an inherited gene mutation. Those with a defect in BRCA1 have a 65 percent risk of getting it, on average.

Once I knew that this was my reality, I decided to be proactive and to minimize the risk as much I could. I made a decision to have a preventive double mastectomy. I started with the breasts, as my risk of breast cancer is higher than my risk of ovarian cancer, and the surgery is more complex.

If a woman has this variant of the BRCA gene, observations suggest she has a higher risk of breast or ovarian cancer than woman who do not. Jolie informs us that this risk is 65%. But then she tells us that her risk is 87%. Not 86% or 88%, but 87%, a number which is suspiciously precise.

Jolie’s medical history (“her reality”) is different than the “average” woman’s, and generally those with cancer in the family line also have higher risk. And she may possess other traits which led her doctor to tell her she had an “87% chance” of breast cancer. This number is scarcely believable in its precision and hints some mathematical model was employed. Stating numbers with unfounded exactness leads to over-confidence, and that makes for weaker decisions.

These numbers are also lifetime risk; that is, the chance of developing these cancers by the time a lady dies. They are not, for instance, the chance the woman will develop cancer (say) next year: that chance would be much lower.

Lifetime risks are very tricky to interpret (and vary by disease). The day-by-day, or year-by-year, risk is not constant, but increases through time, gradually at first and then more rapidly later. Think of the difference in risk (still assuming the female with this variant of the BRCA) between a 13-year-old and a 70-year-old; obviously, the latter has much higher risk. Jolie is 38, an age which is not considered to be especially dangerous (for “average” women).

Everybody dies. Therefore, Jolie will die of something. Might be cancer, might be a worn-out heart, or by apoplexy brought on by reading the NYT. Jolie will not now die from breast cancer (almost certainly), though she might exit via ovarian cancer—or maybe by some other cancer (colon, skin, pancreatic, etc.). Her liver might fail or she may stroke out. Anyway, she will die, though she may (only may) live longer and then dye from something else. All she has done, then, was to remove one of these many, many choices of death.

And then even if she developed breast cancer, it was not certain she would have died from it. Breast cancer is in many cases curable; sometimes by mastectomy. In other words, she could have sweat it out and then gone to the docs when and if she ever developed symptoms. She could have kept her attributes for a longer time, or even until death. But the cancer, assuming she got it, also could have killed her (instead of something else).

Point is: the decision to undergo this most painful and prolonged sequence of procedures is not as simple as noticing you have this variant of BRCA and traipsing down to the two-holed guillotine. The surgery itself has risks: doctors make mistakes, infections sneak in, though rarely. A young woman’s looks—a thing of utmost importance to women—have been forever lessened, though the replacement fakes are looking better all the time. Gone too is the possibility of breast feeding. This is not, and should not be, an easy choice.

It was an easy forecast to say that the legion of women who follow the lives of celebrities, after hearing the news yesterday, would mount their horses and ride immediately to their doctors and ask whether they should have their breasts removed, too. Jolie’s very public announcement was the hyper-equivalent of the pharmaceutical ad which ends “Ask your doctor is sassaffrassium is right for you.” It always is, particularly if the doctor does not enjoy being harangued.

The New York Post (R) reported:

City oncologists yesterday were flooded with calls about genetic screening and the kind of preventative double mastectomy Angelina Jolie revealed she underwent after testing positive for a gene mutation that indicates a likelihood of breast and ovarian cancer.

“This morning, I got two phone calls from women who had tested positive for the BRCA mutation in the past but had not decided to go forward with the surgery yet,” said Dr. Deborah Axelrod, 55, a top breast-cancer expert at NYU’s Langone Medical Center

“They said they wanted to now because they had read the Angelina Jolie article,” said Axelrod…

Ladies, before you head to the hospital, recall the existence of false positives. These are instances where a goof has been made or when a test is not precise. The screening for the BRCA1 variant is imperfect, and so too are screenings for breast cancer itself. You could be told you have the BRCA1 when you do not, and that you have breast cancer when you do not. See this Decision Calculator for more details. (Incidentally, only about 5-10% of breast cancers have this variant; slightly higher in women with ovarian cancer).

Too often, the possibility that “I might die from breast cancer” overwhelms all other knowledge, particularly is all that is talked about is the surgery and the good that can come from it. But there is a chance bad can come from surgery, most egregiously in cases where nothing was really wrong. And there is also good that can come from doing nothing save having frequent checkups. Do not rush to judgment.

We only hit the highlights here; many details were ignored because of space. For example, we didn’t get to cover Jolie’s “holistic doctors”, a term which is might be overheard on Duck Dynasty. More another time.

On Arguing

The traditional way of settling disputes between spouses is now frowned upon.

The traditional way of settling disputes between spouses is now frowned upon.

We often have a series of exchanges with friends or others, seeking to convince them of some proposition which we believe is true, and which may even be true. But these friends think the proposition false, and which may even be false.

To say a proposition is false is to say its negation is true, so that another way to state this dilemma is that both sides believe they are arguing for the sake of truth.

One of two things can happen. The first, one side capitulates and comes to believe what he thought was true is indeed false, a happy ending. The second, and far more common situation, is that an impasse is reached. This is the truest test of personality.

I once had an argument with a full-grown, well educated, degree-holding woman about the numerical result of dividing any real number by one. I stated that the result is always the original number. She agreed, except in the case of 1 divided by 1, the result of which, she vehemently insisted, was 0. Why? Well, “You divide one into one and you have nothing left.” And nothing is zero.

No mathematical trick, example, demonstration, or appeal could shake this woman’s conviction. She patiently listened, at first anyway, to whatever I had to say, but always returned to the certain sure “fact” that if you divide one into one you have nothing left. She eventually gave up on me, dismissing my bizarre opinion as the result of an eccentric mind addled by overexposure to arcane books.

We parted on friendly terms. We had contact a few times afterwards where it became clear she was not going to write any op-eds about my recalcitrance, nor was she going to organize any protest, nor indeed was she going to plead for the government to restrain my speech so that I might not spread my error to the young. She decided to let me be, doubtless reasoning to herself that not everybody can know everything, that some inaccuracy is inevitable.

Some disagreements must necessarily lead to a parting of the ways. Murderer Kermit Gosnell and his counsel disagreed with the State of Pennsylvania over several propositions, and still disagree. Now the State will use force, not to impel Gosnell to believe what he does not, but to restrain and punish him for his actions. The distinction is important. Gosnell is not facing grief because of his belief, but his behavior.

Convincing adults that what they believe is false is always hard labor and often impossible. Many people, particularly those in positions of power, cannot abide dissension, so they use their power to squelch opposition. They create speech codes, restrict the press, implement “fairness” doctrines, or mute opponents physically. This happens on a smaller scale in homes or offices run by bullies.

It’s not the action of others which grates, but it’s that they won’t see reason. Why can’t he just understand! What is wrong with him! Some people are tenacious and will not let a point drop until his opponent lies about agreeing, or his opponent runs away to avoid harassment. Others are so passionate that they will not countenance the company of those with fail to march in step with them. Friendships are ruined over political disagreements neither party has much chance of influencing.

These days it seems the civilized standby “Let’s agree to disagree” is used less frequently, replaced by estrangements. The absence of the polite “out” is a predictor of tumultuous times. Camps are being drawn, sides taken. These things happen.

And now it strikes me that there is one more possibility than the two sides ultimately agreeing or disagreeing. Many years ago, I had to break up a bedtime fight between my two sons because one claimed, “Davy Crockett is too King of the wild frontier!” while the second took the opposite position. A détente was reached when I convinced them that if they didn’t shut up and go to sleep it wouldn’t matter what Davy Crockett was. Thus a proposition can be seen as uninteresting, too.

Subjective Versus Objective Bayes (Versus Frequentism): Part III

Harold Jefferys, Chance Master

Following Part II, here are some examples to show the differences between objectivist, subjectivist, and frequentist probabilities derived from fixed premises and set conclusions.

Example 1

Not all probability is objectively strictly quantifiable. Premise: “Some X are F and x is X”. Conclusion: “x is F”. The objectivist can only say “The probability (given the premises) the conclusion is true is greater than 0 but less than or equal to 1.” This is because the logical “some” implies “at least some and perhaps all.”

The subjectivist is free to say, for example, “The probability (given the premises and my beliefs) the conclusion is true is 42.8%.” But he does so only by some mysterious introspection which, in effect, adds to or subtracts from the fixed premises. Of course, most subjectivists in practice would agree with the objectivist.

The frequentist, as with all his probabilities, must embed this fixed premise in an metaphysical infinite sequence of “identical but randomly different” premises, which is not exactly a coherent description. But again, like subjectivists, the frequentist would often in practice agree with the objectivist. If he disagrees, he is acting like the subjectivist because he is adding to or subtracting from the fixed premises in order to supply details of the infinite sequence. (There isn’t anything necessarily wrong with metaphysical infinite sequences: they are used all the time in analysis, for example. But in analysis, these sequences are precisely explained.)

In other words, the subjectivist and frequentist in disagreeing with the objectivist depart from the fixed premises, which is to say they change the evidence. But they speak as if they use the same evidence. To emphasize: they are not using the same premises. This is the primary reason for confusion and bad blood.

The problem is further highlighted by changing the question (keeping the same fixed premises and conclusion). “How much would you bet that x is F?” In this case, the problem unavoidably becomes subjective. Additional premises not supplied in the “fixed” list must be invented (though there is an infinitesimal bit of wiggle room because we know the probability is strictly greater than 0). These additional premises pertain to each individual’s idea of money or “utility” and the situation of the bet itself (who made it, why, the personal relationship between bettor and bookie, and on an on).

Subjectivists argue that because each individual can eventually come to a monetary amount (or utility), there exists a “true” probability for “x is F”. This is so, but only because the subjectivist supplies new premises to the official list. In other words, he changes the problem. It’s also the case that the subjectivist won’t be able to describe what these premises are; i.e., they will involve “gut feelings.” Frequentists in these cases also act like subjectivists.

Further examples are generated by changing “Some” in the premise with “Many”, “A few”, “Not that many”, “I’ve heard that a lot of”, “Most”, and others. This makes for a good exercise.

Example 2

Donald Williams proposed the label Statistical Syllogism, an example of which is this. Premises: “There is a n-sided object, just one side of which is labeled ‘Q'; the object will be tossed and only one side can show.” Conclusion: “A ‘Q’ will show.” The objective deduction (given the premises) is the probability the conclusion is true is 1/n.

The subjectivist is free to change this number, but only if he changes the premises. The frequentist is on more familiar ground here because it appears “tosses” are ready-made for infinite sequences.

Notice that there is no need to add words about “random” tosses. “Random” only means unknown, and it is already unknown (given the premises) which side will show. That is, there is nothing in the premises which tells us how to deduce the outcome.

Suppose n = 2. The deduced probability is 1/2, given the fixed premises. The premises say nothing about the object being a coin, particularly being this coin in this real situation. If we had a real coin in a real situation, and if we were able to list additional premises which were probative of the conclusion, we might be able to deduce whether the coin would land one side or the other with certainty. People have done this (see the work of Persi Diaconis, for example.)

But if all we know is that we have a two-sided real coin and we are not physicists enough to add any additional premises, then the probability of the real toss is still 1/2. If you want to know about this real coin in this real situation and you won’t learn physics, you can experiment with the coin and add the observations as new premises. That’s what the science of statistics does.

Incidentally, we do not need to add the premise “unbiased” to our tosses. “Unbiased” makes the argument circular, because it has in it the notion that the probability of the conclusion just is 1/n. That would make the argument into this: “Given the probability the outcome is 1/n, i.e. ‘unbiased’, the probability of the outcome is 1/n.”

Another statistical syllogism. Premise: “Two-thirds of the marbles in the bag are white and just one marble will be pulled from the bag.” Conclusion: “The marble pulled is white.” Notice we don’t need words on how marble was pulled, etc.

Example 3

David Stove (a follower of Williams) liked examples like this one. Premise: “Exactly two-thirds of Martians wear hats and George is a Martian.” Conclusion: “George wears a hat.” The objectivist deduces 2/3 for the probability; the subjectiist will usually agree, but etc. The frequentist must remain mute forevermore because there is no infinite sequence of events. This is because there is no event to be embedded. And that is because there are no Martians, hat-wearing or not.

Example 4

Premise: “If the bank would have made a loan to Jones and this list of Jones’s financial pertinents.” Conclusion: “Jones would have defaulted.”

This is a counterfactual, and a common one. The bank didn’t make the loan and is hoping that it was the right decision. Depending on the exact list of Jones’s financial pertinents, and probably given additional premises about how these pertinents are quantified, the objectivist could deduce a probability for the conclusion. So can the subjectivist. Here, both the objectivist and subjectivist are acting subjectively, unless that list of pertinents allows one to deduce—and not guess—what the relevant quantifications are.

The frequentist must again remain mute, for there is no embeddable sequence; there is no observation of any kind.

Example 5

Premise: “Between 1/2 and 2/3 of X are F and x is X.” Conclusion: “x is F.” Objectivist deduction: the probability is the interval [1/2, 2/3], or possibly (1/2, 2/3) depending on what meaning is supplied for “between”. Subjectivists would usually agree, but etc. Frequentists weep, for the idea of probability as in interval is unknown to them. However, we already showed in Example 1 that probability can be an interval.

Example 6

Another Stovian example. Premise: “Bob is a horse.” Conclusion: “Bob is a winged horse.” The objectivist probability of the conclusion is at least greater than the probability of the conclusion of this next argument. Premise: “Bob is a horse.” Conclusion: “It is not the case that Bob is a horse.” Now (quoting, Rationality of Induction, p. 166):

The latter has logical probability=0. So the former has logical probability > 0. But the schema for the former argument,

x is a horse
x is a winged horse,

has relative-truth-frequency=0. For the number of winged horses divided by the number of horses = 0/n, for some positive n.

Frequentism fails again.

More examples

There are many more examples which show frequentism fails but in which objectivism (i.e. logical probability) works (subjectivists in these cases usually agree with objectivists, but etc.). If there are any frequentists left, maybe some day we can go over these.

Statistics finally appeared (in Example 3), but we still haven’t got to the ideas of “priors” and all that. That will be next time. Told you it wasn’t easy! (If it was easy, we wouldn’t have some many arguments for so many years.)

Crucial Update: Example 7

Many people are understandably stuck on Example 2. This is for three reasons. The first is easy: because classical training emphasizes physical and not logical examples, it is natural to fall back to this training and to insist that all examples are physical in a sort of subjectivist frequentist manner.

Second. Change the example to this. Premises: “There is an n-state device, just one state of which is set at ‘Q'; the device will be used and only one state can attain.” Conclusion: “A ‘Q’ will attain.” The objective deduction (given the premises) is the probability the conclusion is true is 1/n. It is now very difficult (or impossible) to insist on adding premises about “equal sides” or “unbiasedness” or any other thing which makes the argument circular (see the comments).

Third. We are making logical not physical arguments. This distinction was easy to make in the counterfactual and Martian examples, but is often blurred in the cases of the statistical syllogism. Objective probability is a strict matter of logic. We must take the argument exactly as it is given, and add or subtract nothing from it. Just think: what if (as I am doing now) you were given just this premise and just this conclusion and asked to give a probability for the conclusion. What would you say? Why? On what grounds would you insist the probability cannot be known?

Lastly, if you’re still stuck, change “device” to this premise: “George the Martian will select from the numbers (integers) 1 through n and pick only one and Q is a number between 1 and n.” Same conclusion. It should now be starkly obvious that this is a logical and not physical argument. Note that we need no premise on how George will pick Q, just that he will pick it.

Incidentally, this example also works if we change “George the Martian” to “Briggs the statistician.”

Government Creates More Speech Codes For Campuses: How To Fight Back

You're contributing to a hostile environment, ladies.

You’re contributing to a hostile environment, ladies.

The Department of Education, like the IRS, is a beneficent and benevolent bureaucracy which only has our best interests at heart and which is in no way political, has decided that all colleges shall hew to a new “blueprint for colleges and universities throughout the country to protect students from sexual harassment and assault” (via Legal Insurrection, via FIRE).

The DOE was reviewing the sexual harassment policies of the University of Montana (why? why not!) and came across policy 406.5.1 (which is not to be confused with policy 406.4.1) and didn’t like what it saw. In a letter written to UM, the DOE said:

This policy provides examples of unwelcome conduct of a sexual nature but then states that “[w]hether conduct is sufficiently offensive to constitute sexual harassment is determined from the perspective of an objectively reasonable person of the same gender in the same situation.” Whether conduct is objectively offensive is a factor used to determine if a hostile environment has been created, but it is not the standard to determine whether conduct was “unwelcome conduct of a sexual nature” and therefore constitutes “sexual harassment.”

The “standard” is whatever upsets is “malicious harassment.” The DOE further worries that UM doesn’t comprehend “that a single instance of sexual assault can constitute a hostile environment” (emphasis added). All it takes is one football player leering at one cheerleader before a fell “hostile environment” exists.

Apparently the way the SH procedure at UM works is like this. Suppose a male football player notices a female cheerleader and, as she walks by, says “Hey, cutie.” The cheerleader, a Wymyn’s Studies major, will of course consider this a form of violent sexual attack. The seriousness of this charge is really all that is needed to convict the football player, but at the insistence of DOE lawyers, what now has to happen is that the college has to find an “objectively reasonable person of the same gender” and recreate the “same situation”.

In other words, a new girl has to parade in front of the football player to see if her trawling has an effect. To be fair, she also has to wear the cheerleader’s outfit, else the situation cannot be said to have a proper control. If in this reenactment the new short-skirted cutie also feels “objectified”, why then the boy is to be pilloried at once. But what if instead she and the boy end up at Applebees sharing a dessert for two?

In that case, I suggest the original complainant be forced to undergo mandatory and extensive sensitivity training, which includes watching the movie Brian’s Song so that she can understand men have feelings too (but only about sports).

Actually, if we may inject a serious statistical point, just one new cutie would not constitute a sufficient sample. No. There would have to be at least twenty or so recreations before we could be certain if an “objectively reasonable person of the same gender in the same situation” felt attacked or not.

FIRE is upset with these new almost-regulations. It’s hard to see why. They ought to be embraced (to keep with the naughty metaphors). If it really is “sexual assault” or “harassment” whenever anybody takes offense at whatever does not tickle their fancy, then that is exactly what people should do. Take offense.

Kids with a sense of logic (and humor) ought to, say, file sexual harassment charges over the text which appears in course catalogs. Have you see these lately? They have passages that would make Hugh Hefner blush.

What about all those posters advertising yet another “daring” performance of the Vagina Monologues? (Note to university females: we understand you have vaginas. Congratulations. Now maybe we can go back to Shakespeare?) And what of the hook-up culture that is allowed, countenanced, encouraged by campus Presidents? Harassment! Hostile environment!

File formal complaints against the administrators, gang, not against the professors. It is the Deans, Associate Deans, Assistant Deans, Senior Vice Presidents, Vice Presidents, Directors, Assistant Directors, and on and on and on—these creatures regularly outnumber teachers—who are responsible for the offensive material which positively drenches college campuses and which create such horrifying environments.

This isn’t a joke: do this. Immediately press charges against senior administrators, and then press more charges. When they complain, press more charges, and tell them it is your right not to be offended. They cannot but agree.

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