Leslie and David's Cancerland Adventures

Thursday, September 8, 2011

Improbability

I thought I might share a bit about why it feels so freaky to have this diagnosis. I mean, beyond the whole “OMG, I’ve got CANCER!!!!” thing.

Endometrial cancer accounts for 6% of all cancers in women. About 43,500 women are diagnosed each year, or 23.8 per 100,000. So, luckily, a particular woman’s chances of getting diagnosed with it are pretty small.

It’s particularly unusual at my age. More than 70% of endometrial cancers are diagnosed in women older than me. Only 19% are diagnosed in women in my age bracket (45-54). (Although, to be fair, the median age at diagnosis is 61, which is not that far off.)

Further, the large majority of endometrial cancers, 68%, are discovered when they are still localized to the uterus. Only 8% have already metastasized, as mine did.

Doing some rough figuring, we multiply the number of new cases times the incidence of detection at my age times the incidence of metastases, and get:

43,500 X 19% X 8% = 661

That’s it. Fewer than 700 women my age get this diagnosis each year. See why it’s freaky? Basically, my faith in probability has been shattered. Events of very small likelihood do happen, and when they happen to you, you feel very vulnerable to other events of very small likelihood.

1 comment:

  1. There's a by now classic article about coincidences, and our perception of them, by Diaconis and Mosteller. It's behind a JSTOR firewall, but can be found at: http://www.people.carleton.edu/~rdobrow/Courses/265f03/coincidences.pdf

    See what they call the "Law of Truly Large Numbers" on page 8 and following.

    They talk about how we are bad at understanding large populations. Certainly hundreds of millions is not a size which our imagination/understanding assesses well (my impression, probably shared by anyone who has taught a large lecture class, is that somewhere around 100 individuals becomes impossible to comprehend except as a unit, and my impressions, probably shared by anyone who has attended a large demonstration, is that the difference between a bunch of 10,000 people and a bunch of 1 million people is not easily perceived, at least without training and care).

    The point here is that the odds you describe - 700 out of however many millions - are in some sense not that bad (compare the odds of winning the lottery) - but the odds (however were one to make this precise) of one of those 700 being you - those are in some sense much worse (see their discussion of the woman who won the lottery twice - the probability that some particular person who had once won the lottery wins again is quite different from the probability that some person wins the lottery twice) - what one perceives, of course, is what happens to oneself.

    At any rate, I found the Diaconis Mosteller article very stimulating when I first saw it in the undergrad class that is probably most responsible for my deciding to study mathematics seriously.

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