Rescission, Decision, Division

August 12, 2009
Posted by Jay Livingston

Mike at Pragmatic Idealists may have had a similar reaction to mine when he heard the “Fine Print” episode of This American Life. Patients testifying before Congress told of how their health insurance companies had rescinded their coverage and refused to pay their claims. These patients were desperately ill and in need of expensive care. But the insurance companies found mistakes in documents submitted when they applied for insurance years earlier and used these minor errors to cancel coverage. It’s called rescission.

Then we heard from insurance company executives testifying before the same committee. They all said that rescission affects only about 0.5% of their policy holders.

Here was my problem: how could I square this statistical reality with the anecdotal data from the woman with aggressive breast cancer whose coverage they rescinded because she had once been treated for acne? How could I balance 0.5% against my absolute knowledge that these executives were heartless bastards?*

Mike points to a post by Taunter that has the answer, and I was a bit embarrassed not to have realized it myself. Both Mike and Taunter see it in terms of Bayesian probability and the Monty Hall problem, and they are right. But there’s a simpler way – not Bayes, but fifth grade arithmetic.

A rate, like the rescission rate, is fraction. So we have a division problem. But what are we dividing by what? What is the numerator, and, more important, what is the denominator?

Let’s say that the Vulcan Fire Insurance company covers 1000 houses. Last year, none of those houses had a serious fire. A very few had small fire damage costing much less than the owners had paid in premiums over the last few years. Is Vulcan going to scan anyone’s documents looking to rescind coverage? Of course not. Those customers are paying premiums in and not taking anything out. But suppose that this year, one house is completely destroyed by fire, with damages of $300,000.

Now Vulcan gets out its magnifying glass and scans the fine print trying to find some basis for rescission, but just for this one customer. They find their pretext, they rescind the coverage, and they don’t pay a dime.

And when the CEO of Vulcan is called before Congress, he says, “Rescission affects only one-tenth of one percent of our customers.”

True enough. One rescission divided by 1000 policy holders equals 0.1%. But if you do the division differently, if you change your denominator from “all customers” to “policy holders whose houses burned down,” the rescission rate is 100%.

With health care, the question isn’t what percentage of all patients are rescinded. The question, which nobody on the Congressional committee thought to ask, is what is the rescission percentage of patients filing expensive claims – people with conditions that require expensive and continuing treatment and care. Taunter estimates that if you draw the line at the top 5% of patients (“top” in terms of medical costs), the rescission rate is more like 10%. And if you look at the top 1%, it’s closer to 50%. **

Check out Mike’s post and the links in it for a more thorough presentation and analysis of the problem.

The fine print problem takes other forms besides rescission. As a Consumer Reports study concluded, “Many people who believe they have adequate health insurance actually have coverage so riddled with loopholes, limits, exclusions, and gotchas that it won't come close to covering their expenses if they fall seriously ill.” Read here about a woman who thought she had health care and wound up paying over $20,000 for a normal pregnancy and childbirth.

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 * Opponents of the public option and “government run” health care, try to scare us by suggesting that “faceless bureaucrats” will be making life-and-death decisions about us. I’ll take a faceless bureaucrat over a heartless bastard any day.

** Another statistic. Several bloggers linked to Taunter’s post – bloggers at important places like Reuters and The Atlantic. Views of Taunter’s posts rarely reach three figures. But this one post got nearly 10,000 hits.

The Conspiratorial Mind

August 11, 2009
Posted by Jay Livingston

“I wanted to punch the guy,” said my son, a young man not given to violence. The guy in question was standing outside the 72nd St. subway entrance wearing a sandwich-board sign that said, “9/11 Was an Inside Job. Prove Me Wrong.”

We had been talking about the Birthers, and that had reminded him of this other conspiracy theorist.


It got me to wondering about conspiracy believers, specifically what they think of other conspiracists. Are they like some religious believers, whose rejections of one another’s ideas about God are so intense they can lead to mass slaughter? Or are they more like New Age religionists who allow that “there are many paths up the mountain”?

I don’t expect that the 9/11 believers also share the specific beliefs of the Birthers, though there’s a remarkable symmetry, as Brendan Nyhan shows in this graph he created with data from different surveys.


Graphed on belief in the two conspiracies, the proportions of Democrats and Republicans are mirror images of one another. And about 5% of each group accepts both conspiracies (I’m assuming that the Democrat Birthers also believe that 9/11 was an inside job; similarly for Republicans who accept the 9/11 story.)

But what about the Birthers who do not themselves believe the 9/11 conspiracy, or the 9/11 “Truthers” who don’t believe the birth idea? Are they more tolerant of other people’s conspiracy theories?

Those of us in the mainstream view both of them as wackos who spend a lot of effort ignoring reality. But do the Birthers reject the 9/11 believers as wackos, or are they generally more tolerant of any conspiracy theory? Or is this purely a partisan thing, as Nyhan implies, with each side accepting the theory that makes the other side look bad?

My hunch is that there’s a conspiratorial mentality that makes any conspiracy seem more reasonable. Conspiracists of all sorts share the assumption that “they” (some powerful cabal) are hiding the truth from the rest us in order to further their quest for political or economic domination. So a Birther seeing the guy with the sandwich board would not think, “What an outrageous and ignorant insult to the families of the victims,” as my son did, but, “Maybe he’s on to something. You never know.”

Surely there is already research on this question. It’s just that I don’t know about it. They must be hiding it from me.

Talking Sophisticated

August 9, 2009
Posted by Jay Livingston

It's very important that -- that there be a robust waste, fraud and abuse oversight of health care, not only in the government programs of Medicare and Medicaid, but clearly the duplicity that we find in our health care system. (Rep. Dave Camp (R-MI) at a Congressional hearing, June 17, 2009).

A sensible health reform plan that coordinates and simplifies all government health programs like Medicare, Medicaid and the proposed public option with one easy-to-understand set of rules would reduce confusion and duplicity, and save money.
Thomas M. Cassidy Setauket, N.Y., Aug. 3, 2009 (NYT, Aug. 3, 2009) The writer, an economist, is a clinical associate professor in the School of Social Welfare at Stony Brook University and a former senior investigator with the New York State attorney general's Medicaid Fraud Control Unit.

I’ve made my peace with solecisms. I don’t even use the word solecism any more. The linguists have converted me. What I used to call “mistakes” I have learned to think of as “interesting.” These interesting word choices call not for correction but for explanation and even appreciation.

If people talking about a lucky break say “fortuitous” instead of the pedestrian “fortunate,” that’s fine with me. If they think characterizing a relationship as “ideal” doesn’t sound sophisticated enough and instead call it “idyllic,” even though the couple live in midtown Manhattan, hey, I can get behind that too. I know what they mean. At dinner I myself no longer use salad “dressing”; chez moi, we pass the dressage.

But sometimes the “interesting” word choice can be confusing. Like duplicity. Rep. Camp seems to be a conservative, linguistically I mean. He even uses the subjunctive. Correctly. And Prof. Cassidy is an educated man, an educator. But by duplicity, does he mean deception or does he mean duplication? No doubt, both are unwanted aspects of Medicare and Medicaid. I just wish I knew which one to be concerned about.

I guess what a good health care system needs is less duplicity and more singularity.

What Are the Chances – Don't Ask.

August 6, 2009
Posted by Jay Livingston

No doubt others will be blogging today’s NY Times story, “For Today’s Graduate, Just One Word: Statistics .”

I probably shouldn’t be saying this on the eve of the ASA, but there are times when statistical, sociological thinking is, well, not wrong, but not quite appropriate. Several months ago, on This American Life, a man told of something that happened early in a romantic relationship. I don’t remember anything about him, except that he was some sort of scientist, or at least he looked at the world in a scientific way.

He and his girlfriend, were talking about “how great it was that we were in love and that we’d found each other, it felt so ‘fated.’ And she asked, ‘Do you really think we were the only one for each other?’” He did some quick mental calculations and figured that out of the six billion people on the planet, the number of girls that he could have matched up so well with would have to be a fairly small number – a teeny tiny fraction of a percent.

“And I said, ‘I don’t know if you’re the only one for me, but I think that you have to be at least one in a hundred thousand.”*

It was their first big fight.

Or as Tim Minchin sings,

Your love is one in a million
You couldn’t buy it at any price
But of the 9 point 9 hundred thousand other loves,
Statistically some of them would be equally nice.

It's just mathematically unlikely
that at a university in Perth
I happened to stumble on
the one girl on earth
specifically designed for me

It’s from his song “If I Didn’t Have You,” which Kieran posted a couple of months ago. In case you missed it then, here it is.

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* For the record, 100,000 out of six billion is 17 one-thousandths of a percent. Even adjusted for sex and age, it will be a small fraction of a percent.