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 Patients testifying before Congress told of how their health insurance companies had rescinded their coverage and refused to pay their claims.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this statistical reality with the anecdotal data from the woman with aggressive breast cancer whose coverage they rescinded because she had once been treated for acne?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 recission 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 recission 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 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.

* 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.

1 comment:

Mike3550 said...

Jay -- Thanks for the shout out! I have always struggled with how to explain this problem (which is embarrassing given that I should know it) and I think that the way that you describe it here is a really great intuitive description of the problem.