Posted by: sayamika, the killer bunny | 2009 August 27

Statistics for dummies…. I mean doctors

Reading on The Happy Hospitalist re: his take on what Obama’s plan would mean in terms of cost per QALY, I noticed something: his stats were appalling. When called on it gently, he confidently reiterated his error, and the commenter backed down.

Clearly, we as doctors need more training in statistics so we can a. spot these sorts of errors and b. be confident in correcting them.

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So what’s my issue with Happy’s math? Here’s a quote from his post:
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Let’s look at the numbers. Let’s round up for easy numbers. 20,000 deaths a year are attributed to lack of insurance. Obama is trying to brainwash the public into believing we need to spend one trillion dollars in public money over the next 10 years to cover everyone. Let us use easy math and assume a linear function over time. That means an additional 100 billion dollars a year are required to insure the entire nation.
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And in the process we will save 20,000 lives a year. That’s 100 billion dollars a year to save 20 thousand lives. That means Obama wants to spend 5 million dollars to save one life for one year. That’s a Quality-adjusted Life Year of 5 million dollars.
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Error #1: Comparing apples to apple trees. Initially he’s talking about lives saved, then suddenly he starts talking about QALYs. He’s linked to the Wiki article, but apparently he didn’t bother to read it.
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Here’s an excerpt:
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The QALY is based on the number of years of life that would be added by the intervention. Each year in perfect health is assigned the value of 1.0 down to a value of 0.0 for death. If the extra years would not be lived in full health, for example if the patient would lose a limb, or be blind or be confined to a wheelchair, then the extra life-years are given a value between 0 and 1 to account for this.
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Clearly, one life saved is going to impact on the total number of QALYs for the duration of the time this person remains alive. The number of QALYs is not necessarily equal to the number of years that person lives, due to the adjustment factor for quality of life. That’s an insurance thing, and if we disregard the quality adjustment, we can call the measure “person-years,” which takes into account both the number of people (multiplied by) and  the number of years each person lives.
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For example, if I live to be eighty, that’s eighty person-years. If my husband lives to be ninety, we live a total of 170 person-years.
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QALYs are different in that, if he spends the last ten years of his life in a wheelchair, some arbiter somewhere might decide that means his life is 50% quality, so, the last ten years might be worth only 50%, so 5 QALYs.
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Presuming we have both been 100% healthy until that point (we had a car crash on the speedway at the age of 80, which killed me and put him in a wheelchair, lolz), we lived a total of 165 QALYs.
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I can’t calculate QALYs based on an estimated number in an article for future deaths based on lack of insurance, due to not having health data on the people involved.
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Error #2: Deny that lives saved are people who will continue to survive. A refutation from Happy when nudged on the person-year aspect:
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Let’s assume every year 20K lives are saved. And each year you just add another 20K lives. […] And at the end of 10 years, using your logic (which does make sense in theory) 200K lives would have been saved if everyone had insurance for 10 years.
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Okay, so he’s got the number of lives saved. But he’s not looked at person-years and not even hinted at QALYs, which are, after all, his original measuring post. And then things get quite fuzzy indeed:
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Now, lets do a back track. Lets take away the insurance that all these people had for the last 10 years and lets look at year 11

Using your logic, all 200K people + an additional 20K people would die if you took away their insurance to the level 11 years prior.[…]

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Pardon me? Why? How? Are you going to go around and shoot them all?
Here’s my reply:
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But if you save a life, you MUST add that person-year to each year.[….] If you take away the insurance at the end of ten years, you really do still have the accumulated person-years saved, which incidentally works out to (using your 20K for easier math) 200K (the people saved in the first year who live 10 years) plus 180K (saved in the second year who live nine years) plus… you get the idea, working out to 1.1M person years. Then people start dying again, but more slowly, because they have had ten whole years of extra care.
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And here’s Happy’s:
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redrabbit, let’s just assume lives saved. Even better. 5 million dollars to save one life. Same conclusion.Your conclusion would assume after 10 years that removing insurance would kill 200K lives. That’s not what the statistic says. It says 20K lives.
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Error #3: Look for common ground where there isn’t any.
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Oh dear. I think he really sucks at math. Or reading comprehension. Or something. What is a life worth? Even insurance companies baulk at that one. Certainly, a “life saved” is worth more than a QALY, insofar as the person is likely to live more than a year.
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No, Happy, that was your conclusion. My conclusion was that 1.1 million person-years would be saved over ten years, in this case equal to about 200 thousand people. I also stated that people would again begin dying once insurance was taken away, but not all at once.Maybe at a rate of about the same or less than previously, so these people keep on living, and maybe 20 thousand die (assuming same as before insurance, right?), but you still have an accumulated group of live people who continue to be alive. So the savings of people and person-years actually will continue to accumulate.

I thought that was clear from my math, but I guess not.

So, at 11 years, having cancelled the whole programme at 10, because Happy was elected POTUS, we still have a savings of 1.28 million person-years. At 12 years, even with the 20 thousand people a year dying again, still saving 1.44 million person-years, at 13 years still benefitting by lessee 1.56 million person-years. Still 120 thousand people alive who would have died otherwise.

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I didn’t do the QALY numbers here, but you can see that $5 million per QALY price tag he quotes is something of an exaggeration. In terms of person-years, at 20 years, assuming the programme is cancelled and people are dying off at the same rate, this would mean that all 200 thousand people die. We still had a savings of 2.2 million person years, with a cost of about $50 thousand per person-year saved.
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Now, to be fair, it probably will be more per QALY. But if I was Happy, I might not have pointed that out.
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Let’s just hope Happy stays in the hospital and out of policy, because he sure doesn’t seem to get it.
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Ah, I see what Happy’s problem is. He wants to credit the insurance for not only saving a life, but for keeping that person alive, so each life saved in the first year is a person who will die in the second year without insurance.
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For some people/situations, I can see his point. A heart failure patient who has an acute event might not live very long without recurrent intervention, etc. However, the estimates he uses are based on the current situation in the USA, and represent actual lives lost due to lack of intervention due to lack of insurance. Meaning, people who died in the first year didn’t survive to get counted in the group that died in the second year. Meaning, there’s one hell of a burden of disease out there.
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So the meaning of all this is: you can use my calculations to look at lives lost in the past 10 years due to lack of insurance. The truth about the future is probably not as cut-and-dried, as he has a point, many of the people “saved” will not live the full 10 or 20 or however many years.
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But many will. Acute trauma patients. Patients suffering acute events such as DVT, PE, pneumonia. People diagnosed with cancers, diagnosed early and treated appropriately. Some people will get many more years, and many more QALYs.
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He’s right on one thing: it’s wrong to think every person “saved” in the first year will survive right on through. But he’s really pushing it to say every person (or even a majority) saved by medicine this year would die next year without it.
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Responses

  1. Doesn’t sound very much as though your Dr. Happy really cared to know the truth: “Public option is bad! Nyah, nyah!”

    Either that or he’s a fairly egregious narcissist.

    • This argument took place on his blog. You’re just seeing my side of it.

      But, IMHO, you’re right on both points….


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