Numbers can be tricky

When I teach about statistics and research, one of the things I see residents having the hardest time with is the difference between relative and absolute risk. The difference is critical.

Let’s say there is a disease that has a 50% chance of killing you. But, if you take drug A, your risk of dying goes down to 25%. Drug A will make you 50% less likely to die: (25/50 = 0.5)

Let’s say there is another disease that has a 0.0002% chance of killing you. If you take drug B, your risk of dying goes down to 0.0001%. Drug B also makes you 50% less likely to die: (0.0001/0.002 = 0.5)

They both have a relative risk reduction of 50%. But I think we can all agree that drug A is way more important than drug B. The absolute risk reduction also tells us that.

Since Drug A reduced the chance of killing you from 50% to 25%, its absolute risk reduction is 25%: (50-25 = 25). This means the number needed to treat (NNT) is 4: (100/25 = 4). Drug B, on the other hand, has an absolute risk reduction of 0.0001% : (0.0002-0.0001 = 0.0001). It’s NNT is 1,000,000: (100/0.0001 = 1,000,000).

In other words, the makers of these companies can both put a commercial on the air saying that their drug halves your risk of death. But you need to treat 4 people with drug A to save one life, and 1,000,000 people with drug B to save one life.  There’s a big difference.

I bring this up because you can use relative percentages to make things look much better or worse depending on how you use them. Take this from the WSJ on Medicaid by Peter Suderman:

At roughly 21% of total state spending, Medicaid is already the single largest item in state budgets, according to the National Association of State Budget Officers. Between 2008 and 2009 (the latest year for which figures are available), annual spending growth on the program nearly doubled, growing to 9% from 4.9%.

Medicaid currently covers 53 million people at an overall cost of $373.9 billion (states are responsible for about half). But starting in 2014, ObamaCare rules will add about 20 million more, according to Richard Foster, the program’s chief actuary.

That first paragraph makes Medicaid sound huge. I’m not saying it’s small. It’s a large part of state budgets, and it’s growing. But so is all health care spending, as we’ve been saying here many, many times. The numbers in the second paragraph look scary, too. $373 billion is a LOT of money. The question is, of course, compared to what?

We spend about $2.4 trillion per year on health care. There are about 310 million people in the US. That means, overall, we spend about $7700 per person on health care.

For 2009, Medicare covered about 43 million people at a cost of $499 billion.  That means, overall, we spent about $11,600 per person on Medicare.

According to Peter’s numbers (which I don’t doubt, but can’t find) we spent $374 billion to cover 53 million people. That means, overall, we spent about $7050 per person on Medicaid.

Again – I’m not disputing that when you get into the hundreds of billions of dollars, then it’s a lot of money. I’m not disputing that we have hard facts to face about budgets and that shortfalls exist all over. But we need to apply some reason here.

Complaints about Medicaid seem to fall into two camps: (1) we need to cut it, and (2) it doesn’t reimburse enough. The odd part is that I often hear these same arguments coming from the same people.  Please understand that the reason that Medicaid doesn’t reimburse enough is that it is underfunded. The Medicaid population, on the whole, is sicker and more costly than the privately covered pool. But, because we underfund it,  it’s cheaper to put people in Medicaid than to pay for them to get private insurance. The reason that the PPACA puts 20 million more people in Medicaid is that it was cheaper than putting them in the exchanges to get private insurance.

Let me say that again – it was cheaper.

We can complain about the cost of Medicaid. We can complain about how fast it’s increasing. But we have to remember that at some point we have to compare it to something else. The Medicaid shortfall is big, but much smaller than many, many other things in the budget. It’s costs are rising, but so are all health care costs. It reimburses too little and doesn’t do enough, but it’s underfunded and a terrible risk pool.

Remember all those things when we talk about what to do. There are other solutions than cutting an already struggling program that absolutely, positively is the last line of support for many of the poorest among us.

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