• 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.

    • Austin: when claims are made such as:

      “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.”

      I worry that we are ignoring opportunity costs. Perhaps we know that – all other things being equal – this Medicaid coverage is cheaper. But does this ignores anything that would have gone on in its stead.

      It ignores the crowding out that government spending does in general. If we devote public resources towards X, then aren’t we facing a) ignoring other areas where we could have possibly gotten a (better?) return on those public resources, which is a cost in itself and b) crowding out private incentives to create more efficient ways to produce the same goods?

      Thus I feel that such cost estimates are too simplistic, and need to at least be stated as such, or caveated.

      I know my comments don’t offer alternative solutions to the issues you bring up, and seem to only point out potential faults, but I feel it should be recognized.

      • @love actuary – Not my post (was Aaron’s). In any case, crowd out is nontrivial for other Medicaid expansions. Something like a 75% rate has been found with prior expansions (for every 4 people newly enrolled in Medicaid, private coverage went down by 3).* This obviously increases government spending in a world without subsidies. Overall spending may go down for those who experience crowd out since Medicaid rates are lower. With subsidies the story may be different, as Aaron suggested. CBO is aware of crowd out, as is Gruber, so I doubt this was completely overlooked in their estimates.

        Watch this blog for more on crowd out. It’s not coming imminently, but perhaps in a few weeks.

        * Gruber J, and K Simon. 2008. “Crowd-out 10 years later: have recent public insurance expansions crowded out private health insurance?” Journal of Health Economics. 27 (2): 201-17.

    • Thanks for addressing, Austin. My apologies on switching your / Aaron’s name 🙂

    • I regularly read right of center health care blogs. They all make the same argument that Medicaid does not pay enough, so docs will soon stop accepting it. They also claim that we pay too much for Medicaid care. You are correct about your assessment. When we got to their solutions, things get a bit fuzzy. They seem to think that if give them HSAs, low budget HSAs to be precise, that these same patients will get the same level of care and spending will go down. They point to a couple of programs in existence for a couple of years that this can work.

      I think that any program can hold down costs for a short while. It takes people a while to navigate a new system. It takes people a while to start complaining and looking for better care. If HSAs cannot make a big dent in private spending, I doubt they make much difference for Medicaid patients, unless you just limit the amount they can spend, ie, ration.


    • Well, there is certainly one way to increase Medicaid payments to providers and lower the cost of the program at the same: greatly reduce the number of people who are on the rolls. Not very nice for the people who are removed, however.

    • The problem of rising health care costs shouldn’t be blamed on Medicaid or Medicare; those programs actually reimburse less than most private health insurance policies. The problem is that we need an efficient health care system in this country but we have instead a medical industry. We in the health care field have become so focused on maximizing revenue that we continuously drive up medical costs without ensuring that it produces overall improvement in the quality of health of our patients.