{"id":790,"date":"2009-07-22T12:51:29","date_gmt":"2009-07-22T12:51:29","guid":{"rendered":"http:\/\/scientopia.org\/blogs\/goodmath\/2009\/07\/22\/bad-healthcare-cost-models-produce-silly-results-anyone-surprised\/"},"modified":"2009-07-22T12:51:29","modified_gmt":"2009-07-22T12:51:29","slug":"bad-healthcare-cost-models-produce-silly-results-anyone-surprised","status":"publish","type":"post","link":"http:\/\/www.goodmath.org\/blog\/2009\/07\/22\/bad-healthcare-cost-models-produce-silly-results-anyone-surprised\/","title":{"rendered":"Bad Healthcare Cost Models Produce Silly Results (anyone surprised?)"},"content":{"rendered":"<p> This morning, my good friend Orac sent me a link to an interesting piece<br \/>\nof bad math. Orac is the guy who really motivated me to start blogging; I<br \/>\njokingly call him my blogfather. He&#8217;s also a really smart guy, not to mention<br \/>\na genuinely nice one (at least for a transparent box of blinking lights). So<br \/>\nwhen he sends me a link that he thinks is up my alley, I take a look at<br \/>\nthe first opportunity.<\/p>\n<p> Today, he sent me a link to a guy who claims to have put together<br \/>\na mathematical model showing that it&#8217;s impossible to create a national<br \/>\nhealthcare system without rationing. The argument is a great example<br \/>\nof what I always say about mathematical modeling: you can&#8217;t just<br \/>\nput together a model and then accept its results: real mathematical models<br \/>\nmust be validated. It&#8217;s easy to put together something that looks<br \/>\nright, but which produces drastically wrong results. <\/p>\n<p> The common way of saying it is &#8220;Garbage In, Garbage Out&#8221;. I personally<br \/>\ndon&#8217;t like that way of describing it &#8211; because in the most convincing examples<br \/>\nof this, it looks like what&#8217;s going in isn&#8217;t garbage.<\/p>\n<p><!--more--><\/p>\n<p> One way of looking at a mathematical model of something like healthcare is<br \/>\nas a dynamical system. Each point in the phase space of that system is<br \/>\na possible situation. The model predicts how that will evolve over time. The<br \/>\nGIGO argument makes it sound like what matters is: which point do you choose<br \/>\nto describe today&#8217;s situation? If you choose the right starting point, then<br \/>\nrun it forward, you&#8217;ll get the right end point. But the evolution function is<br \/>\nalso important: if your evolution function doesn&#8217;t accurately model how the real<br \/>\nworld changes over time, then the end point will be wrong, no matter how perfectly<br \/>\nyou selected the starting point.<\/p>\n<p> The selection of the evolution function is a part of the modeling process. You <em>can<\/em><br \/>\n(and probably should) view it as an <em>input<\/em> to the model &#8211; in which case GIGO is<br \/>\nabsolutely right. But most people&#8217;s intuitive understanding of GIGO doesn&#8217;t do that.<\/p>\n<p> Anyway&#8230; I&#8217;m getting positively Oracian here, babbling on this long without getting to<br \/>\nreal point. (Except, of course, that I&#8217;m not doing it nearly as well as Orac. Anyone else think<br \/>\nit&#8217;s unfair that a lucite box of blinking lights  writes with more style and eloquence than me?).<\/p>\n<p> The article is called <a href=\"http:\/\/covertrationingblog.com\/general-rationing-issues\/theres-not-enough-waste-and-inefficiency-in-healthcare\">There&#8217;s Not Enough Waste and Inefficiency in Healthcare<\/a>, by a guy who writes under the name &#8220;DrRich&#8221;.<\/p>\n<p> His model, as he describes it, is based on four assumptions. I&#8217;ll tell you about them,<br \/>\nand then I&#8217;ll try to explain both why the look right, and why they&#8217;re actually completely wrong.<br \/>\nI&#8217;m not going to quote him precisely &#8211; I&#8217;m going to rephrase in a way that makes the<br \/>\nproblem more obvious &#8211; but I recommend that you look at his original article to verify<br \/>\nthat I&#8217;m <em>not<\/em> misrepresenting his argument.<\/p>\n<ol>\n<li> The proportion of healthcare spending that is wasteful is currently 25%.<\/li>\n<li> The annual rate of growth of healthcare spending is <em>constant<\/em>, and is<br \/>\napproximately 10%.<\/li>\n<li> The annual growth rate of non-wasted healthcare spending is the same as the current<br \/>\ninflation rate.<\/li>\n<li> The difference between the 10% growth rate and the non-wasted spending is<br \/>\nwasteful spending.<\/li>\n<\/ol>\n<p> He admits that the first point is a total wild-ass guess. And that&#8217;s fine. No one is really<br \/>\nsure of what the correct number is, and for the sake of argument, a nice round number<br \/>\nlike 25% is a reasonable starting point.<\/p>\n<p> The second point is where things start to go awry. Health-care spending<br \/>\ngrowth isn&#8217;t constant &#8211; and that should be completely obvious. The growth<br \/>\nin health-care spending has been absolutely ridiculous in recent times &#8211;<br \/>\nbut it varies enormously, depending on economic conditions. Exactly how to<br \/>\npredict it is very uncertain &#8211; no one is really sure exactly which variables<br \/>\ninfluence it. But we know that there are lots of factors, which push and pull<br \/>\nthe rate in different directions. For example, in bad times, people delay<br \/>\ntreatments &#8211; which can decrease some costs. Bad economic conditions also<br \/>\nincrease the incidence of many stress related disorders, which can increase<br \/>\nsome costs. Health care spending is also affected by weather, by natural disasters,<br \/>\nby medical innovations, by the average age of the population, and by the size of the<br \/>\npopulation. Given all that uncertainty, there&#8217;s one thing that&#8217;s very clear: the<br \/>\nrate of increase of health-care spending is <em>not<\/em> constant, and its<br \/>\nrelationship to the economic environment that surrounds<br \/>\nit is non-linear. <\/p>\n<p> The third point is also not correct. It <em>sounds<\/em><br \/>\nreasonable. In fact, if you measure health care spending<br \/>\n<em>per capita<\/em>, then in the long term, the increase in healthcare<br \/>\nspending per year must eventually level out at the rate of inflation. But<br \/>\nthat&#8217;s <em>not<\/em> what DrRich is saying. He&#8217;s saying that the total<br \/>\nrate of increase of healthcare spending should match inflation. And<br \/>\nthat&#8217;s just wrong. In fact, it&#8217;s totally ridiculous. Once again,<br \/>\nDrRich is trying to model things using a single-variable linear model<br \/>\nfor something that is manifestly not a single-variable linear phenomenon. And<br \/>\nany attempt to validate that model, by comparing it to real observations<br \/>\nwill make it abundantly clear that the model is total rubbish.<\/p>\n<p> Ignore for the moment that healthcare spending per year is highly<br \/>\nvariable and, likely, chaotic. After all, in the long term, the chaotic<br \/>\nfactors should damp out. (You can see it as being very similar to weather:<br \/>\nshort-term, it&#8217;s chaotic. Long term, it can&#8217;t be.) In the long-term, what<br \/>\nwe should expect is that <em>on average<\/em>, the rate of increase of<br \/>\nnon-wasteful medical care would, roughly, match <em>the rate of<br \/>\neconomic growth<\/em> in the economy, not the rate of inflation. That,<br \/>\nright there, is a major flaw. The population is, at the moment, constantly<br \/>\nincreasing. That means that if health care prices stayed exactly the<br \/>\nsame, total healthcare spending would <em>increase<\/em> every year, because<br \/>\nthe number of people be treated increases. But by that same argument, the<br \/>\neconomy should also grow because the number of productive workers increases<br \/>\nwith the population. If you take a conservative model of health-care spending<br \/>\nincreasing at a rate based on <em>just<\/em> inflation plus population growth,<br \/>\nbut you claim that the rate of non-wasteful healthcare spending grows with<br \/>\ninflation, then you&#8217;ll wind up with a picture where the percentage of<br \/>\nhealthcare spending that is going to waste\/inefficiency is increasing,<br \/>\nwithout bound, every year. In fact, you&#8217;ll find that in fairly short order,<br \/>\nit&#8217;s pretty much 100% of cost-growth.<\/p>\n<p> And &#8211; surprise! That&#8217;s exactly what DrRich&#8217;s model shows. From<br \/>\nthat, he concludes that the rate of growth in healthcare spending<br \/>\n<em>cannot<\/em> be blamed on waste.<\/p>\n<p> The evolution function that he chose for measuring the portion of<br \/>\nincrease in healthcare spending that&#8217;s wasteful is totally bogus. And so,<br \/>\neven if the numbers that he puts into his model are absolutely, 100%<br \/>\ncorrect, his conclusions can&#8217;t be.<\/p>\n<p> How much of health-care growth is really due to waste? I don&#8217;t<br \/>\nknow. I haven&#8217;t sat down and tried to model it. But the experience<br \/>\nof numerous other countries, using a variety of public, private, or<br \/>\nhybrid universal insurance systems without experiencing the kind of<br \/>\ncost-growth that we see in the US is a pretty good indicator that<br \/>\nit&#8217;s <em>not<\/em> unmanageable. But again &#8211; I don&#8217;t know. Someone<br \/>\nwho knows more about health care spending than I do could put together<br \/>\na model that tries to show how much is wasted, and what the rate of<br \/>\ngrowth of wasteful spending really is. But it&#8217;s not an easy job. And<br \/>\nDrRich&#8217;s silly linear model based on the rate of inflation is clearly<br \/>\n<em>not<\/em> the right model.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This morning, my good friend Orac sent me a link to an interesting piece of bad math. Orac is the guy who really motivated me to start blogging; I jokingly call him my blogfather. He&#8217;s also a really smart guy, not to mention a genuinely nice one (at least for a transparent box of blinking [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[71],"tags":[],"class_list":["post-790","post","type-post","status-publish","format-standard","hentry","category-bad-economics"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p4lzZS-cK","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts\/790","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/comments?post=790"}],"version-history":[{"count":0,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts\/790\/revisions"}],"wp:attachment":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/media?parent=790"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/categories?post=790"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/tags?post=790"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}