### Studies probably understate the cost of ER misuse

**Matthew Martin**2/28/2014 03:29:00 PM

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I've been thinking about Emergency Room (ER) misuse lately. It seems to me that many of the studies out there probably understate the cost of ER misuse.

Most studies of healthcare costs use "charges" as the dependent variable. Charges are the prices that hospital pricers have negotiated with various individuals and insurers, representing the actual charge to the healthcare recipient.This data is easy to get but not particularly meaningful because in reality charges are not perfectly correlated with the costs of treatment--the hospital's markups over cost vary widely both by proceedure and by recipient, influenced by things such as elasticity of demand and bargaining power. Relatively costly procedures with cheaper alternatives like, say, proton-beam therapies, may have relatively small margins over costs, while little everyday things like aspirin have massive margins relative to their tiny costs. (Even worse, of course, are studies that use list prices which are mostly about bargaining with insurers and bear little relation to costs).

Some studies do a little extra diligence and get the hospital pricers to divulge the baseline "costs" they use, before markups are factored in. Costs are certainly an improvement over charges, but they aren't really what many researchers seem to think--the hospital pricers didn't literally tabulate the cost of every little thing that goes into a given procedure to come up with the cost, nor did they use any kind of reduced form modeling to estimate the cost of individual procedures. Actually, what they do is produce a table of relative factor intensities and linearly scale them by the division's total cost. Here's an example of what I mean:

Suppose that the division performs only two types of procedures, called procedure X and procedure Y. They performed procedure X twice last quarter, performed procedure Y only once last quarter, and the division as a whole incurred a grad total of $100 worth of expenses, including all capital, labor and whatever other costs. The pricing division has determined that procedure Y uses twice as much resources, including all capital and labor inputs, as procedure X uses, which means that Y has a relative factor intensity of 2. To cover the costs of the division, then, we must have 100=cx+2cy where x is the number of X procedures and y is the number of Y procedures, and c is a scalar on the relative factor intensity. X was performed twice and Y performed once, so that implies c=25. Thus, the "costs" used in all these studies are just the scalar c times the relative factor intensity, in our case our data set would say that the cost of X is $25 and the cost of Y is $50.My point in all this is that the cost data used in all these studies aren't true costs, they are actually linearly homogeneous factor intensities, and the scalar c above provides absolutely no additional information of any kind. This has important implications for cost comparison studies in situations where costs do not actually scale linearly.

Here's a concrete example. Consider a pediatric hospital that has a clinic for children with sickle cell disease. Sickle cell is a chronic condition with frequent complications such as pain and fever that often, for various reasons, leads patients to be admitted to ERs even though the sickle cell clinic could treat those complications. So want to know the cost difference between treating a sickle cell patient experiencing pain or fever in the ER versus treating them in the sickle cell clinic. One way of approaching that question would be to estimate the effect of treating sickle cell patients on total division costs for the ER and the sickle cell clinic. So for the ER, we get a regression of the form:[$$]Y_t=\beta_0+\beta_1S_t+\beta_2P_t+\beta_3S_t*P_t+\epsilon_t[$$] where [$]Y_t[$] is the ER division's total cost in period [$]t[$], [$]S_t[$] is the number of sickle cell patients treated in period [$]t[$], [$]P_t[$] is the number of non-sickle-cell patients treated in period [$]t[$], and [$]\epsilon[$] is the error term. Assuming that the necessary OLS assumptions etc. are satisfied, estimating this model let's us easily calculate the average marginal cost (AMC) of treating sickle cell patients in the ER, which is given by [$$]AMC_{ER}=\frac{\partial Y_t}{\partial S_t}=\beta_2+\beta_3P_t.[$$] That gives us the cost of treating sickle cell patients in the ER, which we can then compare to the cost of treating them in the sickle cell clinic. The sickle cell clinic, obviously, does not treat all the other kinds of patients that the ER treats, so the sickle cell clinic's cost regression looks like this: [$$]X_t=\gamma_0+\gamma_1S_t+\mu_t[$$] where [$]X_t[$] is the clinic's total costs in period [$]t[$], [$]S_t[$] is the number of sickle cell patients treated in the clinic in period [$]t[$], and [$]\mu_t[$] is the error term. As before, we can compute the average marginal cost of treating a sickle cell patient in the sickle cell clinic as [$$]AMC_{SCC}= \frac{\partial X_t}{\partial S_t}= \gamma_1[$$] and we can now present the difference in average marginal cost of treating them in the ER rather than the clinic as [$$]AMC_{ER}-AMC_{SCC}= \beta_1+\beta_3 \bar{P_t} -\gamma_1,[$$] where [$] \bar{P_t}[$] is the average value of [$]P_t[$] in the data (ie, the average number of non-sickle-cell patients treated in the ER each period).

But that's not what existing studies are doing. Existing studies are using the hospital provided "costs," which are really just linear factor intensities. Thus, they are estimating a model that looks more like this: [$$]Z_i=\gamma_0+\left(\beta_1-\gamma_1\right)S_i+\nu_i[$$] where [$]Z_i[$] is the "cost" of treating patient [$]i[$] based on the "cost" data given to them by the hospital pricers, [$]S_i[$] is a dummy variable equal to 1 for sickle cell patients that were treated in the ER and zero for sickle cell patients treated in the sickle cell clinic, and [$]\nu_i[$] is the error term. Thus in these papers, [$$]AMC_{ER}-AMC_{SCC}= \beta_1 -\gamma_1.[$$]

My point is that papers that use hospital "costs"--which are really just linear factor intensities--will underestimate the cost of treating patients in the ER by [$] \beta_3\bar{P_t}[$]. In economics terms [$]\beta_3\bar{P_t}[$] is the gains from specialization, or alternatively, the economies of scale. The problem is that linear factor intensities are by definition linear--they will never, ever, let you estimate economies of scale which are by definition non-linear. Actually, there are other problems with hospital-provided "costs" as well. For example, "costs" are calculated in a way so that they include a proportion of the divisions' fixed costs as part of the cost of treating a patient. That means that cost-effectiveness studies that use this "cost" data are actually basing their recommendations on sunk-costs--that is, costs that actually would be the same under either policy--which is a huge no-no. The ER is going to be equipped to treat sickle cell patients regardless of whether a particular sickle cell patient goes to the clinic or to the ER, so the fixed costs of equipping the ER to treat sickle cell should not be counted as part of the gains from triaging sickle cell patients to the sickle cell clinic--but by using hospital-provided "costs" much of the literature is implicitly committing this fallacy. The implication for future research is that we should favor reduced-form estimates of average marginal cost over hospital-provided "costs" per procedure.