*[This post originally appeared on Forbes.com on August 29, 2016.]*

Does the EpiPen cost more than the value it delivers?

That’s not a philosophical question, it’s an economic one – and it’s at the core of ensuring we pay appropriately for products and services that deliver clinical benefits to patients, and less (or not at all) for ones that don’t.

But to discuss “value-based pricing” of pharmaceuticals, we need to determine if a drug’s price is greater or less than its “value” – which means we need to convert both to the same units, dollars. So, let’s take a rudimentary stab at calculating the health economic value of an EpiPen.

If you buy an EpiPen, what you’re really buying is insurance against a bad outcome – and simplistically, you could consider its “value” as the product of the odds of the bad outcome it could prevent and the cost of the bad outcome. To make a simple analogy: if I think the odds of a fire in my house are 1% per year, and that a fire would cost me $500,000 in damages, then I might be willing to spend 1% x $500,000 = $5,000 annually on fire extinguishers, smoke detectors and fire insurance to prevent my home from burning down.

(Note that this highly simplified argument based on “expected value” doesn’t take into account many other factors, like one’s level of risk aversion, but it’s a useful starting point for a discussion of value-based drug pricing.)

There are several “bad outcomes” an EpiPen might prevent, like ER visits and hospitalizations, but let's focus on just one – preventing death from a very severe allergic reaction (anaphylaxis) – because most patients probably see averting death as the drug’s main value. Also, to make the analysis less complex, let's limit our analysis to anaphylaxis due to food allergies, even though EpiPen has clinical value in other settings as well.

So with these simplifying assumptions, let’s try to answer the following question: if you’re a patient with food allergies, how much should you be willing to spend on EpiPens each year in order to avoid death from anaphylaxis?

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First, let’s calculate the odds of death from a fatal food reaction in the absence of treatment. Using data from the literature and some reasonable assumptions, we can estimate there could be about 2.4 EpiPen-preventable deaths from food anaphylaxis per million people in the U.S. per year:

- A recent review pegs the annual odds of an anaphylactic reaction in the general population as 6.7 to 112.2 per 100,000 people–so let’s take the midpoint of that range, or about 60 per 100,000 individuals.
- In a recent European registry study of 1,970 patients who had had an episode of anaphylaxis from 2007 to 2015, 2/3 were due to food allergies–so let’s revise the number above, and estimate the annual odds of food-induced anaphylaxis as 40 per 100,000 (0.04%).
- That same study of 1,970 patients identified five deaths, implying a death rate from anaphylaxis of 0.25%--but that doesn’t account for deaths that were prevented in the 67 patients who received EpiPen in the field. We don't know how those EpiPen-treated patients would have fared without it, but if we assume (somewhat arbitrarily) that about 10% would have died, we would re-estimate the odds of death after an anaphylactic episode, in the absence of EpiPen, as 0.61% ([7+5]/1,970).
- Putting those two numbers together, we would estimate the annual odds of death from food-related anaphylaxis in the general population as 0.04% x 0.61% = 2.4 deaths per million individuals (i.e., about 780 deaths per year in the U.S.).

So, if EpiPen could save all 780 of those lives each year in the U.S., how much would it be worth? Before we get to the dollars, we need to calculate the number of “life-years” those 780 lives represent. The average age of death from food anaphylaxis for 63 patients across two U.S. registries (here and here) was about 20, so if we assume a median lifespan of 79 years, each life saved by EpiPen would yield 59 additional life-years–or 46,020 life-years for those 780 fatalities.

As Americans, we’re generally unused to the idea of converting life-years to dollars – but across the pond, the British health authorities have been doing it for years, so we’ll use their methodology. The U.K.’s National Institute for Health and Clinical Excellence (NICE) generally uses an upper bound of 30,000 GBP ($39,000) per quality-adjusted life year (QALY) to determine the cost-effectiveness of new medical products. (Importantly, some have argued this value is three- to five-fold too low.) For simplicity (and rather generously), we’ll assume that all life-years saved by the EpiPen would be of maximum quality–so the total economic value of EpiPen is about $1.8 billion.

But wait – we’re not done yet! To get to the value per patient per year – in other words, what we should be willing to pay annually for an EpiPen–we need to divide the total value by the number of customers. Thus, using a reported estimate of 15 million U.S. patients (6 million kids and 9 million adults) diagnosed with food allergies, this analysis yields an annual value of an EpiPen to each of these diagnosed patients of $120.

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In closing: a caveat, and some conclusions. The caveat is that this particular analysis isn’t an academically rigorous assessment of EpiPen’s health economic value or its “appropriate” price – it’s an illustrative exercise. This model is full of shortcuts to make it digestible by a general audience in the context of a blog post, virtually every input and assumption is up for debate and discussion, and like all “expected value” models, it is highly simplified and stylized. A "quick and dirty" analysis like this one is intended mainly to illustrate a way to think about the problem, not to generate a specific numerical “answer.”

But if there’s a useful conclusion to be drawn from this exercise, it’s that more rigorous analyses of this type are the only way to make progress in value-based pharmaceutical pricing. Congressional hearings, op-eds and television interviews make for good theater, but to really solve the drug pricing problem, we’re going to have to start doing some math. Any group that wants to argue about whether a drug like EpiPen is or isn’t “worth the price” – including manufacturers, payers, health economists, patient groups and legislators – owes it to themselves and the public to put some numbers behind their analyses, defend their assumptions and explain how they purport to link a drug’s cost to its value.