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Flattening the curve on the back of an envelope

I don’t do back of the envelope calculations, largely because the harm of a bad estimate can be worse than the harm of no estimate. A rough guess will be biased in ways we cannot possibly predict. This is acutely true in a pandemic, where academic work is being quoted out of context, discussed on Fox News, and people drink fish tank cleaner as a result.

Apparently undeterred, the Incidental Economist blog has published a piece attempting to calculate the cost-effectiveness of ‘flattening the curve’, a catch-all phrase for the various public health preventive approaches being applied to reduce transmission and avoid the collapse of health systems globally as a result of the coronavirus pandemic. While I applaud the authors’ attempt to bring the tools of cost-effectiveness analysis to the current discussion, their analysis is limited, and unfortunately will confirm many people’s worst suspicions about the application of economics to issues in health.

Health losses

To get into specifics, the authors estimate an average QALY loss by subtracting median patient age at death from COVID-19 from life expectancy, applying a rough blanket adjustment for quality of life. This approach also assumes non-fatal cases incur no health loss. Health professionals have been keen to point out that acute respiratory distress requires physiotherapy and can have long lasting effects on patient respiratory health.

Just as important to the health losses from COVID-19 are the health losses from non-COVID illnesses going untreated. This opportunity cost is fundamental to any economic analysis. A hospital swamped with infectious disease cases cannot treat cancer or heart attacks. It cannot safely perform hip and knee replacements. These are all QALY-saving interventions, and over the year or more that an unmitigated pandemic may play out, these health losses may well outweigh those from COVID-19 itself.


The costs included in this analysis are estimated to be a $1 trillion stimulus package intended to support businesses and individuals who lose income as a result of a lockdown. The stimulus package is not part of the healthcare budget. If your perspective is that of the healthcare system – as implied by the authors’ reference to NICE’s cost-effectiveness threshold – then the included costs should only be those of the healthcare system. The cost of hospital admissions for patients in intensive care can easily reach thousands of pounds. Estimates have put the number of patients requiring any admission at 20%, and those requiring ICU admission at up to 5% of total cases. To take the UK example, the predicted deaths without flattening the curve number around 500,000. To break my own rule for a second, this could equate to a million ICU admissions, and 4 million hospital admissions. Notably these are not admissions for which the health system has current capacity, hence why new field hospitals in convention centres are being built, adding further costs to the healthcare budget. These costs are separate to those included in any stimulus package.

If we were to evaluate the cost-effectiveness of the stimulus package, we would need to consider its purpose (reducing unemployment and poverty) along with any resultant harms, including to health. The authors of the blog post mention harms from economic damage, and these are legitimate, but the counterfactual of flattening the curve is not the status quo. On the contrary, no action will result in millions of deaths and tens of millions of workers (and informal carers) taking short or long term sick leave. These effects are guaranteed to be catastrophic to the wider economy.

Applying a healthcare-based threshold, mixing health benefits and non-health costs, and not considering all costs of the counterfactual. Together these add up to an analysis that is at best meaningless, and at worst actively harmful.

On the other hand…

Where I agree with the authors is that these questions are worth asking. It is worth considering the many harms that will result from whichever course of action policy makers choose, and weighing them against each other. There are no good choices right now, and health economists have a unique opportunity to ensure the opportunity costs of each choice are considered, thereby maximising the chance that we end up with the best possible outcomes for society. There are a number of problems decision makers face in this crisis to which health economists could contribute. For example, what are the equity implications of pandemic spread (who gets to work from home and who loses their job, how does this affect their risk of infection?). Do societal preferences for health change in pandemics? What are the ethics of resource allocation (recently addressed in the NEJM)?

Cost-effectiveness analysis is a powerful tool, but it is limited. It is particularly limited when there are enormous uncertainties, and those uncertainties are correlated. There has been a lot of discussion of exponential growth, and while some epidemiologists are sceptical about such language, it does neatly illustrate what we’re up against. Each choice has the potential to have a dramatic impact, starting a chain reaction of consequences on a scale far beyond the norm.

I am not an infectious disease specialist, but I have done some work on antimicrobial resistance, and I think there is common ground. In AMR, the challenge is how to value potentially catastrophic future harms. Reducing antibiotic use will have real and meaningful costs now, in exchange for an increased chance that we benefit from effective antibiotics in the future. The changes necessary to increase that chance feel disproportionate. We must sacrifice real, present benefits for uncertain future ones. It is closer to the problem we face in an insurance market than that which we normally consider in cost-benefit trade-offs.

In a pandemic, the timelines are compressed but the challenge is similar. The costs right now feel disproportionate, and plugging them into a simple cost-effectiveness calculation is likely to result in significant uncertainty, or even indicate that our responses are not cost-effective. This is partly because what we’re paying for – with social distancing and enormous stimulus packages and arena-sized field hospitals – is not a guaranteed health benefit, but the chance to avert the worst possible predicted scenario.

This is not a decision problem that will fit on the back of an envelope.

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