The Covid-19 pandemic has brought a very thorny issue to the forefront. How much money can we, as a society, spend on keeping people healthy or alive? No one has ever fully got to grips with this question, but it has never been more important than now.

America has set aside $2 trillion to deal with the crisis, and Britain £350 billion – which is almost three times the current yearly budget for the entire NHS. Is this a price worth paying?

Many people will instantly dismiss such a question as being coldhearted or stupid: "You cannot put a value on a human life" is an argument I have heard many times, whenever health economics is discussed.

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The counter-argument is that, if funds are not limitless (which they aren’t and can’t be), then we must focus on funding things that do the greatest good. This is why the National Institute for Health and Care Excellence (NICE) was established.

NICE reviews interventions and decides if they provide value for money. The economic term for this is cost-effectiveness. It is complex and often relies on assumptions that can be difficult to verify.

However, to keep things (relatively) simple, NICE attempts to compare healthcare interventions against each other by using a form of “currency” called the cost per QALY. A QALY is a Quality Adjusted Life Year. One added year of completely healthy life is one QALY.

People with conditions such as cancer, or severe heart disease, or who are suffering from chronic pain, can be considered to have a quality of life less than one. We can say that their quality of life is, say, 50 percent. Thus, one year of additional life gained for them has a value of 0.5 of a QALY.

Not everything that is measured using a QALY relates to saving, or extending, lifespan. For example, someone could have chronic hip pain, and a quality of life of 0.5. A hip replacement may remove the pain, and their quality of life will improve from 0.5 to 1. If they live another 20 years, they will have gained 20 x 0.5 QALYs = 10 QALYs.

Whichever way you look at QALYs, the fundamental question always comes down to 'How much can we afford to pay for one QALY?' In the UK, the current answer is that NICE recommends interventions which cost less than £30,000 ($36,933) per QALY.

This figure can vary. Interventions for young children tend to receive more per QALY, and powerful lobbying groups can bring pressure to bear on that figure. However, £30,000 is generally accepted – if not widely publicized.

Therefore, if we are willing to spend £350 billion ($430 billion) on managing coronavirus, how many QALYs do we hope to get back? The simple answer is to divide £350 billion by 30,000 = 11,666,666 QALYs.

(For those who think this an impossible or inhuman calculation, you need to consider how many other lives could be saved, how much other suffering or death could be prevented, by spending £350 billion in other ways.)

Are we likely to achieve this level of benefit? Of course, any attempt to model this requires several assumptions to be made. However, the model here only has four variables, two of which are (pretty much) known. They are:

• How many people will die?
• What is the average age of death?
• What is the average reduction in life expectancy in those who die?
• What is the average quality of life of those who die?

So, for example:

• 500,000 die (based on the upper level of the Imperial College study)
• Average age at death 78.5 (based on figures taken from Covid deaths in Italy)
• Average reduction in life expectancy three years (based on modeling of life expectancy) 
• Average quality of life of those who die 0.7 (based on studies done to work out the “reported” quality of life in those with multi-morbidity)

We get 500,000 x 3 x 0.7 = 1,050,000 QALYs lost.

Using these figures, spending £350 billion to reduce the “QALYs lost” figure to zero means that each QALY will have cost £333,000 ($410,000), more than 10 times the NICE level. And, if the death toll does not reach the 500,000 upper estimate, then the cost per QALY will be even higher.

People will immediately object to this calculation. How do we know how many will die? How can we be certain about the average quality of life of those who die or the average reduction in life expectancy?

All I can say is that these calculations, while complex, are based on robust statistical data. However, it is usually best to input different figures to outline best and worst cases, to look at more than one scenario. So, were we to stick using the upper limit of 500,000, but adjust the average life expectancy gained to 4.5 years and the average quality of life to 0.8, you get: 500,000 x 4.5 x 0.8 = 1,800.000 QALYS. The cost per QALY then becomes: £194,444 ($239,397) [£350 billion ÷ 1.8 million]