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Towards global healthcare equity: Covid-19 testing

Towards global healthcare equity: Covid-19 testing

Now let’s see what the implications of probability are in terms of our two types of test; expensive and accurate versus cheap and less accurate.

Even when bought by an institution or a big organisation, an expensive test is around £100 in the UK and $100 in the US. The cheap tests cost one-tenth of that or less, and in reality the probability of a cheap test giving an accurate result is better than a coin toss (let’s assume a particular cheap test is 60% accurate). So, if you have Covid, the probability of the test correctly recording a positive (+) outcome is 60%. If you only do one test, you get two possible outcomes: a plus or a minus. But if you do two tests, there are four possible outcomes (+ +; + –; – –; – +.) Now you have to decide whether to call a plus-plus outcome a definitive positive result, and what to do if you get a plus-minus. That means you have to decide which costs are greater when it comes to false negatives.

Consider a doctor attempting to diagnose whether an elderly patient has asthma or another potentially serious condition. Here the cost of a false negative is great – the patient is likely to end up on a ventilator in intensive care, which could be a life-or-death situation (and expensive to treat).  

 

Classification rules

 

Combining cheap and inaccurate tests requires classification rules to inform your decisions. We have developed a data-driven methodology that generates optimal classification rules to inform decision-making. Where false negatives are costly, you believe any positive test result (the ‘any’ rule), because the probability of both the first and the second test giving a false negative is very low. If false positives are costly, you believe only a double positive. (Consider, for example, a scenario where a young worker who is not living near any elderly people and is sending money home – you would only call a plus-plus outcome a positive.) This is the ‘and’ rule. It gives you very few false positives on the one hand; the problem is that it gives many more false negatives on the other. You get a similar outcome with the ‘any’ rule – less false negatives but many more false positives. That means, in terms of decision-making, you have to make a trade-off between outcomes, weighing the likely costs of false negatives against those of false positives. Now add a third cheap test and we see that combining three such tests breaks the trade-off.

Say it costs £100 for one rRT-PCR test and £10 for a cheap test. You can tailor the cheap testing to very different types of patient population. For patient populations where there is a high cost of false negatives, you choose one classification rule. Where there is a medium cost of false negatives, you use a different rule. You use another one again where there is a high cost of false positives, and so on. The cost for the three cheap test is £30 – a 70% cost-saving over the price of one expensive test. The cheap tests are also much faster and easier to do, even in developing countries, because they don’t need to be carried out in a laboratory setting.

In March last year Director-General of the World Health Organization Tedros Ghebreyesus said: “Testing should be strategic, make the best use of available resources and link to clear public health goals.” Using a data-driven methodology for cheap Covid tests is a simple way to allocate resources efficiently in order to increase health equity globally.

 

This article is based on an LBS seminar. View the full seminar discussion here: www.dropbox.com/s/pwnrq75n6am6tn4/GMT20210303-165924_Health-Equ_2560x1440.mp4?dl=0

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