The ostensible purpose of the paper is to estimate the percentage of the UK population that already has been exposed to SARS-CoV-2 and that therefore reasonably might be expected to have developed some degree of immunity to the virus. If this proportion is sufficiently large, it may imply that the UK population already has developed a degree of herd immunity, in which case public policy measures designed to slow the spread of the virus -- including those that are hobbling the economy -- may be relaxed.
The authors use the same sort of SIR model that I've discussed in previous posts. More specifically, they assume a range of plausible values for most of the parameters appearing in this model, and then they calibrate the model -- in particular, the day on which the virus first appeared in the population -- to a small subset of initial data. In particular, they use reported deaths for the first fifteen days after the first reported death in the population. They perform separate analyses for the UK and for Italy.
With this approach, the authors suggest that the virus was introduced into each population roughly one month before the first reported death in each population. In that case, the implication is that the virus would have spread widely among individuals in both populations by now. For the UK, they suggest that between 36% and 68% of the population would have been exposed to the virus by now. For Italy, the figure is estimated to be between 60% and 80%.
If true, this would mean that the policy of isolation is not necessary and that policy measures that have been crippling the UK and Italian economies can be relaxed. But does their analysis really support their conclusions?
One insurmountable problem with this analysis is the size of the data set: 15 days in each country. The authors choose this small subset in order to avoid using data from periods during which public policy interventions may have changed the course of the epidemic in each population.
Fifteen data points is far too small to reasonably calibrate the various parameters of their model, so the authors assume values that they believe are reasonable for many of these parameters, including
- the basic reproduction number, R0
- the duration of an infection
- the time between infection and death
- the probability of dying with severe disease
- the proportion of the population at risk of developing a severe infection.
But even if the authors had only one parameter to estimate -- the time of introduction of the virus into each population -- fifteen data points is almost surely far too few to estimate this time with any reasonable level of confidence. In fact, the authors don't report standard errors or confidence intervals for these estimates. Even with their many assumptions, I suspect these confidence intervals would be quite large. And if they were required to estimate all the parameters of their model using their fifteen data points, the results almost surely would be nonsensical, as there are simply too few data points per parameter.
A reasoned critique of the Oxford paper appeared today in a BMJ article titled, Covid-19: experts question analysis suggesting half UK population has been infected. It's useful to quote an excerpt from the BMJ critique. [Emphasis added.]
Neil Ferguson, director of the MRC Centre for Global Infectious Disease Analysis at Imperial College London, was asked about the study when he appeared before a parliamentary select committee hearing on 25 March. It was his analysis that showed that without physical distancing there would be 260 000 deaths in the UK from covid-19 and that led to change in government policy.
Ferguson said, “We’ve been analysing data from a number of Italian villages at the epicentre for the last few weeks where they did a viral swab on absolutely everybody in the village at different stages of the outbreak. And we can compare that with official case numbers, and those data all point to the fact that we are nowhere near the Gupta [the Oxford analysis] scenario in terms of the extent of the infection.”
Paul Hunter, professor in medicine at the University of East Anglia, said that the simple model “assumes complete mixing of the population,” which is “almost always wrong” at a country level. “We do not all have an equal random chance of meeting every other person in the UK.” He said that reproduction number was a “very clumsy” measure of how disease spreads, which is likely to change over time. He also criticised the researchers’ assumption that only a very small proportion of the population was at risk of being admitted to hospital because of the disease. “This is a big assumption and it is far too early in the epidemic to know what this value is,” he said.
Market Implications
If the Oxford results were true, we might reasonably expect significantly less economic disruption than many in the market have been expecting, in the UK, in Italy, and quite possibly across Europe and in the US as well. Given the historic reduction in economic activity that appears to be occurring, such a result would have significant implications for equity prices, bond yields, credit spreads, commodity prices, etc.
To be clear, I do believe the number of infections in the UK, the rest of Europe, and the US are very likely to be significantly higher than reported, particularly since there has been relatively little testing in these regions.
But the results of the comprehensive tests in Italian villages, mentioned by Dr Ferguson, suggest that the infection rates are likely significantly lower than suggested in the Oxford paper.
As I result, I continue to expect that the peak infection rates in the US and the UK are still weeks if not months ahead, with much higher infection rates becoming clear in coming weeks. As a consequence, I expect public policy measures will become more disruptive for the economy rather than less disruptive. And in that scenario, it seems quite unlikely that we've already seen the lows in the S&P 500 and in Treasury yields.
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