Those of you following the technical websites about the spread of the COVID-19 pandemic will have noticed the extraordinary international differences in infection and fatality rates. It appears that Italy has been the unluckiest of the European countries: fatalities are high relative to known infections and Italy’s experience has encouraged others to ramp up their efforts at what they hope is an earlier point in the pandemic. But available data is poor – the experts do not know how many are infected, not least because people do not know themselves.

The suspicion is that the apparent fatality rate in Italy is telling a different story – the true infection rate may be much higher, since so few have been tested, and the fatality rate, a percentage of the underestimated number infected, not such an outlier.

The experts do not know how many are infected, not least because people do not know themselves

In Germany, testing has been more extensive and the fatality rate appears to be very low. There is a further factor – the infected population in Germany may be atypical, younger and less susceptible people returning from skiing trips to Italy and Austria, for example. All this is speculative at this stage and the epidemiologists have been slow to draw conclusions.

When the pandemic has been controlled, there will be searching public inquiries in all countries, with lessons learned about missed opportunities to act and unfavourable comparisons with more decisive early interventions in China and elsewhere in Asia.

In Ireland, there was speculation that the true number infected could have reached 10,000 or even more at the beginning of the week

The World Health Organisation has been calling for more widespread testing and is conscious that the extent of infection is unknown – in Ireland, there was speculation that the true number infected could have reached 10,000 or even more at the beginning of the week, when the numbers tested positive were around a thousand.

Sampling strategy

There is a catch-22 about nailing down the numbers infected, and hence the true fatality rate, in the early stages of a pandemic. The proportion of the population infected is simply too low to permit a feasible sampling strategy based on standard procedures.

If some percentage of the population is likely to vote for the most popular party, let’s say 35%, then a sample of 1,000 chosen randomly should show around 350 voters who favour that party. There will be sampling error, but it will not be too large. This does not work if the party in question is tiny and just two people out of a thousand are felt to favour it. That was the position early this week – if 10,000 were positive then, one fifth of one per cent of the population, testing a random sample of 1,000, a big undertaking, would yield just a handful of positives, perhaps none or one rather than the true figure of two, perhaps three or four, and nothing much could be concluded from the sampling exercise.

The epidemiologists know that they are flying blind in the early stages and have been commendably cautious about claiming to know more than can be known

Technically (you may skip this paragraph if you hated maths in school) the sampling error of a proportion varies inversely with the size of the proportion, for a given sample size. The formula is non-linear and it means that if you want to nail down the likely size of a proportion known to be very small, you will have to take a huge sample. This is simply not worth it and the proportion will have changed anyway by the time you get the results – it’s an epidemic after all. The epidemiologists know that they are flying blind in the early stages and have been commendably cautious about claiming to know more than can be known.

Because different countries have chosen different strategies, there will be recriminations when all this is over, as it surely will be whenever a vaccine is found, perhaps a year from now.

The decision to let Cheltenham go ahead, attracting 60,000 fans on each of four days from all over Britain and Ireland, looked risky at the time and did the image of horseracing no favours

Governments will be faulted for not having acted earlier and at this stage it looks as if the recriminations will be biggest in Europe and in the US, where the handling of the outbreak will be a big issue in the presidential election. It is easy to be wise after the event but the decision to let Cheltenham go ahead, attracting 60,000 fans on each of four days from all over Britain and Ireland, looked risky at the time and did the image of horseracing no favours.

Several thousand Atletico Madrid fans journeyed to Anfield for the game against Liverpool on 11 March from a city which was a known infection centre in Spain at the time. The rugby game in Dublin against Italy scheduled for 7 March was cancelled but several thousand fans were permitted to travel anyway, again from an area known to have a high infection rate.

Detailed data on infected persons and their contacts is being collected diligently and will be available to researchers in the years ahead. There will be a mammoth stewards’ inquiry when the pandemic is over and plenty of blame to be distributed.