“Don’t trust any statistics you haven’t falsified yourself” – this saying is often used when confronted with results that contradict one’s own ideas. But in fact, real studies can also lead to results that are hard to believe: For example, Covid-19 proved to be more deadly in Italy than in China in relation to the total population, even though each individual Italian age group had a higher chance of survival.
In order to assess the risk of a disease, epidemiologists use, among other things, what is known as case mortality. This is the proportion of those infected who die from the disease. As early as February 17, 2020, China published statistics on the case mortality from Covid-19 in its own country, and about three weeks later Italy also provided data on this. Overall, China had a case fatality rate of 2.3 percent, while Italy had a case fatality rate of 4.3 percent – almost double that.
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On closer inspection, however, the data came as a surprise: if you break down case mortality by age, it was lower for each individual age group in Italy than in China. How can it be that Covid-19 is less deadly for people of all ages in Italy than in China – but more deadly for the Italian population as a whole?
This counter-intuitive statement is a consequence of the so-called Simpson’s paradox, a phenomenon that is now well known in statistics. It was first noticed by the mathematician Karl Pearson in 1899, who described it in a paper; four years later it was rediscovered by his colleague George Udny Yule. However, as is so often the case in science, the essays fell into oblivion – until Edward Simpson published a paper on the subject in 1951. Accordingly, assessments of different groups can be different, depending on whether they are divided into subgroups or not. In this case, the assessment corresponds to a higher or lower case mortality and the subgroups are determined by the age of the patients.