Statistical fallibility and the longevity of popes: William Farr meets Wilhelm Lexis

Abstract

We write to follow up on the editorial1 on the use of statistical aggregates. We focus on the reaction, in it, to the letter from two of us (MPC and DS) in the same issue suggesting that the ‘longer (average) life expectancy of popes relative to artists2 reflects the lives characterized by social instability, high-risk behaviours and geographical mobility (and thus infection risk) of the artists.’ The Editorial presented evidence that the ‘assumption of better behaviour by the popes is perhaps unjustified’. We have now looked behind the summary longevity statistics, and present individualized data showing that the initial, but tentative, conclusion about their longer life expectancy should be reversed. Even if the assumption of better behaviour ‘on average’ of popes is justified, these behaviours were not—even on average—accompanied by longer life expectancy. We now show the longevity data in Figure 1, using the Lexis diagram,3 a device sadly neglected by modern epidemiologists. It plots advancing age on the vertical, and calendar time on the horizontal, axis. The ‘pope-years’ (i.e. after they were elected) are shown in black and the artist-years (all of them) in grey. In the initial report, the statistics, aggregated over centuries, suggested that popes had a longevity advantage of several years. However, if we proceed papacy by papacy, the inter-ocular traumatic test4 (IOTT)—another under-used analytic device—applied to Figure 1 reveals that among those who were alive at the age at which each papacy commenced, the average remaining life of the popes was shorter than that of the corresponding peer artists—at least up until 1750 or so, after which the distributions became more similar.

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