Simpson's Paradox in COVID-19 Case Fatality Rates: A Mediation Analysis of Age-Related Causal Effects
Julius von Kügelgen, Luigi Gresele, Bernhard Schölkopf
Abstract
We point out an instantiation of Simpson's paradox in COVID-19 case fatality rates ( <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">cfr</small> s): comparing a large-scale study from China (February 17) with early reports from Italy (March 9), we find that <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">cfr</small> s are lower in Italy for every age group, but higher overall. This phenomenon is explained by a stark difference in case demographic between the two countries. Using this as a motivating example, we introduce basic concepts from mediation analysis and show how these can be used to quantify different direct and indirect effects when assuming a coarse-grained causal graph involving country, age, and case fatality. We curate an age-stratified <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">cfr</small> dataset with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$>$</tex-math></inline-formula> 750 k cases and conduct a case study, investigating total, direct, and indirect (age-mediated) causal effects between different countries and at different points in time. This allows us to separate age-related effects from others unrelated to age and facilitates a more transparent comparison of <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">cfr</small> s across countries at different stages of the COVID-19 pandemic. Using longitudinal data from Italy, we discover a sign reversal of the direct causal effect in mid-March, which temporally aligns with the reported collapse of the healthcare system in parts of the country. Moreover, we find that direct and indirect effects across 132 pairs of countries are only weakly correlated, suggesting that a country's policy and case demographic may be largely unrelated. We point out limitations and extensions for future work, and finally, discuss the role of causal reasoning in the broader context of using AI to combat the COVID-19 pandemic. <p xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>Impact Statement</i>—During a global pandemic, understanding the causal effects of risk factors such as age on COVID-19 fatality is an important scientific question. Since randomised controlled trials are typically infeasible or unethical in this context, causal investigations based on observational data—such as the one carried out in this article—will, therefore, be crucial in guiding our understanding of the available data. Causal inference, in particular mediation analysis, can be used to resolve apparent statistical paradoxes; help educate the public and decision-makers alike; avoid unsound comparisons; and answer a range of causal questions pertaining to the pandemic, subject to transparently stated assumptions. Our exposition helps clarify how mediation analysis can be used to investigate direct and indirect effects along different causal paths and thus serves as a stepping stone for future studies of other important risk factors for COVID-19 besides age.