Monitoring trends and differences in COVID-19 case fatality rates using decomposition methods: Contributions of age structure and age-specific fatality

Christian Dudel; Tim Riffe; Enrique Acosta; Alyson A. van Raalte; Mikko Myrskyla

The intuition behind the formulas is as follows. The first two terms in brackets in the equation for are − ∑ , or, replacing with its definition, ∑ − ∑ . The second sum in this expression captures how high the CFR would have been if group had the same age distribution of infections as group . The difference to the actual CFR (the whole expression) then captures to what extent the CFR is higher than this hypothetical CFR because of the actually observed age distribution of detected infections. The third and the fourth term in brackets in the equation for are following a similar logic, but using a different hypothetical comparison, asking how much the CFR of group would differ if the detected cases had the age distribution of group . The formula for again follows a similar logic, but now replacing the age-specific CFRs instead of the age distribution. In summary, to decompose the difference between two CFRs requires nothing more than the two CFRs themselves as well as a few additional hypothetical CFRs.