Critique of “Projecting the transmission dynamics of SARS-CoV-2 through the postpandemic period” — Part 2: Proxies for incidence of coronaviruses

This is the second in a series of posts (previous post: Part 1, next post: Part 3) in which I look at the following paper:

Kissler, Tedijanto, Goldstein, Grad, and Lipsitch, Projecting the transmission dynamics of SARS-CoV-2 through the postpandemic period, Science, vol. 368, pp. 860-868, 22 May 2020 (released online 14 April 2020).  The paper is also available here, with supplemental materials here.

In this post, I’ll start to examine in detail the first part of the paper, where the authors look at past incidence of “common cold” coronaviruses, estimate the viruses’ reproduction numbers (R) over time, and use those estimates to model immunity and cross-immunity for these viruses, and seasonal effects on their transmission. The results of this part inform the later parts of the paper, in which they model the two common cold betacoronaviruses together with SARS-CoV-2 (the virus for COVID-19), and look at various scenarios for the future, varying the duration of immunity for SARS-CoV-2, the degree of cross-immunity of SARS-CoV-2 and common cold betacoronaviruses, and the effect of season on SARS-CoV-2 transmission.

In my previous post, I used the partial code released by the authors to try to reproduce the results in the first part of the paper. I was eventually able to do this. For this and future posts, however, I will use my own code, with which I can also replicate the paper’s results. This code allows me to more easily produce plots to help understand issues with the methods, and to try out alternative methods. The code (written in R) is available here, with GPLv2 licence. The data used is also included in this repository.

In this second post of the series, I examine how Kissler et al. produce proxies for the incidence of infection in the United States by the four common cold coronaviruses. I’ll look at some problems with their method, and propose small changes to try to fix them. I’ll also try out some more elaborate alternatives that may work better.

The coronavirus proxies are the empirical basis for the remainder of paper.