Estimates of the severity of COVID-19 disease

Robert Verity; Lucy C Okell; Ilaria Dorigatti; Peter Winskill; Charles Whittaker; Natsuko Imai; Gina Cuomo-Dannenburg; Hayley Thompson; Patrick Walker; Han Fu; Amy Dighe; Jamie Griffin; Anne Cori; Marc Baguelin; Sangeeta Bhatia; Adhiratha Boonyasiri; Zulma M Cucunuba; Rich Fitzjohn; Katy A M Gaythorpe; Will Green; Arran Hamlet; Wes Hinsley; Daniel Laydon; Gemma Nedjati-Gilani; Steven Riley; Sabine van-Elsand; Erik Volz; Haowei Wang; Yuanrong Wang; Xiayoue Xi; Christl Donnelly; Azra Ghani; Neil Ferguson

An added complication to this analysis was that many samples had missing onset dates. For samples with missing onset dates we assumed that symptom onset occurred prior to report date, i.e. = − , where was the date of report (present in all cases) and was a free parameter. This resulted in an additional set of parameters 1 , … , , where is the number of cases with missing onset data. Note that when onset data are present, = − represents observed data, but when onset data are not present this reduces to = . Assuming a gamma distribution for the onset-to-report distribution ( • | , ) we obtain We assumed Uniform(10,100) priors on and , and Uniform(0.2,0.8) priors on and . We also assumed Uniform(0,50) priors on all parameters, which were treated as nuisance parameters when summarising other parameters. Due to the high dimensionality of this problem, parameters were estimated via MCMC in the R package drjacoby v1.0 1 .