Simple statistical models can reliably infer the peak of infections and subsequent deaths from the virus, according to a Bristol statistician.
Professor Simon Wood used simple models with few assumptions, together with Imperial College’s estimate of the distribution of times from disease onset to death for fatal cases, to infer the time course of fatal infections from the subsequent death data.
Diagram shows the inferred time course of the number of fatal infections, where day 0 is March 23rd. The continuous curve is the median estimate. The dashed curves delimit 80% and 95% credible intervals. The vertical grey line shows day of lock down. The overlaid scaled bar chart summarizes the probability distribution for the day of the infection peak.
By simply separating out weekly reporting variability, the long-term death rate profile becomes clear, and its peak can be located with confidence. Using the distribution of times from disease onset to death, it is possible to extend the model to infer the time course of fatal infections required to produce the later deaths. Because of the wide variability in onset to death times, a quite sharply peaked infection curve produces a death curve that declines only slowly. The inferred infection curve peaks a few days before lockdown, with fatal infections now likely to be occurring at a much-reduced rate.
Professor Wood said: “Effective epidemic management requires sound statistical estimation of the epidemic’s course. This approach offers a substantial improvement on the running average smoothing often presented, without relying on complicated model assumptions. But statistically well-planned direct measurement would be even better.”
The paper is part of Professor Wood’s ongoing research program on smooth statistical regression models, covered in his book on the subject, and implemented in the mgcv package supplied with the R statistical software.
The Bayesian modelling used here also forms part of our third and fourth year undergraduate teaching, particularly in the module ‘Theory of Inference’.
Further information
Read the paper (not yet peer reviewed) at: https://arxiv.org/abs/2005.02090
You can see all the modules we teach at undergraduate level in our unit catalogue.
