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From ‘R rate’ to ‘nowcasts’

A farewell to R: study by University of Cambridge researchers suggests that “nowcasts” based on a new time series model are more effective in tracking later-stage pandemics than the traditional ‘R rate’ used during an outbreak.

Statistics of financial market data about a epidemic disease. Analysis graphs and reports numbers about a pandemic virus crisis.

When the COVID-19 pandemic emerged in 2020, the ‘R rate’ became well-known shorthand for the reproduction of the disease. Yet a new study by University of Cambridge researchers being published today (29 September) in the Journal of the Royal Society Interface suggests it is time for ‘A farewell to R’ in favour of a different approach based on the growth rate of infection rather than contagiousness.

The paper is based on time series models developed in Cambridge using classical statistical methods, which produce nowcasts and forecasts of the daily number of new cases and deaths that have already proved successful in predicting new coronavirus waves and spikes in Germany, Florida and many states in India.

The study’s title – “A farewell to R: time series models for tracking and forecasting epidemics” – is a play on the title of A Farewell to Arms, Ernest Hemingway’s famous novel set in Italy during World War I. The Journal of the Royal Society Interface is a journal published by the Royal Society in London that focuses on physical and life sciences cross-disciplinary research.

Paul Kattuman.
Paul Kattuman

The study is co-authored by Andrew Harvey, Emeritus Professor of Econometrics at the Faculty of Economics of the University of Cambridge, and by Dr Paul Kattuman, Reader in Economics at Cambridge Judge Business School, whose time series model reflecting epidemic trajectories, known as the Harvey-Kattuman model, was introduced last year in a was introduced last year in a paper published in Harvard Data Science Review.

“The basic R rate quickly wanes in usefulness as soon as a pandemic begins,” says co-author Dr Paul Kattuman of Cambridge Judge Business School. “The basic R rate looks at the number of infections expected to result from a single infectious person in a completely susceptible population, and this changes as immunity builds up and measures such as social distancing are imposed.

“In later stages of a pandemic, we conclude that use of the effective R rate that takes these factors into account is also not the best route: the focus should be not on contagiousness but rather on the growth rates of new cases and deaths, examined alongside their predicted time path so we can forecast a trajectory. These are the numbers that really help guide policymakers in making the crucial decisions that will hopefully save lives and prevent overcrowded hospitals as a pandemic plays out – which as we have seen with COVID-19 can occur over months and even years. The data generated through this time-series model has already proved accurate and effective in countries around the world.”

The new study examines “waves and spikes” in tracking an epidemic, noting that after an epidemic has peaked daily cases begin to fall as policymakers seek to prevent new spikes morphing into waves. “The monitoring of waves and spikes raises different issues, primarily because a wave applies to a whole nation or a relatively large geographical unit, whereas a spike is localised,” the paper says.

Thus, a localised outbreak in a country with low national infection numbers can result in a jump in the national R rate, as occurred in the Westphalia area of Germany in June 2020 after an outbreak at a meat processing factory, but this sort of jump “does not indicate that there has been a sudden change in the way the infection spreads and so has few implications for overall policy.”

The Harvey-Kattuman model has been adapted into two trackers. The two University of Cambridge academics worked with the National Institute of Economic and Social Research to produce a UK tracker which is published biweekly by the National Institute of Economic and Social Research. Alongside, they produce an India tracker which is published by the Center for Health Leadership and Excellence at Cambridge Judge Business School. District-level pandemic trajectory forecasts using the model are used by public health policymakers in three states in India – Punjab, Tamil Nadu and Kerala – to identify regions at high risk and to frame containment and relaxation policies.