How Covid-19 Death-Rate Predictions Have Changed Since March

In March, estimates of how many Americans would die from Covid-19 in the coming months ranged from 81,000 to 2.2 million.

That disparity—which arguably produced as much confusion as insight—prompted one independent data scientist to build his own model in hopes of arriving at a better forecast. (He did.)

Now, as many as 50 different research groups make predictions, but one of the most accurate assembles all of the individual models, calculates the median value and looks no more than four weeks into the future.

The ensemble forecast was founded by the Reich Lab at the University of Massachusetts, Amherst, in collaboration with the Centers for Disease Control and Prevention and is based in part on models previously developed to forecast influenza and other infectious diseases.

In the next four weeks, it predicts the total number of deaths attributed to the new coronavirus will surpass 240,000—adding roughly 17,000 deaths to the current tally.

Such projections help policy makers and health-care officials decide how to manage resources and implement or relax interventions intended to curb the spread of the disease.

“It gives you guideposts,” said Jeffrey Shaman, an infectious-disease modeler at the Mailman School of Public Health at Columbia University. “Are you going in a bad or good direction? Is it under control?”

But even now, the projections of individual models sometimes differ substantially, according to Michael Johansson, co-leader of the CDC’s Covid-19 modeling team. In June, one model predicted that by July, the death toll would top 263,000. Another anticipated that it would be less than 120,000.

By focusing on the median, the ensemble forecast has consistently provided reliable four-week projections. In this case, its projection was 130,558, and the actual figure was 130,089.

“That’s been one of the big advantages,” Dr. Johansson said. “By leveraging all the information from all the model approaches, we get forecasts that are demonstrably robust.”

The Covid-19 Forecast Hub is the central repository for individual forecasts. Those included in the ensemble—currently more than 40—are probabilistic forecasts that look four weeks into the future; provide a point estimate of the expected number of deaths in the period; and include the range within which the actual number will likely fall with prediction intervals of 95% and 50%.

The ranges for each forecast are divided into 23 quantiles. The Hub calculates the median for each quantile, and the ensemble forecast is the median of those values.

“Because of previous work, we know you don’t want to exclude models unless there is a clear reason to do so,” Dr. Johansson said. “They capture different things.”

By confining the forecasts to the short term, changes in policy or public behavior are also less likely to upset the projections.

In contrast, the earlier models tried to predict the number of deaths that would occur months later.

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“Forecasts beyond a relatively short prediction window are not going to be very robust,” Dr. Johansson said. “You

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