For a full description of the methodology used to create covidestim, read our preprint. Since posting the preprint in July 2021, we have made additional updates to the model, described below.

August 26 Model Update

Uncertainty Bounds for all States

To generate state-level results, we have been using a Bayesian sampling method, which produces a large set of epidemic trajectories that are consistent with the available data. We use this set of trajectories to produce a best estimate (the median), and an uncertainty interval (the 2.5% and 97.5% percentiles) for each outcome on any given date. The time limit on our daily runs for state-level estimates is currently 10 hours. If a state is not finished sampling within that time, we produce estimates using an optimization algorithm (see the last bullet on the 2-10-2021 update), which produces a point estimate but no uncertainty intervals. In this update we have introduced a method for computing uncertainty intervals for states run using the optimization routine.

To create these new intervals, a spline regression is estimated using the upper and lower credible bounds for those states that did sample. This creates a prediction equation for the upper and lower intervals, based on thepoint estimate. This equation is used to compute intervals for the states run using the optimizer.

Above: Results for Alaska on August 26 with the two approaches for generating intervals. The results of the sampling approach are shown in blue, and the new prediction equation are shown in red. As this example illustrates, both approaches produce similar results.

August 16 Model Update

Vaccination Data

In this model revision, we have combined multiple data sources on vaccination coverage and include these in the model. Vaccination data at the county level are pulled daily from the CDC. These data include the number of fully vaccinated people in the 18+, 65+, and overall population. We redistribute these counts over more fine grained age groups (age 0-11, 12-15, 16-17, 18-25, 25-39, 40-49, 50-64, 65-74, 75+) using national level data and the county census data. The state vaccination coverage is computed as the sum of the number of vaccinated individualsof all counties within that state. As a result of these changes, estimates of infection rates after February 2021 may be revised higher, given that vaccination changes the ratio between infections and COVID-19 deaths.

Mortality Adjustment

Vaccination lowers the COVID-19 mortality rate. To accommodate this change in mortality, we compute the relative risk (RR) of dying in each age group for those vaccinated and for those unvaccinated for each day since vaccinations started. This is computed using the age stratified deaths data from December 12, 2020 (before vaccinations started) and the age-specific Covid-19 IFR. We assume that vaccination prevents 87.5% of infections amongst the vaccinated population, and that it prevents 96% of deaths amongst the vaccinated population (this is included in the model as a 68% reduction of deaths amongst those vaccinated and infected), relative to the baseline of no-vaccinations (more details available here).

IFR adjustment for vaccination coverage

Probability adjustment

We assume that the probabilities of becoming symptomatic if infected, severe if symptomatic and dying if severe are all reduced proportionally to achieve the 68% reduction in mortality among infected individuals, while allowing for uncertainty in these values.

Switch from Odds Ratio to Risk Ratio

In the previous version of the model, we adjusted the probability of dying if severe using an odds ratio (OR). The current version of the model adjusts these probabilities using a risk ratio (RR).

County level death data

Some counties have stopped reporting deaths data (since approximately June 2021). The corresponding data reports 0 counted deaths for those dates, which created unrealistic estimates. For counties that have discontinued reporting of COVID-19 deaths, we now exclude deaths data in the model after the last date of reporting.

Revised prior on probability of diagnosis if severe

The prior for the probability to die if infected has been altered from a Beta(5, 2) to a Beta(20, 5). This increases the mean probability from 0.71 to 0.80, and reduces the variance of the prior distribution.

Configuration changes

We made some small tweaks to our pipeline to improve the number of state models which successfully complete Hamiltonian Monte Carlo sampling in the 10 hours they are allotted.