A very interesting article by Rick Wicklin, PhD ( a distinguished researcher in computational statistics at SAS) appeared recently on SAS blog. The article describes a method to predict the total number of COVID-19 cases by estimating the „doubling time“ from the most recent case data. The doubling time is the length of time required to double the number of total confirmed cases, assuming nothing changes.

Even though predictions have to be treated with caution, as they depend on a various number of known and unknown factors, it is interesting to compare these predictions among different countries.

As the SAS code is free to download, it was adjusted to show also the uncertainty interval (95% confidence interval for the mean) and to include data for any number of countries.

The analysis was performed for selected European countries, including Croatia, neighboring Slovenia and Serbia (Graph 1. and Table 1.)


Graph 1. and Table 1. Estimates of doubling time as of April 8th


Due to strict measures, Croatia has been keeping the numbers of confirmed cases low, to this point, showing linear, rather than exponential growth. Based on data for the most recent five days, the graph shows the tendency of how quickly the total number of confirmed cases for selected countries are predicted to double. That is, the tip of each arrow indicates the time at which the number of cases are predicted to double.  

This model provides early warning signals of the pandemic taking a dangerous turn at a certain point in time.

Hence, it may help governments to make decisions regarding when and what additional measures to introduce.

Doubling time predictions should be made frequently so as to early identify possible effects (of the additional measures) in terms of flattening the curve, i.e. extending the doubling time. In other words, this is a dynamic process, not a static one.

Furthermore, for better understanding of the results, it is important to have available not just the estimates, but also the uncertainty range for these estimates.

Therefore we provided the uncertainty range (i.e., 95% confidence intervals) for both the doubling time and predicted total number of cases.

Details of the prediction model as of the 8th of April (with data from the 2nd to 7th of April used to predict the total number of cases for the 8th of April on) are posted below.

For demonstration purposes, the results of the prediction model (for the selected European countries) updated on the 9th and 11th of April are also provided (“If you have to forecast, forecast often”.)


We strongly believe that forecasts and predictions should not be used for rating or criticizing any country, but only as a tool for better understanding and possibly containing the virus.


The original programs and interpretation may be found at https://blogs.sas.com/content/iml/2020/04/01/estimate-doubling-time-exponential-growth.html
data source:   https://www.ecdc.europa.eu/en/publications-data/download-todays-data-geographic-distribution-covid-19-cases-worldwide