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One major bottleneck in the ongoing COVID-19 pandemic is the limited number of critical care beds. Due to the dynamic development of infections and the time lag between when patients are infected and when a proportion of them enters an intensive care unit (ICU), the need for future intensive care can easily be underestimated. To infer future ICU load from reported infections, we suggest a simple statistical model that (1) accounts for time lags and (2) allows for making predictions depending on different future growth of infections. We have evaluated our model for three regions, namely Berlin (Germany), Lombardy (Italy), and Madrid (Spain). Before extensive containment measures made an impact, we first estimate the region-specific model parameters. Whereas for Berlin, an ICU rate of 6%, a time lag of 6 days, and an average stay of 12 days in ICU provide the best fit of the data, for Lombardy and Madrid the ICU rate was higher (18% and 15%) and the time lag (0 and 3 days) and the average stay (4 and 8 days) in ICU shorter. The region-specific models are then used to predict future ICU load assuming either a continued exponential phase with varying growth rates (0-15%) or linear growth. Thus, the model can help to predict a potential exceedance of ICU capacity. Although our predictions are based on small data sets and disregard non-stationary dynamics, our model is simple, robust, and can be used in early phases of the disease when data are scarce.