Shape-based Evaluation of Epidemic Forecasts

Infectious disease forecasting for ongoing epidemics has been traditionally performed, communicated, and evaluated as numerical targets - 1, 2, 3, and 4 week ahead cases, deaths, and hospitalizations. While there is great value in predicting these numerical targets to assess the burden of the disease, we argue that there is also value in communicating the future trend (description of the shape) of the epidemic -- for instance, if the cases will remain flat or a surge is expected. To ensure what is being communicated is useful we need to be able to evaluate how well the predicted shape matches with the ground truth shape. Instead of treating this as a classification problem (one out of $n$ shapes), we define a transformation of the numerical forecasts into a ``shapelet''-space representation. In this representation, each dimension corresponds to the similarity of the shape with one of the shapes of interest (a shapelet). We prove that this representation satisfies the property that two shapes that one would consider similar are mapped close to each other, and vice versa. We demonstrate that our representation is able to reasonably capture the trends in COVID-19 cases and deaths time-series. With this representation, we define an evaluation measure and a measure of agreement among multiple models. We also define the shapelet-space ensemble of multiple models as the mean of their shapelet-space representations. We show that this ensemble is able to accurately predict the shape of the future trend for COVID-19 cases and trends. We also show that the agreement between models can provide a good indicator of the reliability of the forecast.