Phenomenological forecasting of disease incidence using heteroskedastic Gaussian processes: a dengue case study

In 2015 the US federal government sponsored a dengue forecasting competition using historical case data from Iquitos, Peru and San Juan, Puerto Rico. Competitors were evaluated on several aspects of out-of-sample forecasts including the targets of peak week, peak incidence during that week and total season incidence across each of several seasons. Our team was one of the top performers of that competition, outperforming all other teams in multiple targets/locals. In this paper we report on our methodology, a large component of which, surprisingly, ignores the known biology of epidemics at large---in particular relationships between dengue transmission and environmental factors---and instead relies on flexible nonparametric nonlinear Gaussian process (GP) regression fits that "memorize" the trajectories of past seasons, and then "match" the dynamics of the unfolding season to past ones in real-time. Our phenomenological approach has advantages in situations where disease dynamics are less well understood, e.g., at sites with shorter histories of disease (such as Iquitos), or where measurements and forecasts of ancillary covariates like precipitation are unavailable and/or where the strength of association with cases are as yet unknown. In particular, we show that the GP approach generally outperforms a more classical generalized linear (autoregressive) model (GLM) that we developed to utilize abundant covariate information. We illustrate variations of our method(s) on the two benchmark locales alongside a full summary of results submitted by other contest competitors.