Four different methods were used to design Texas ILINets that effectively predict state-wide influenza hospitalizations. Submodular optimization (Submodular) outperforms random selection proportional to population density (Random), greedy selection strictly in order of population density (Greedy), and geographic optimization to maximize the number of people that live within 20 miles of a provider [17] (Geographic). The theoretical upper bound for performance (Upper Bound) gives the maximum possible for a network designed by an exhaustive evaluation of all possible networks of a given size. For each network of each size, the following procedure was repeated times: randomly sample a set of reporting profiles, one for each provider in the network; simulate an ILI time series for each provider in the network; perform an ordinary least squares multilinear regression from the simulated provider reports to the actual statewide influenza hospitalization data. The lines indicate the mean of the resulting values, and the error bands indicate the middle 90% of resulting values, reflecting variation stemming from inconsistent provider reporting and informational noise.

(a) Shading indicates zip code level population sizes, as reported in the 2000 census. (b) Major populations centers exhibit covariation in influenza activity. We performed a principal component analysis (PCA) on the centered hospitalization time series of all zip codes and calculated the time series of the first principal component. Zip codes are shaded according to the obtained from a regression of the first principal component time series to the influenza hospitalization time series for the zip code. Dark shading indicates high synchrony between influenza activity in the zip code and the first principal component. The correspondence between darkly shaded zip codes in (a) and (b) results from the high degree of synchrony in influenza activity between highly populated zip codes in Texas.

This compares theoretical upper bounds (dashed lines) to the performance of a submodular optimized ILINet built by first subsampling the zip codes of providers actually enrolled in Texas' 2008 ILINet (green) and then adding additional providers from elsewhere in the state (gray). The error bands indicate the middle 90% of resulting values, and reflect variation stemming from inconsistent provider reporting rates and informational noise.

Data from the 2001–2007 period were used to design ILINets and estimate multilinear regression prediction models. The predictive performance of the ILINets (y-axis) is based on a comparison between the models' predictions for 2008 hospitalizations (from mock provider reports) and actual 2008 hospitalization data. For almost all network sizes, Submodular optimization (Submodular) outperforms random selection proportional to population density (Random), greedy selection strictly in order of population density (Greedy), and geographic optimization to maximize the number of people that live within 20 miles of a provider [17] (Geographic). The leveling-off of performance around 100 providers is likely a result of over-fitting, given that there were only 222 historical time-points used to estimate the original model.

Statewide hospitalizations are estimated using data from three ILINets: the 2008 Texas ILINet (ILINet 2008), which consisted of providers, and ILINets of the same size that were designed using submodular optimization (Submodular) and maximum coverage optimization with a 20 mile coverage distance (Geographic). (a) The estimates from each network are compared to actual Texas state-wide influenza hospital discharges from 2001–2008 (Observed). (b) The submodular ILINet yields estimates that are consistently closer to observed values than the other two ILINets. For each of the three networks, the following procedure was repeated times: randomly sample a set of reporting profiles, one for each provider in the network; simulate an ILI time series for each provider in the network; perform an ordinary least squares multilinear regression from the simulated provider reports to the actual Texas influenza hospitalization data; and apply resulting regression model to the simulated provider time series data to produce estimates of statewide hospitalizations. The figures are based on averages across the estimated hospitalization time series for each ILINet.

(a) Shading indicates zip code level population sizes, as reported in the 2000 census. Circles indicate the location (zip code) of the first ten providers selected when Google Flu Trends is included as a provider (green) and when it is not (pink). Numbers indicate selection order, with zero being the first provider selected and nine the tenth provider selected. (b) The cumulative population densities covered increase as each ILINet grows. Cumulative density is estimated by dividing total population of all provider zip codes by total area of all provider zip codes. While ILINets designed using the geographic (orange) and random (green) methods primarily target zip codes with high population densities, submodular optimization (purple) targets zip codes that provide maximal information, regardless of population density. All three networks cover approximately the same total number of people.

When state-level Google Flu Trends is treated as a possible provider, submodular optimization choses it as the first (most informative) provider for the Texas ILINet, and results in a high performing network (pink line). Alone (black line), the Google Flu Trends provider performs as well as a traditional submodular optimized network (blue line) containing providers (intersection of black and purple lines) and outperforms the actual 2008 Texas ILINet (green dot).