Tracking and predicting U.S. influenza activity with a real-time surveillance network

Each year in the United States, influenza causes illness in 9.2 to 35.6 million individuals and is responsible for 12,000 to 56,000 deaths. The U.S. Centers for Disease Control and Prevention (CDC) tracks influenza activity through a national surveillance network. These data are only available after a delay of 1 to 2 weeks, and thus influenza epidemiologists and transmission modelers have explored the use of other data sources to produce more timely estimates and predictions of influenza activity. We evaluated whether data collected from a national commercial network of influenza diagnostic machines could produce valid estimates of the current burden and help to predict influenza trends in the United States. Quidel Corporation provided us with de-identified influenza test results transmitted in real-time from a national network of influenza test machines called the Influenza Test System (ITS). We used this ITS dataset to estimate and predict influenza-like illness (ILI) activity in the United States over the 2015-2016 and 2016-2017 influenza seasons. First, we developed linear logistic models on national and regional geographic scales that accurately estimated two CDC influenza metrics: the proportion of influenza test results that are positive and the proportion of physician visits that are ILI-related. We then used our estimated ILI-related proportion of physician visits in transmission models to produce improved predictions of influenza trends in the United States at both the regional and national scale. These findings suggest that ITS can be leveraged to improve “nowcasts” and short-term forecasts of U.S. influenza activity.


ANOVA
We developed a baseline model similar to a previous publication [3] which used historical CDC influenza data to estimate current CDC metrics. Following the gold standard procedure, we estimated the current CDC week's metric using only the previous week's CDC metric. As this baseline model was nested in the ITS model, we were able to compare the two using ANOVA in order to determine if including ITS data improved upon the baseline model. The ANOVA tests whether the addition of the ITS term leads to a significant improvement over the null model. The null hypothesis is that the null model estimates the current CDC week's metric as well as the ITS model. The alternative hypothesis is that the null model estimates the current CDC week's metric differently than the ITS model. A low P-value indicates that the ITS model estimates the current CDC week's metric better than the null model. We used an α of 0.05 as the threshold for statistical significance. For most of our models, the P-value for the ANOVA was less than 0.05 (Table A in S1 Text).
The baseline model for the proportion of diagnostic tests was the relationship between the historical proportion of diagnostic tests that are positive as recorded by CDC (ILI ppt (t (a−1) )) and the current proportion of tests that are positive as reported by the CDC at the present (ILI ppt (t a )) (Equation 3) logit(ILI ppt (t a )) = β 1 logit(ILI ppt (t (a−1) )) + ( 3) where β 1 is the coefficient; t is the time variable with the current epidemiological week as t a and the previous epidemiological week as t (a−1) ; and is the error term.
The baseline model for the weighted ILI-related proportion of physician visits was the relationship between the historical weighted proportion of all physician visits that are ILI-related as reported by the CDC (ILI prop (t (a−1) )) and the current weighted proportion of all physician visits that are ILI-related as reported by the CDC (ILI prop (t a )) (Equation 4) logit(ILI prop (t a )) = β 1 logit(ILI prop (t (a−1) )) + (4) where β 1 is the coefficient; t is the time variable with the current epidemiological week as t a and the previous epidemiological week as t (a−1) ; and is the error term.

Computational model
We used a humidity-based susceptible-infected-recovered-susceptible (SIRS) influenza model published by Shaman et al., 2013 [32]: with an average duration of immunity α, a mean infectious period γ and a transmission rate β(t). The transmission rate β(t) is defined as β(t) = R 0 (t)/γ with an R 0 (t) = exp(−180q(t)+log(R 0max −R 0min ))+R 0min where R 0max and R 0min describe the maximal and minimal daily reproductive number. The function q is used to describing the absolute humidity. In [17], we independently reconstructed the specific humidity dataset following the method detailed by the Text S1 of [15]. As in [16] the specific humidity dataset was compiled from the primary forcing dataset from Phase 2 of the North American Land Data Assimilation System (NLDAS-2) [33]. This data was obtained though the National Center for Environmental Prediction North American Regional Reanalysis. The hourly data is available on a 0.125°grid from 1979 to present. After extracting the specific humidity data for 121 cities, we then averaged the hourly data to obtain a daily climatology for each city from 1979 to 2016. We then averaged data for each year from 1979 until 2016 to develop an average year-long humidity profile for each city. To develop regional or national humidity profiles, we took the average of year-long humidity profiles of applicable cities.
For a proxy for the weekly number of incident infections, we used the CDC ILI data with a one-week lag or the real-time estimate of the CDC ILI data using ITS data, and it is linked to the number of people in the computational model that transition from susceptible to infectious in each time interval. Like previous analyses [5], we do not account for different influenza strains or non-influenza causes of ILI.

Calibration and Prediction
We summarized our existing knowledge in a prior distribution π 0 (θ) over the parameter θ. Whenever new observations y i at time points t i occurs, we iteratively updated our knowledge by multiplying the prior with the probability to observe y i : The previous posterior serves as the prior for the next observation. As there are no observations for the initial time t 0 , we set π 0 (θ|y 0 ) = π 0 (θ). We calculated the probability P in equation (8) by conditioning at the epidemic state ν i at time t − i and ν i−1 at time t i−1 : [Probability for current observation conditioned on history] = [Sum over all possible current states] [Sum over all possible previous states] [Probability for observation conditioned on specific current state] * [Transition probability to move from specific previous to specific current state] * [Belief state probability to be in specific previous state given history] Π(·|y 1 , y 2 , . . . , y i ) denotes the "belief state" which describes the probability distribution over the epidemic state ν i−1 . Ω i is the support of the belief state at time t i and p is the transition probability to move from state ν i−1 at time t i−1 to state ν i at time t i . The observation probability P maps the state ν i to the observation y i accounting for additional uncertainty in the data such as reporting errors.
We used a linear noise approximation (LNA) to approximate the transition probability p [17,18,34]. The LNA approximates the distribution of ν i |ν i−1 with a normal distribution of which the mean is the solution of the ordinary differential equation representation of the system on the interval [t i−1 , t i ] and the covariance is the solution of the LNA system (equation 5  Benchmark results taking into account exact time stamps of reporting CDC's ILI is reported with a one week delay and, then, is still corrected for several more weeks before it stabilizes to its final value. Therefore, we repeated the analysis carefully considering a) the time stamps of reporting of ILI for when calculating ITS nowcasts, and b) the exact time stamps of ITS data being delivered.
We used the time period from epiweek 40 in 2015 to epiweek 19 in 2016 for training the regression model. As this is a very short time, we note that training region-specific models is not feasible. Therefore, we trained one model averaging across all regions being aware that this will result in a loss in accuracy in general, but otherwise would not be possible due to the limited amount of data.
Most of the ITS data which was weekly was sent to us on Friday. We selected Monday as the due date of forecasts as the CDC's ILI forecasting challenge also uses this due date (except for the post-Christmas and post-New Year week, when the CDC delays this due date and we did, therefore, correspondingly). Whenever, ITS data was not available for the full corresponding epi week until the due date, we used the available days and up-weighted them (e.g. for 5 available days, multiplied by 7/5. Nonetheless, we see a valuable contribution of the ITS data source in Figure A  Fig A in S1 Text. Benchmark results considering exact time stamps of reporting: Each panel shows comparison between two data scenarios, columns are geographical regions, and rows are forecasting week targets. Red number is the fraction of first data scenario results better than the second in terms of log-score in the test time from epi week 46 in 2016 to epi week 19 in 2017. ITS improves clearly over lagged ILI. ILINearby is on average better than ITS but not in all cases. For some target-region combinations, ITS is better than more than half the forecasts, for others, it performs worse but rarely more than 10% worse. As ILINearby is an extremely challenging test case, this shows that ITS is a promising addition to the currently available data sources. . The proportion of influenza tests that are positive is along the left y-axis, and the real-time proportion of influenza tests that are positive as recorded by ITS (V ppt (t a )) is along the right y-axis. ITS Model 1 estimates the CDC proportion of influenza tests that are positive (ILI ppt (t a )) by using the proportion of influenza tests that are positive as recorded by ITS (V ppt (t a )), the CDC proportion of influenza tests that are positive with a 1-week lag (ILI ppt (t (a−1) )), and the absolute value of the difference between the proportion of tests that are positive as recorded by ITS with a 1-week lag and the proportion of influenza tests that are positive as reported by the CDC with a 1-week lag (|V ppt (t (a−1) ) − ILI ppt (t (a−1) )|). The CDC proportion of influenza tests that are positive are in black, the ITS model estimates are in red, the 95% prediction intervals are outlined by dark red dotted lines, and the real-time proportion of influenza tests that are positive as recorded by ITS (V ppt (t a )) are the blue stars. x-axis % ILI, y-axis posterior probability. Posterior distribution binned in steps of 0.1% ILI. The CDC's influenza forecasting challenge [20] uses a log-score that sums the probability of the bin containing the true value plus the five preceding and five following bins. The log-score is then calculated as the natural logarithm of this probability.