Modeling Influenza-Like Illness Activity in the United States

Abstract

Influenza causes yearly costs for hospitalization and outpatient visits of more than $10 billion in the United States. The prediction of influenza epidemics is thus relevant for health insurance providers and public health facilities, among others. A useful piece of information is the probability distribution of influenza epidemics occurring within a given time horizon of one or two years. We present a model that delivers confidence intervals for future influenza activity in different regions in the United States. The model takes into account the specific statistical characteristics of influenza activity such as volatility clusters, seasonal effects, and dependencies between different regions. Confidence intervals for the regions are obtained using ARMA-GARCH models, and regional dependencies are captured by a pair-copula construction, describing jointly the residuals of the ARMA-GARCH models. Our model allows us to simulate influenza activity over a future time horizon.

Notes

1 World Health Organization: Influenza Fact Sheet, http://www.who.int/mediacentre/factsheets/2003/fs211/en/.

2 Centers for Disease Control and Prevention: Seasonal Flu Vaccine, http://www.cdc.gov/flu/pdf/business/toolkit_seasonal_flu_for_businesses_and_employers. pdf.

3 Centers for Disease Control and Prevention: National and Regional Level Outpatient Illness and Viral Surveillance, http://gis.cdc.gov/grasp/fluview/ fluportaldashboard.html.

4 Google Flu Trends, https://www.google.org/flutrends/about/.

5 For example, the Kaiser Foundation Group is the largest health insurer in California with a market share of over 34%, while being inactive in 41 of the 49 other states. See the National Association of Insurance Commissioners, 2014 Market Share Reports—For the Top 125 Accident and Health Insurance Groups and Companies by State and Countrywide, http://www.naic.org/documents/prod_serv_statistical_msr_hb.pdf.

6 Centers for Disease Control and Prevention, Overview of Influenza Surveillance in the United States, http://www.cdc.gov/flu/weekly/overview.htm#Outpatient.

7 Centers for Disease Control and Prevention, MMWR Weeks, https://wwwn.cdc.gov/nndss/document/MMWR_Week_overview.pdf.

8 That means for week 1 we calculate the standard deviation of (x_{N, 1}, x_{N, 53}, x_{N, 105}, …), for week 2 the standard deviation of (x_{N, 2}, x_{N, 54}, x_{N, 106}, …), and so on. During weeks 10 to 30 (April to July) the average standard deviation is 0.398% compared to 1.169% in weeks 40 to week 8 of the following year (October to February).

9 The F statistics and coefficients of the regression models are given in Table 1.

10 , and , i = 1, …, 10, are found Table 2.

11 For an overview of the p values of the different tests see Table 3.

12 The resulting models and BIC values for both approaches are displayed in Table 4.

13 The resulting p values for the KS test and the goodness-of-fit test with a varying number of bins can be found in Tables 5 and 6.

14 The resulting p values for the Ljung-Box test and the test for serial independence based on the empirical copula process can be found in Tables 7 and 8.

15 The ACF of the errors and the fit of the theoretical distribution in HHS region 1 are shown in Figure 13.

16 In Table 10 the empirical correlations of the errors z₁, …, z₁₀ are given.

17 See Table 11 for the frequency of outliers above 15%, 50%, and 100%.

18 To calculate the national ILI levels we have replaced outliers in the ILI levels in each region above 50% by 50%. The reason is that outliers in one region would greatly distort the predicted national ILI levels and are clearly unrealistic.