Finding Leading Indicators for Disease Outbreaks: Filtering, Cross-correlation, and Caveats

Abstract

Bioterrorism and emerging infectious diseases such as influenza have spurred research into rapid outbreak detection. One primary thrust of this research has been to identify data sources that provide early indication of a disease outbreak by being leading indicators relative to other established data sources. Researchers tend to rely on the sample cross-correlation function (CCF) to quantify the association between two data sources. There has been, however, little consideration by medical informatics researchers of the influence of methodological choices on the ability of the CCF to identify a lead-lag relationship between time series. We draw on experience from the econometric and environmental health communities, and we use simulation to demonstrate that the sample CCF is highly prone to bias. Specifically, long-scale phenomena tend to overwhelm the CCF, obscuring phenomena at shorter wave lengths. Researchers seeking lead-lag relationships in surveillance data must therefore stipulate the scale length of the features of interest (e.g., short-scale spikes versus long-scale seasonal fluctuations) and then filter the data appropriately--to diminish the influence of other features, which may mask the features of interest. Otherwise, conclusions drawn from the sample CCF of bi-variate time-series data will inevitably be ambiguous and often altogether misleading.

Monitoring the Impact of Influenza by Age: Emergency Department Fever and Respiratory Complaint Surveillance in New York City

“…Aggregate interseasonal time series analysis can be valid for seasonal influenza mortality, where a single wave of mortality predominates each season. Assessment of aggregated seasonal time series of ILI, fever, or respiratory morbidity data, where multiple etiologically distinct within-season waves are common, however, must be done with caution and at the appropriate scale [43]. …”

Ten-year performance of Influenzanet: ILI time series, risks, vaccine effects, and care-seeking behaviour

“…Since both time series are autocorrelated and share a common seasonal trend, this direct crosscorrelation could give a misleading indication of their relationship (Bloom et al, 2007). Therefore, both time series are also prewhitened by fitting seasonal ARIMA models using the Box-Jenkins approach (Allard, 1998), where the model with the lowest Akaike information criterion is selected (Hyndman and Athanasopoulos, 2014).…”

Structural models used in real-time biosurveillance outbreak detection and outbreak curve isolation from noisy background morbidity levels

“…A detailed discussion of ARIMA models, EWMA models and their relationship to structural modeling can be found in Harvey. 5 For a discussion of problems of moving average filters applied to EED, see Bloom et al 6 Here we demonstrate a method for EED in biosurveillance data, which overcomes all of these limitations, while maintaining excellent early detection characteristics. This method is also easily modified to address the problem of formulating a NBM and separating background count data from the epidemic signal.…”

“…This requires determining the local slope at a point within the data, and projecting the structural model forward and including the slope (equation 6). An example of this procedure is shown in supplementary figure S1, available online only.…”