Finding leading indicators for disease outbreaks: filtering, cross-correlation, and caveats.
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.