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.

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We present a statistical method, predicated on the use of surrogate models, for the "real-time" characterization of partially observed epidemics. Observations consist of counts of symptomatic patients, diagnosed with the disease, that may be available in the early epoch of an ongoing outbreak. Characterization, in this context, refers to estimation of epidemiological parameters that can be used to provide short-term forecasts of the ongoing epidemic, as well as to provide gross information on the dynamics of the etiologic agent in the affected population e.g., the time-dependent infection rate. The characterization problem is formulated as a Bayesian inverse problem, and epidemiological parameters are estimated as distributions using a Markov chain Monte Carlo (MCMC) method, thus quantifying the uncertainty in the estimates. In some cases, the inverse problem can be computationally expensive, primarily due to the epidemic simulator used inside the inversion algorithm. We present a method, based on replacing the epidemiological model with computationally inexpensive surrogates, that can reduce the computational time to minutes, without a significant loss of accuracy. The surrogates are created by projecting the output of an epidemiological model on a set of polynomial chaos bases; thereafter, computations involving the surrogate model reduce to evaluations of a polynomial. We find that the epidemic characterizations obtained with the surrogate models is very close to that obtained with the original model. We also 3 find that the number of projections required to construct a surrogate model is O(10) − O(10 2 ) less than the number of samples required by the MCMC to construct a stationary posterior distribution; thus, depending upon the epidemiological models in question, it may be possible to omit the offline creation and caching of surrogate models, prior to their use in an inverse problem. The technique is demonstrated on synthetic data as well as observations from the 1918 influenza pandemic collected at Camp Custer, Michigan.