Recursive least squares background prediction of univariate syndromic surveillance data

<p>Abstract</p> <p>Background</p> <p>Surveillance of univariate syndromic data as a means of potential indicator of developing public health conditions has been used extensively. This paper aims to improve the performance of detecting outbreaks by using a background forecasting algorithm based on the adaptive recursive least squares method combined with a novel treatment of the Day of the Week effect.</p> <p>Methods</p> <p>Previous work by the first author has suggested that univariate recursive least squares analysis of syndromic data can be used to characterize the background upon which a prediction and detection component of a biosurvellance system may be built. An adaptive implementation is used to deal with data non-stationarity. In this paper we develop and implement the RLS method for background estimation of univariate data. The distinctly dissimilar distribution of data for different days of the week, however, can affect filter implementations adversely, and so a novel procedure based on linear transformations of the sorted values of the daily counts is introduced. Seven-days ahead daily predicted counts are used as background estimates. A signal injection procedure is used to examine the integrated algorithm's ability to detect synthetic anomalies in real syndromic time series. We compare the method to a baseline CDC forecasting algorithm known as the W2 method.</p> <p>Results</p> <p>We present detection results in the form of Receiver Operating Characteristic curve values for four different injected signal to noise ratios using 16 sets of syndromic data. We find improvements in the false alarm probabilities when compared to the baseline W2 background forecasts.</p> <p>Conclusion</p> <p>The current paper introduces a prediction approach for city-level biosurveillance data streams such as time series of outpatient clinic visits and sales of over-the-counter remedies. This approach uses RLS filters modified by a correction for the weekly patterns often seen in these data series, and a threshold detection algorithm from the residuals of the RLS forecasts. We compare the detection performance of this algorithm to the W2 method recently implemented at CDC. The modified RLS method gives consistently better sensitivity at multiple background alert rates, and we recommend that it should be considered for routine application in bio-surveillance systems.</p

An adaptive prediction and detection algorithm for multistream syndromic surveillance

<p>Abstract</p> <p>Background</p> <p>Surveillance of Over-the-Counter pharmaceutical (OTC) sales as a potential early indicator of developing public health conditions, in particular in cases of interest to biosurvellance, has been suggested in the literature. This paper is a continuation of a previous study in which we formulated the problem of estimating clinical data from OTC sales in terms of optimal LMS linear and Finite Impulse Response (FIR) filters. In this paper we extend our results to predict clinical data multiple steps ahead using OTC sales as well as the clinical data itself.</p> <p>Methods</p> <p>The OTC data are grouped into a few categories and we predict the clinical data using a multichannel filter that encompasses all the past OTC categories as well as the past clinical data itself. The prediction is performed using FIR (Finite Impulse Response) filters and the recursive least squares method in order to adapt rapidly to nonstationary behaviour. In addition, we inject simulated events in both clinical and OTC data streams to evaluate the predictions by computing the Receiver Operating Characteristic curves of a threshold detector based on predicted outputs.</p> <p>Results</p> <p>We present all prediction results showing the effectiveness of the combined filtering operation. In addition, we compute and present the performance of a detector using the prediction output.</p> <p>Conclusion</p> <p>Multichannel adaptive FIR least squares filtering provides a viable method of predicting public health conditions, as represented by clinical data, from OTC sales, and/or the clinical data. The potential value to a biosurveillance system cannot, however, be determined without studying this approach in the presence of transient events (nonstationary events of relatively short duration and fast rise times). Our simulated events superimposed on actual OTC and clinical data allow us to provide an upper bound on that potential value under some restricted conditions. Based on our ROC curves we argue that a biosurveillance system can provide early warning of an impending clinical event using ancillary data streams (such as OTC) with established correlations with the clinical data, and a prediction method that can react to nonstationary events sufficiently fast. Whether OTC (or other data streams yet to be identified) provide the best source of predicting clinical data is still an open question. We present a framework and an example to show how to measure the effectiveness of predictions, and compute an upper bound on this performance for the Recursive Least Squares method when the following two conditions are met: (1) an event of sufficient strength exists in both data streams, without distortion, and (2) it occurs in the OTC (or other ancillary streams) earlier than in the clinical data.</p