Trigonometric Regression for Analysis of Public Health Surveillance Data

Statistical challenges in monitoring modern biosurveillance data are well described in the literature. Even though assumptions of normality, independence, and stationarity are typically violated in the biosurveillance data, statistical process control (SPC) charts adopted from industry have been widely used in public health for communicable disease monitoring. But, blind usage of SPC charts in public health that ignores the characteristics of disease surveillance data may result in poor detection of disease outbreaks and/or excessive false-positive alarms. Thus, improved biosurveillance systems are clearly needed, and participation of statisticians knowledgeable in SPC alongside epidemiologists in the design and evaluation of such systems can be more productive. We describe and study a method for monitoring reportable disease counts using a Poisson distribution whose mean is allowed to vary depending on the week of the year. The seasonality is modeled by a trigonometric function whose parameters can be estimated by some baseline set of data. We study the ability of such a model to detect an outbreak. Specifically, we estimate the probability of detection (POD), the average number of weeks to signal given that a signal has occurred (conditional expected delay, or CED), and the false-positive rate (FPR, the average number of false-alarms per year).