Online sequential monitoring of spatio-temporal disease incidence rates

Abstract

Online sequential monitoring of the incidence rates of chronic or infectious diseases is critically important for public health. Governments have invested a great amount of money in building global, national and regional disease reporting and surveillance systems. In these systems, conventional control charts, such as the cumulative sum (CUSUM) and the exponentially weighted moving average (EWMA) charts, are usually included for disease surveillance purposes. However, these charts require many assumptions on the observed data, including the ones that the observed data should be independent at different places and/or times, and they should follow a parametric distribution when no disease outbreaks are present. These assumptions are rarely valid in practice, making the results from the conventional control charts unreliable. Motivated by an application to monitor the Florida influenza-like illness data, we develop a new sequential monitoring approach in this article, which can accommodate the dynamic nature of the observed disease incidence rates (i.e., the distribution of the observed disease incidence rates can change over time due to seasonality and other reasons), spatio-temporal data correlation, and arbitrary data distribution. It is shown that the new method is more reliable to use in practice than the commonly used conventional charts for sequential monitoring of disease incidence rates. Because of its generality, the proposed method should be useful for many other applications as well, including spatio-temporal monitoring of the air quality in a region or the sea-level pressure data collected in a region of an ocean.

Key Words:

• Change detection
• correlation
• disease surveillance
• dynamic systems
• early detection
• nonparametric methods
• process control
• sequential monitoring

Acknowledgments

The authors thank the editors and three referees for many constructive comments and suggestions which improved the quality of the paper greatly.

Additional information

Funding

This research is supported in part by an NSF grant with the grant number [DMS-1914639].

Notes on contributors

Kai Yang

Kai Yang is currently a Ph.D. student in the Department of Biostatistics at the University of Florida. His thesis research is mainly on spatio-temporal data modeling and monitoring under the supervision of Professor Peihua Qiu. He has published two papers on nonparametric estimation of the mean and variance/covariance structures of spatial data, and has several other papers currently under review. In addition to that topic, his thesis research also discusses effective process monitoring by using covariate information.

Peihua Qiu

Peihua Qiu received his Ph.D. in statistics from the Department of Statistics at the University of Wisconsin - Madison in 1996. He worked as a senior research consulting statistician of the Biostatistics Center at the Ohio State University during 1996–1998. He then worked as an assistant professor (1998–2002), an associate professor (2002–2007), and a full professor (2007–2013) at the School of Statistics of the University of Minnesota. He is an elected fellow of the American Statistical Association, an elected fellow of the Institute of Mathematical Statistics, an elected member of the International Statistical Institute, a senior member of the American Society for Quality, and a lifetime member of the International Chinese Statistical Association. He served as an associate editor for Journal of the American Statistical Association, Biometrics, Technometrics, Surgery, and Statistical Papers, and guest co-editor for Multimedia Tools and Applications, and Quality and Reliability Engineering International. He was the editor-elect (2013) and editor (2014-2016) of Technometrics. He is currently an associate editor of Quality Engineering, and the Professor and Founding Chair of the Department of Biostatistics at the University of Florida.

Peihua Qiu has made substantial contributions in the areas of jump regression analysis, image processing, statistical process control, survival analysis, and disease screening and surveillance. So far, he has published about 120 research papers in referred journals, many of which appeared in top journals, including Technometrics, Journal of the American Statistical Association, Annals of Statistics, Annals of Applied Statistics, Journal of the Royal Statistical Society (Series B), Biometrika, Biometrics, IEEE Transactions on Pattern Analysis and Machine Intelligence, and IISE Transactions. His research monograph titled Image Processing and Jump Regression Analysis (2005, Wiley) won the inaugural Ziegel prize in 2007 for its contribution in bridging the gap between jump regression analysis in statistics and image processing in computer science. His second book titled Introduction to Statistical Process Control was published in 2014 by Chapman & Hall/CRC.