Causality in scale space as an approach to change detection

PLoS One. 2012;7(12):e52253. doi: 10.1371/journal.pone.0052253. Epub 2012 Dec 27.

Abstract

Kernel density estimation and kernel regression are useful ways to visualize and assess the structure of data. Using these techniques we define a temporal scale space as the vector space spanned by bandwidth and a temporal variable. In this space significance regions that reflect a significant derivative in the kernel smooth similar to those of SiZer (Significant Zero-crossings of derivatives) are indicated. Significance regions are established by hypothesis tests for significant gradient at every point in scale space. Causality is imposed onto the space by restricting to kernels with left-bounded or finite support and shifting kernels forward. We show that these adjustments to the methodology enable early detection of changes in time series constituting live surveillance systems of either count data or unevenly sampled measurements. Warning delays are comparable to standard techniques though comparison shows that other techniques may be better suited for single-scale problems. Our method reliably detects change points even with little to no knowledge about the relevant scale of the problem. Hence the technique will be applicable for a large variety of sources without tailoring. Furthermore this technique enables us to obtain a retrospective reliable interval estimate of the time of a change point rather than a point estimate. We apply the technique to disease outbreak detection based on laboratory confirmed cases for pertussis and influenza as well as blood glucose concentration obtained from patients with diabetes type 1.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Blood Glucose / analysis
  • Blood Glucose Self-Monitoring / statistics & numerical data
  • Cluster Analysis
  • Data Interpretation, Statistical*
  • Diabetes Mellitus, Type 1 / blood
  • Humans
  • Influenza A virus / physiology
  • Influenza, Human / epidemiology
  • Regression Analysis
  • Whooping Cough / epidemiology

Substances

  • Blood Glucose

Grants and funding

The research is performed as part of Troms Telemedicine Laboratory in part funded by the Norwegian Research Council under grant no 174934. The Diabetes data is gathered and analyzed under project ID3919/HST952-10 funded by the regional health authority of North Norway. No additional external funding received for this study. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.