Change Point Analysis in BioSense 2.0
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Change Point Analysis in BioSense 2.0
David Buckeridge MD PhD1 and Nabarun Dasgupta PhD21Associate Professor, Epidemiology and Biostatistics, McGill
University, Canada Research Chair In Public Health Informatics
2BioSense Redesign Team
Introduction to the Change Point Algorithm
One of two aberration detection algorithms currently implemented in BioSense 2.0
The change point algorithm was developed by Taylor
The general idea is to iteratively Apply cumulative sums to the residuals of a time series Use resampling of the original series to estimate
significance An application of the change point
algorithm to biosurveillance is described by Kass-Hout et al.Taylor, W. Change-Point Analysis: A Powerful New Tool For Detecting Changes. 2010; Available from: http://www.variation.com/anonftp/pub/changepoint.pdf.
Kass-Hout TA, Xu Z, McMurray P, Park S, Buckeridge DL, Brownstein JS, Finelli L, Groseclose SL. Application of change point analysis to daily influenza-like illness emergency department visits. J Am Med Inform Assoc. 2012 Nov-Dec;19(6):1075-81. http://jamia.bmj.com/cgi/content/full/amiajnl-2011-000793
Understanding the Change Point Algorithm
Objective: Find the date(s) in a time series where the mean value of the series ‘shifts’ significantly
Algorithm1. Calculate cumulative sum of the residuals for the time
series2. Find change point — absolute maximum of the
cumulative sum3. Assess significance of change point through resampling4. Split time series in two on either side of change point
and repeat steps 1-3 for each subsection of the time series
5. Report statistically significant change points
An Example Time Series from BioSense 2.0
ILI visits to all DOD and VA facilities
between 2012-01-01 and 2012-12-31
1. Cumulative Sum of the Residuals for a Time Series
The mean of the series is
0.0419
1. Cumulative Sum of the Residuals for a Time Series
Date X(t) Residual
Cusum
0
2012-01-01
0.0552 0.0132 0.0132
2012-01-02
0.0818 0.0399 0.0531
2012-01-03
0.0105 -0.0314 0.0218
2012-01-04
0.0091 -0.0328 -0.0110
… … … …
2. Absolute Maximum of the Cumulative Sum
The absolute maximum of the cumulative sum
of the residuals is -5.79.
2. Maximum of the Cumulative Sum = Change Point
The date at the absolute
maximum, or the change point, is
2012-11-10.
3. Assess Significance through Resampling
The difference between the maximum and
minimum of the cumulative sum of the residuals is used as a
measure of the change point.
3. Assess Significance through Resampling
A. Shuffle the observed values in the original series
so that they are in a random order.
B. Measure and record the difference between the
maximum and minimum of the cumulative sum of the
residuals.
3. Assess Significance through Resampling
Repeat...
3. Assess Significance through Resampling
Repeat...
3. Assess Significance through Resampling
The observed difference is greater than the differences calculated from cumulative sums of 999 permutations of the time series. So, the observed break point is likely to be observed by chance fewer than 1 in 1000 times, or p < 0.001.
3. Assess Significance through Resampling
2012-11-10‘Up’p <
0.001
4. Split Time Series in Two and Repeat on Sub-Series
First break point
4. Split Time Series in Two and Repeat on Sub-Series
First break point
Sub-series A
Sub-series B
4. Split Time Series in Two and Repeat on Sub-Series
First break point
Sub-series A
Break point in A
Sub-series B
Break point in B
5. Report Statistically Significant Change Points
2012-02-18‘Up’p <
0.025
2012-11-10‘Up’p <
0.001
2012-04-09
‘Down’p <
0.001
Applying the Change Point Algorithm (CPA)
The CPA detects shifts in the mean and indicates the direction of the shift.
Algorithm is straightforward and results are easy to understand.
CPA can be used alone, but probably more informative when used with aberration detection method, such as C2.
Further practical and theoretical results will help to define the role of CPA in surveillance analysis.
Upcoming BioSense 2.0 Webinars
A webinar will be scheduled for March; the topic is to be determined.
For more information, please visit our Collaboration Web Site www.biosense2.org
If you have any suggestions for future webinars, please contact us at [email protected]