Change Point Analysis in BioSense 2.0 To access the slides for today’s

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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

02012-01-01

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 info@biosen.se