The Analysis Use Cusum And Bootstrapping Biology Essay

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This paper discusses CUSUM CPA approach for detecting changes in mean of a process using malaria time series data. The analysis use s CUSUM and bootstrapping so to locate the change point and make inferences respectively.

The change points detected corresponds to specific events in the period between 2010 and 2011. For the impact detection there were more change points detected after June 2011 than before May 2010. There is a strong body of knowledge regarding the interventions which were put in between May 2010 and June 2011 which we might have anticipated to reflect the detected change points with reduction in the trends of number of malaria cases. Further research should be done to ascertain the claim of the changes detected to rule out if the changes may have been due to changing climatic conditions, co-interventions effects or good medical practices.

We compared our results with those from the standard epidemic detection techniques and found that our method detected some of the change points which were detected by the EDS. However, there were those points which were detected by our method only. This shows that the method could detect subtle changes which could not be detected by the EDS. The same results shows that the points detected coincided with the time when there were epidemics. For epidemic detection, malaria EDS detected 34 points, control charts 4 points, CUSUM charts 28 points and CUSUM CPA 3 change points.

Our CPA results are similar to those of CUSUM CPA detection method which was used by (Kass-Hout et al. 2012) to detect changes in emergency admission trends due to influenza illness in USA. The confidence levels, the magnitude and the location of change points were given. It also detected subtle changes during that period. There is a graphical representation of the location of change points just as change point detection techniques used by (Killick et al., 2011, Barry and Hartigan, 1993; Bai and Perron, 2003)

Just as other change point detection techniques which uses the likelihood-ratio test (Killick et al, 2011) and Bayesian (Barry and Hartigan, 1993), our method starts with single change point detection. If change point is detected, then the data set is split into two segments and the procedure for detecting the change point is repeated recursively till no change point is detected

The method is using the non-parametric approach (CUSUM estimator) to locate the change point. These method seems effective since its using the deviations from the mean across the whole series. In addition, there is a threshold for deciding when a threshold has been detected. A minimum confidence level of is required for the change point to be significant. And it's also the guiding factor for the number of segments to be splitted in a given series. The likelihood ratio test statistics is usually compared with a threshold to test for the hypothesis of the change point.

Since change point detection is the problem of discovering where the time series data is experiencing a shift, it can be used effectively to detect point of change due to intervention impacts and epidemics. The only methods used are the EDS and Malaria Indicator Survey to detect epidemics and assess impacts respectively.

One criticism of this approach is that it does not detect isolated abnormal points. To address this concern change-point analysis should be supplemented with a Shewhart control chart when such points are of concern. Another drawback of the CUSUM CPA is that the bootstrapping approach will not produce identical results every time it is performed because of the random selection of the bootstrap samples. This shortcoming can be addressed by increasing the number of bootstraps so as to increasingly have more precise results. A minimum number of 1000 bootstraps are usually recommended.

5.2 Conclusions

We have shown how recent methodological advances in detecting change point in mean of a process can be applied to some data sets. The method allows for visualization and graphical analysis which convey information about the presence and the location of change points in the data. In addition there is a significance test for making inference for the change point detected using bootstrapping which in turn helps to calculate the confidence level.

The algorithm is non parametric since it does not assume any distribution just like any other non parametric algorithms.

5.3 Recommendations

CUSUM CPA is an effective tool for detecting changes in mean for time series data and should be adopted so as to detect points of change due to epidemics or intervention impact together with the existing methods so as to get meaningful results.

For further research one should try change point analysis using structural change models, binary segmentation procedures or Bayesian change point analysis with application to malaria cases as an outbreak or impact detection method. Detecting change points in variance should also be done.

5.4 Limitations of the study

In this study data from one case area was used to detect changes mean of malaria cases due to epidemics and due to impacts of interventions. However, the research could have been more representative if a slightly larger sample and data set for longer time frame was used to give the results more validity.

Because these results only show short-term trends in the malaria cases associated with the introduction of these control strategies, they need confirmation in longer studies.


Amin, R.W., Reynolds M.R. and Bakir S. (1995), 'Nonparametric quality control charts based on

the sign statistics', Comm. Stat. Theory Methods 24, 1597-1623.

Bai J, Perron P (2003). Computation and Analysis of Multiple Structural Change Models."

Journal of Applied Econometrics, 18, 1-22.

Barker, N. (2010), 'A practical introduction to the bootstrap using the SAS system'.

Barry D, Hartigan JA (1993). "A Bayesian Analysis for Change Point Problems." Journal of the

American Statistical Association, 35(3), 309-319.

Basseville, M. and Nikiforov, I.V. (1993). Detection of abrupt changes: theory and application.

Infor-mation and system science series. Prentice Hall, Englewood Cliffs, NJ.

Box, G.E.P, Jenkins G.M. and Reinsel G.C. (1994), Time series analysis: Forecasting and

Control, Prentice Hall, Englewood Cliffs, NJ.

CDC (1986), Comprehensive plan for epidemic surveillance. Atlanta, Center for Disease


Chen, J. and Gupta A.K. (2000), Parametric Statistical Change Point Analysis, Boston,


Cullen, J.R., Chitprarop U., Doberstyn E.B and Sombatwattanangkul K. (1984), 'An

epidemiological early warning system for malaria control in northern thailand', Bull

World Health Organ 62, 107-114.

De Vries, A., and Reneau J.K (2010), Application of statistical process control charts to monitor

changes in animal production systems. J. Animal Sci, 10, 2009-2622

Downey, A.B (2008). A novel changepoint detection algorithm. Application Statistics, 1-11

Efron, B. and Tibshirani R. (1993), An Introduction to the Bootstrap, Chapman & Hall.

Efron, B. (1987) "Better Bootstrap Confidence Intervals", Journal of the American Statistical

Association, 92, 171-185

Efron, B. (1982) "The Jackknife, the Bootstrap and Other Resampling Plans", Society for

Industrial and Applied Mathematics, Philadelphia, Pennsylvania

Erdman C, Emerson JW (2007). bcp: A Package for Performing a Bayesian Analysis of Change

Point Problems. Journal of Statistical Software, 23, 1-13

Gavit, P., Baddour Y. and Tholmer R. (2009), 'Use of change-point analysis for process

monitoring and control', BioPharm International 22, 1-13.

Hawkins, D.M., Qui P. and King C.W. (2003), 'The change point model for statistical process

control', Journal of Quality Tecnology 35, 355-366.

Hawkins, D M and Zamba, K D. (2005) Statistical Process Control for Shifts in Mean or

Variance using a Change Point Formulation. Technometrics 47, 164-173

Hay, S.I., Simba M., Busolo M., Noor A.M., Guyatt H.L., Ochola S.A. and Snow R.W. (2002),

'Defining and detecting malaria epidemics in the highlands of western kenya',

Emerg. Infect Dis 8, 555-562.

Hensen B (2001). The new econometrics of structural change: dating changes in U.S. labor

productivity. J Econ Perspect;15:117e28.

Hinkley, D. and Schechtman E. (1987), 'Conditional bootstrap methods in the mean-shift

model', Biometrika 74, 85-93.

Hinkley, D.V. (1971), 'Inference about the change-point from cumulative sum tests', Biometrika

58, 509-523.

Kass-Hout, T.A., Xu Z., McMurray P., Park S., Buckeridge D.L. Brownstein J.S., Finelli L. and

Groseclose S.L. (2012), 'Application of change point analysis to daily to daily influenza-

like-illness (ili) emergency department visits', Journal of American Medical Informatics

Association; pp. 1-16.

Killick, R., Eckley, I.A., Ewans, K., Jonathan, P. (2010) Detection of changes in variance of

oceanographic time-series using changepoint analysis. Ocean Engineering 37, 1120-1126

McKelvie, W.R., Haghdoost A.A. and Raeisi A. (2012), 'Defining and detecting malaria

epidemics in south-east iran', Malaria journal 11, 1-16.

Montgomery, D.C. (2000), Introduction to Statistical Quality Control, 4th edn, New York: John

Wiley & Sons.

Okiro, E.A., Hay S.I., Gikandi P.W., Sharif S.K., Noor A.M., Peshu N., Marsh K. and Snow

R.W. (2007), 'The decline in paediatric malaria admissions on the coast of kenya',

Malaria journal 6, 1-16.

Olshen AB, Venkatraman ES (2004). Circular Binary Segmentation for the Analysis of Array

based DNA Copy Number Data. Biostatistics, 5(4), 557-572.

Page, E.S. (1954), 'Continuous inspection schemes', Biometrika 41, 100-115.

Roll Back Malaria (RBM) (2001): Malaria early warning systems: a framework for field research

in Africa: concepts, indicators and partners Geneva: RBM;

Sallis, P., Claster, W., and Hernandez, S. (2011) An algorithm for preciting wind gust events.

Computers and the Geosciences, Elsevier [in print for 2011]

Sastri, T., Flores B. and Valdes J. (1989), 'Detecting points of change in time series', Computers

Open Research 16, 271-293.

Sanghvi P (2008). Detection of switching time. MS Thesis, Texas Tech University

Taylor, W. (2000b), 'A pattern test for distinguishing between autoregressive and meanshift

data', Submitted to Journal of Quality Technologies .

Taylor,W.A. (2010), 'Change-point analysis: A powerful new tool for detecting changes'. URL: (Accessed 30.04.2012)

Teklehaimanot HD, Schwatrz J, Teklehaimanot A, Lipsitch M (2004): Alert threshold algorithms

and malaria epidemic detection. Emerg Infect Dis, 10:1220-1226.

Wagner, A.K., Soumerai, S.B, Zhang, F. and Ross-Degnan, D. (2002). Segmented regression

analysis of interrupted time series studies in medication use research. Journal of Clinical

and Therapeutics 27, 299-309

Wangdi, K., Kaewkungwal J., Singhasiranon P., Silawan T., Lawpoolsri S and White N.J.

(2011), 'Spatio-temporal patterns of malaria infection in bhutan: a country embarking on

malaria elimination', Malaria journal 10, 1-16.

Wetherill, G.B. and Brown D.W. (1991), Statistical Process Control, New York: Chapman & Hall.

WHO (2001), Malaria early earning system, a framework for field research in Africa: concepts,

indicators and partners WHO/CDS/RBM/2001.32., Geneva: The Organisation.

Yao YC (1984). Estimation of a Noisy Discrete-time Step Function: Bayes and Empirical Bayes Approaches. The Annals of Statistics, 12(4), 1434-1447.

Yao, Y., (1988). Estimating the number of change-points via Schwarz' criterion. Statistics and

Probability Letters 6, 181-189.

Yigiter, A. (2012). Change Point Analysis in Earthquake Data, Earthquake Research and

Analysis - Statistical Studies, Observations and Planning, InTech, Available from:

observations-and-planning/change-point-analysis-in-earthquake-data, 1-16 (Accessed