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.
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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.
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.
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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.
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