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• SPC Versus GAM for hospital adverse events arising in a complex system
  Anthony P Morton
  Published on: 23 September 2016
• Statistical Process Control and Interrupted Time Series
  Alan J Poots
  Published on: 7 April 2016
• Public website for interrupted time series and segmented regression
  Robert G Badgett
  Published on: 18 December 2015

• Published on: 23 September 2016

  SPC Versus GAM for hospital adverse events arising in a complex system

  • Anthony P Morton, senior scientist

  Statistical process control works well when there is independence and linearity. Complex systems produce data that are often not independent, often nonlinear and display self-organisation and emergent behaviour. To say that statistical process control works when behaviour is emergent may make little sense. Increasingly adverse events like colonisation with antibiotic-resistant organisms arise in a complex system. Although...

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  Statistical process control works well when there is independence and linearity. Complex systems produce data that are often not independent, often nonlinear and display self-organisation and emergent behaviour. To say that statistical process control works when behaviour is emergent may make little sense. Increasingly adverse events like colonisation with antibiotic-resistant organisms arise in a complex system. Although the latter may be influenced favourably by using bundles, checklists and morbidity and mortality analysis, this is not the same as statistical process control. Each recent year and especially the most recent, we have seen the apparent superiority of generalised additive models in preparing summaries of the hospital's infection management annual report. The idea that generalised additive models work best when there is a complex system could be important if substantiated.

  Conflict of Interest:

  None declared

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  Conflict of Interest:
  None declared.

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• Published on: 7 April 2016

  Statistical Process Control and Interrupted Time Series

  • Alan J Poots, Information Analyst

  I read Fretheim and Tomic's article [1] with interest as I trained in frequentist stastistics and now work primarily with Stastistical Process Control (SPC) in quality improvement (QI) initiatives.

  I concur that there are missed opportunities for using Interrupted Time Series (ITS) in QI; however, I note cautions in doing so:

  Regression models applied in ITS often have the assumption of homoscedastici...

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  I read Fretheim and Tomic's article [1] with interest as I trained in frequentist stastistics and now work primarily with Stastistical Process Control (SPC) in quality improvement (QI) initiatives.

  I concur that there are missed opportunities for using Interrupted Time Series (ITS) in QI; however, I note cautions in doing so:

  Regression models applied in ITS often have the assumption of homoscedasticity - i.e. that the process is no more or less variable over time. In evaluation of QI initiatives we are seeking to violate that assumption in that we wish to change a variable and non-performing system into a reliable and highly performing system. This means that the ordinary least squares estimators would not be best linear unbiased, with a risk of overestimating the goodness of fit. This can be addressed using generalised least squares estimators. [2]

  Applying an ITS break point immediately on "intervening" assumes that the intervention is immediately and consistently applied from that point on. This might be true for a total replacement of one drug with another, but is less clear for behavioural change interventions, such as hand hygiene in hospitals. A similar case can be made for care bundle interventions - one may start bundle in all cases, yet all aspects of the bundle may not be consistently conducted.

  I suspect that, as with statistics in general, that care is required in selecting one's test, which will depend on the purpose required.

  Perhaps a mixed method of SPC and ITS could be preferred?

  [1] A. Fretheim, O.Tomic. Statistical process control and interrupted time series: a golden opportunity for impact evaluation in quality improvement. BMJ Quality and Safety 2015;24:748-752

  [2] A. H. Welsh, R. J. Carroll, D. Ruppert, Fitting Heteroscedastic Regression Models. Journal of the American Statistical Association 1994;89:100-116

  Conflict of Interest:

  None declared

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  Conflict of Interest:
  None declared.

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• Published on: 18 December 2015

  Public website for interrupted time series and segmented regression

  • Robert G Badgett, Professor of Preventive Medicine and Public Health
  • Other Contributors:
    • Kelsey Lu, MS

  We agree with the authors that interrupted time series should be used more often (1). We also agree that the statistics are difficult. We find segmented regression to be the preferable form of interrupted time series (ITS) as traditional ITS with the Davies tests only looks for a change in slope at the breakpoint. This works well if there is not a simultaneous change or shift in the level of the outcome at the breakpoint; howev...

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  We agree with the authors that interrupted time series should be used more often (1). We also agree that the statistics are difficult. We find segmented regression to be the preferable form of interrupted time series (ITS) as traditional ITS with the Davies tests only looks for a change in slope at the breakpoint. This works well if there is not a simultaneous change or shift in the level of the outcome at the breakpoint; however, when both a change in slope and a shift in level occur, the Davies test is problematic. In addition to segmented regression, we use multivariable linear regression to detect secular trends in outcomes over time.

  In response to the difficulties, we have placed online at http://qitools.github.io/ a resource for using and teaching segmented regression. The website accepts data sets by pasting or uploading values.

  The underlying source code is written in R and is publicly available at GitHub (https://github.com/qitools/charts). In addition to being open-source, the code is implemented online at openCPU so users do not have to install R on their own computers. The combination of GitHub and openCPU allows for crowdsourcing improvements or alternative versions. We encourage other investigators to improve the source code at https://github.com/qitools/charts for implementation that we have started.

  References:

  1. Fretheim A, Tomic O. Statistical process control and interrupted time series: a golden opportunity for impact evaluation in quality improvement. BMJ Qual Saf. 2015 Dec;24(12):748-52. doi: 10.1136/bmjqs-2014-003756. PMID: 26316541

  Conflict of Interest:

  None declared

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  Conflict of Interest:
  None declared.

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