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• Limits of agreement and confidence intervals
  J Martin Bland
  Published on: 29 April 2016
• Confidence interval incorrectly explained
  Marcus Müllner
  Published on: 29 April 2016

• Published on: 29 April 2016

  Limits of agreement and confidence intervals

  • J Martin Bland, Prof. of Health Statistics

  Dear Editor,

  Dr Müllner is wrong and Johnston and Murphy are correct. The limits of agreement are not a confidence interval but a range within which we expect most differences to lie. We expect for any sample from a Normal distribution that 95% of observations will be within 1.96 standard deviations from the mean. Here, 95 of differences, between arterial and venous potassium measurements will lie between –1.182...

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  Dear Editor,

  Dr Müllner is wrong and Johnston and Murphy are correct. The limits of agreement are not a confidence interval but a range within which we expect most differences to lie. We expect for any sample from a Normal distribution that 95% of observations will be within 1.96 standard deviations from the mean. Here, 95 of differences, between arterial and venous potassium measurements will lie between –1.182 mmol/l and 1.394 mmol/l (see Bland and Altman, Lancet 1986; i: 307-310).

  The same paper describes what to do if the differences between the two measurements get larger for larger average values, i.e. when the potassium level is greater. From Figure 2. in Johnston and Murphy, this is the case here. A log transformation enables us to estimate the 95% limits of agreement for the transformed data as −0.247 to 0.293. If we antilog these, we get 0.78 to 1.34, meaning that we estimate that the arterial measurement may be as little as 78% of the venous measurement, i.e. 22% smaller, or as high as 34% greater. If we drop the obvious outlier, where there may be some reporting or transcription error, these limits become 17% smaller to 22% greater. Whether this means that agreement is inadequate is, of course, a clinical rather than a statistical decision.

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  Conflict of Interest:
  None declared.

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• Published on: 29 April 2016

  Confidence interval incorrectly explained

  • Marcus Müllner, Clinical epidemiologist

  Dear Editor,

  While the results of this study appear very useful there are two issues. One is more of a theoretical nature: the interpretation of the 95% confidence interval; the second has something to do with external validity: potential selection bias.

  Interpretation of the confidence interval:
  In the abstract the authors state that "...the 95% limits of agreement were wide (–1.182 mmol...

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  Dear Editor,

  While the results of this study appear very useful there are two issues. One is more of a theoretical nature: the interpretation of the 95% confidence interval; the second has something to do with external validity: potential selection bias.

  Interpretation of the confidence interval:
  In the abstract the authors state that "...the 95% limits of agreement were wide (–1.182 mmol/l to 1.394 mmol/l) — that is, 95% of differences will lie between these limits." This is wrong. The 95% confidence interval means that in 95% of the cases (i.e. if we would repeat such a study many, many times), the average(!) difference will lie within. In terms of clinical practice this means something completely different.

  It seems that this observed mean bias and the wide confidence interval are cause by a single or maybe two outliers (patients #1 and #9). This makes the confidence intervals of this study not very trustworthy

  Potential selection bias:
  Over 10 months 50 patients were recruited. How many were admitted for cardiac arrest and what were the reasons for not having both analyses? Without this information we cannot interpret the findings.

  In conclusion, this study is a first step but the findings should be validated in a prospective study before they can inform clinical practice.

  Marcus Müllner, MD MSc

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  Conflict of Interest:
  None declared.

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