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Simple nomograms to calculate sample size in diagnostic studies
  1. S Carley1,
  2. S Dosman2,
  3. S R Jones3,
  4. M Harrison4
  1. 1Manchester Royal Infirmary, Manchester, UK
  2. 2Cambridge, UK
  3. 3Hope Hospital, Salford, Manchester, UK
  4. 4North Staffordshire Hospital, UK
  1. Correspondence to:
 Dr S Carley
 Manchester Royal Infirmary, Manchester M13 9WL, UK;


Objectives: To produce an easily understood and accessible tool for use by researchers in diagnostic studies. Diagnostic studies should have sample size calculations performed, but in practice, they are performed infrequently. This may be due to a reluctance on the part of researchers to use mathematical formulae.

Methods: Using a spreadsheet, we derived nomograms for calculating the number of patients required to determine the precision of a test’s sensitivity or specificity.

Results: The nomograms could be easily used to determine the sensitivity and specificity of a test.

Conclusions: In addition to being easy to use, the nomogram allows deduction of a missing parameter (number of patients, confidence intervals, prevalence, or sensitivity/specificity) if the other three are known. The nomogram can also be used retrospectively by the reader of published research as a rough estimating tool for sample size calculations.

  • diagnosis
  • nomogram
  • power
  • sample size
  • sensitivity
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  • Erratum Please note that there is an error in the example line given on the specificity nomogram (figure 1 part B) in this article. The calculation lines on the nomogram are correct but the worked example given clearly does not meet the calculating lines. The correct example can be seen in the larger version of the nomogram at . It should be noted that the error only affects the example and not the underlying nomogram itself.

    • Figure 1: Larger version

      A larger version of figure 1 is available here.

      Figure 1 (A) Specificity plot for pα = 0.05. Example: P = 0.55, CI = 0.04, SP = 0.90 giving n = 480.

      Figure 1 (B) Sensitivity plot for ppα = 0.05. Example: P = 0.55, CI = 0.04, SP = 0.90 giving n = 393.

      Files in this Data Supplement:


    • Competing interests: none declared

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      BMJ Publishing Group Ltd and the British Association for Accident & Emergency Medicine