Bland-Altman Plots

Introduction

• Bland and Altman developed the Bland-Altman plot to assess the level of agreement between two quantitative measurement techniques.^1,2
  • They proposed quantifying this agreement by calculating limits of agreement, derived from the mean and SD of the differences between measurements.^1,2
  • The resulting plot is a scatter diagram where the Y-axis represents the difference between the two measurements (A − B), and the X-axis represents their average ((A + B)/2).^1,2
• In essence, it visualizes how differences vary relative to the means of the two measurements.
• Bland and Altman suggest that about 95% of the data points should fall within ±2 SDs of the mean difference.^1,2
  • While this is the standard form of the Bland-Altman plot, variations exist. The differences can also be plotted as percentages or ratios.¹
    • Expressing differences as percentages of the mean, [(A − B) / mean × 100], can be useful when variability increases with the magnitude of the measurement.¹
    • In anesthesiology, Bland-Altman analysis can be used to assess agreement between monitoring methods, such as invasive vs noninvasive blood pressure.

Example of Bland-Altman Analysis

This example compares invasive arterial line and non-invasive cuff blood pressure measurements in five patients.

• The difference (Cuff − Arterial) was calculated for each patient, with a mean difference (bias) of −1.6 mmHg.
  • This indicates that the cuff slightly underestimates arterial pressure compared to the invasive method.
• The standard deviation (SD) of these differences was approximately 2.6 mmHg.
  • Calculated by finding the mean, subtracting it from each data point, squaring the results, summing them, dividing by (n − 1) for a sample (or N for a population) to obtain the variance, and finally taking the square root to yield the SD.
• Using the Bland–Altman approach, the 95% limits of agreement is calculated as:
  • Mean Difference ± 1.96 × SD^1,4
  • Applying this formula gives limits of −6.7 mmHg and +3.5 mmHg, meaning that in 95% of cases, the cuff measurement is expected to fall between 6.7 mmHg lower and 3.5 mmHg higher than the arterial line measurement
• On a Bland–Altman plot:
  • The x-axis represents the average of the two methods for each patient.⁴
  • The y-axis represents the difference between the two methods (Cuff − Arterial).⁴
  • A horizontal line is drawn at the mean difference (−1.6 mmHg), and two more lines at the limits of agreement (−6.7 and +3.5 mmHg).
  • Each point on the plot represents one patient’s data.

Interpretation of Bland-Altman Plots

• The scatterplot can be interpreted by examining the dispersion of the data points.⁴
• In cases of good agreement, the points cluster closely around the line representing the mean bias, with minimal scatter.⁴
• The mean bias and limits of agreement serve as quantitative indicators of the degree to which the two measurement methods correspond and of whether one can be substituted for the other.⁴