How to Use Bland-Altman Analysis

What is Bland-Altman Analysis?

Bland-Altman analysis evaluates the agreement between two measurement methods. It assesses whether the two methods can be used interchangeably by quantifying the bias (systematic difference) and the limits of agreement (random variability).

Reading the Plot

• X-axis: Mean of the two measurements ((A + B) / 2). Represents the 'best estimate' of the true value.
• Y-axis: Difference between methods (A - B). Positive values mean A > B.
• Red solid line: Mean bias. If close to 0, no systematic difference between methods.
• Orange dashed lines: Limits of Agreement (LoA) = Bias ± 1.96 × SD. ~95% of differences fall within this range.
• Pink shaded band (optional): 95% CI for the bias. Narrow band = precise bias estimate.
• Orange error bars (optional): 95% CI for the LoA. Shows precision of the agreement limits.

Interpretation Rules

• If the bias is close to 0 and the LoA range is within clinically acceptable limits, the methods agree and can be used interchangeably.
• If the LoA range is too wide, the methods disagree and cannot be substituted.
• Check for proportional bias : if differences increase/decrease systematically with the mean, consider a regression approach or use the %BA plot.
• Normality of differences should be checked (Shapiro-Wilk test). If non-normal, consider a log transformation or non-parametric approaches.

Percentage BA Plot (%BA)

When the measurement scale varies widely or the error is proportional to the magnitude, the %BA plot (difference / mean × 100%) is more appropriate than the absolute difference plot.

Statistics Table

• Bias: Mean of (A - B). Systematic difference.
• SD: Standard deviation of differences. Random variability.
• LoA: Limits of Agreement = Bias ± (multiplier × SD). Default multiplier = 1.96 for 95% range.
• CI for Bias: 95% confidence interval for the bias (t-distribution).
• CI for LoA: 95% CI for each limit of agreement, based on SE = SD × √(3/n).
• Shapiro-Wilk test: Tests normality of differences. p > 0.05 suggests normal distribution. Assumed for valid LoA; if non-normal, consider transformation or non-parametric bounds.

Data Requirements

• Method A & B: Two numeric columns with paired measurements.
• Pairing: Each row must contain measurements from both methods on the same subject/sample.
• Missing values: Rows with NA in either method are removed before analysis.
• ID columns: Automatically detected and excluded from variable selection.

Formulas

• Bias = mean(A - B)
• SD = sd(A - B)
• LoA = Bias ± z × SD (z = 1.96 for 95%)
• SE(bias) = SD / √n
• SE(LoA) ≈ SD × √(3/n)
• 95% CI = estimate ± t₀.₀₂₅ × SE

Demo Data

Simulated blood pressure measurements (n=120) from two devices. Method B has a slight positive bias (+1.5 mmHg) and slightly higher variability.

Reference

Bland JM, Altman DG. Statistical methods for assessing agreement between two methods of clinical measurement. Lancet. 1986;1(8476):307-310.