Sample size calculation: Bland-Altman plot
Calculates the required sample size for a method comparison study using the Bland-Altman plot.
In this method, limits of agreement (LoA) are calculated as the mean of differences between two measurements ± 1.96 x their standard deviation (Bland & Altman, 1986)
Two methods are considered to be in agreement when a pre-defined maximum allowed difference (Δ) is larger than the higher limit of agreement, and -Δ is lower than the lower limit of agreement.
Proper interpretation takes into account the 95% confidence interval of the LoA, and to be 95% certain that the methods do not disagree, Δ must be higher than the upper 95 CI limit of the higher LoA and -Δ must be less than the lower %95 CI limit of the lower LoA:
- With smaller sample sizes, the CI becomes larger and the probability that Δ lies within the 95 CI increases.
- With larger sample sizes, the CI becomes smaller and the probability that Δ lies within the 95 CI decreases.
To show that two methods are in agreement, an adequate sample size must be established to have a high probability (power) that Δ will fall outside the 95 CI of the Limits of Agreement.
- Type I error - alpha: the probability of making a Type I error (α-level, two-sided), i.e. the probability of rejecting the null hypothesis when in fact it is true.
- Type II error - beta: the probability of making a Type II error (β-level), i.e. the probability of accepting the null hypothesis when in fact it is false.
- Expected mean of differences: the expected mean of differences between measurements by the 2 methods that are compared in the study.
- Expected Standard Deviation of differences: the expected Standard Deviation of differences between measurements by 2 methods.
- Maximum allowed difference between methods: this is the pre-defined clinical agreement limit. Differences below this limit are clinically irrelevant or neglectable.This difference must be larger than expected mean + 1.96 x expected standard deviation of differences.
You want to show that two laboratory methods are in agreement. A preliminary study has shown that the mean difference is 0.001167, and the standard deviation of the differences is 0.001129. The maximum allowed difference between the methods is 0.004 units (example by Lu et al., 2016).
You enter 0.001167 for Expected mean of differences, 0.001129 for Expected Standard Deviation of differences and 0.004 for Maximum allowed difference between methods.
For α-level you select 0.05 and for β-level you select 0.20 (power is 80%).
After you click Calculate the program displays the required total number of cases in the study. The calculation may take some time to complete.
For the example the minimum required total sample size is 83.
A table shows the required sample size for different Type I and Type II Error levels.
MedCalc uses the method by Lu et al. (2016) to calculate the sample sizes.
Note that the Bland-Altman plot implemented by MedCalc (and as described in Bland & Altman, 1986) has a fixed alpha level of 0.05.
- Bland JM, Altman DG (1986) Statistical method for assessing agreement between two methods of clinical measurement. The Lancet i:307-310.
- Lu MJ, Zhong WH, Liu YX, Miao HZ, Li YC, Ji MH (2016) Sample size for assessing agreement between two methods of measurement by Bland-Altman method. The International Journal of Biostatistics 12: issue 2 (8 pp).