Diagnostic Accuracy and Agreement
Calculate the number of paired measurements required to demonstrate agreement between two measurement methods using the Lu et al. noncentral-t method. The design evaluates whether the confidence intervals around the Bland-Altman limits of agreement fall within a prespecified maximum allowable difference.
The Bland-Altman method evaluates agreement between two measurement methods by forming paired differences. The conventional limits of agreement are the anticipated mean difference plus or minus a normal quantile times the standard deviation of the differences. the sample-size procedure then evaluates whether the confidence intervals around both limits remain within the prespecified agreement boundaries of −δ and δ.
Here, D is the anticipated mean difference, SD is the anticipated standard deviation of the paired differences, and γ = 1 − the LoA confidence level. For a 95% LoA, the usual multiplier is approximately 1.96.
For a sample of N paired measurements, This calculator uses the Lu et al. formulation. The standard-error term used for the confidence limits is
With t denoting the appropriate Student's t critical value, the lower and upper confidence limits around the Bland-Altman limits are formed from the corresponding mean, LoA term, and t × SE.
The power calculation uses the cumulative distribution function of a noncentral Student's t distribution. For a confidence level of 1 − α for the confidence intervals around the LoAs, the two noncentrality parameters are
The power is calculated as the probability that both confidence limits satisfy the agreement criterion. Equivalently, using the noncentral-t CDF, the this method/Lu formulation is
The calculator searches over integer values of N and returns the smallest number of measurement pairs whose calculated power reaches the requested target.
This worked example uses a 95% confidence level for both the limits of agreement and their confidence intervals, maximum allowable difference δ = 7, anticipated mean difference D = 0.5, and anticipated SD = 2.5. At 80% target power, This yields 60 measurement pairs.
The calculator is initialized with these values. Its independent noncentral-t implementation reproduces the this method example's reported sample-size result of 60 pairs and displays the achieved power at that N.
Lu, M.J., Zhong, W.H., Liu, Y.X., Miao, H.Z., Li, Y.C., & Ji, M.H. (2016). Sample Size for Assessing Agreement between Two Methods of Measurement by Bland-Altman Method. The International Journal of Biostatistics, 12(2), Article 20150039. DOI: 10.1515/ijb-2015-0039.
Bland, J.M. & Altman, D.G. (1986). Statistical Methods for Assessing Agreement Between Two Methods of Clinical Measurement. The Lancet, i, 307–310.
the software/this method. Bland-Altman Method for Assessing Agreement in Method Comparison Studies, Chapter 427. the relevant methodological literature identifies the procedure as a sample-size and power calculation based on Lu et al. (2016).