Recently, studies on the agreement between two instruments or clinical trials in the ophthalmological literature have multiplied. McAlinden et al. used a method of calculating sample size for agreement studies based on the method proposed by Bland . The sample size was calculated without taking into account the effectiveness of the statistical method, so the probability of obtaining the required width was only 0.50 . During the study phase, consideration of performance in sample size calculations could result in expected conclusions below the pre-established level of performance. Cesana et al. provided another estimate of sample size that was needed to establish a pearson correlation coefficient between the differences and the means of the measurements , and we feel that this method is not appropriate. Indeed, the correlation coefficient indicated by Cesana reflected proportional distortion. As we know, one of the hypotheses of application of the Bland-Altman method is not a proportional bias. In the absence of the hypothesis, this method would not be applicable. Based on the principle of statistical inference and mathematical theory of distribution, we deduced the sample size calculation formula for the Bland-Altman method under different parameter parameters. For simplicity`s sake, we provided a table that makes it easy to determine sample size for different standardized difference limits (μ/σ), standardized tuning limits (δ/σ) and type errors (β) under α-0.05. The α and β should be considered large enough for sample size to have the half-width of a 100 (1x α) confidence interval less than a predefined width of 100 (1-β%).
We have carried out monte-caro simulation studies to validate the accuracy of the proposed method. The results of the simulation show that the forces reached could correspond to the specified level of power, which validates the accuracy of the formulas. 4. JM Bland, DG Altman. The measurement agreement in method comparison studies. Stat Methods Med Res 1999;8:135-160. 17. Lin SC, Whipple DM, Ho CS. Assessing statistical equivalence using match limits and calculating the sample size associated with it. Common Stat Theor Methods 1998;27:1419-1432.