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### Agreement Between The Two Methods

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. Suppose measurements of two methods are made on each of the N themes that come from a particular population. Suppose also that the two measures xi or yi or difference, di for the subject i (i-1,2, …, n) We show a clinical example from a series of measured data of free prostate antigen (FPSA), commonly used to assess the presence of prostate cancer and other prostate diseases. The AIA-1800 and I2000 methods were used to measure FPSA. For the measurement, the same random sequence of the sample was used in both instruments . Thanks to preliminary experience, we obtain the average and typical difference between the AIA-1800 and I2000 methods are respectively 0.001167 mmol/l and 0.001129 mmol/l respectively. If we define α-0.05, β-0.20, (-δ.δ) (0.004,004)mmol/l, we can calculate that a sample size of 83 would be required to provide 80% power to assess the consistency between two measurement methods.

The monte-carlo simulation is used to obtain the corresponding power of 80.51%, that of the predefined power (80%) approaching. Considering that the LOA confidence interval estimate has a symmetry of μ and μ (μ ≥ 0) and that the size estimates for these two situations should be the same, we only discuss the situation if μ ≥ 0. According to the principle of statistical inference of the Bland-Altman agreements, we can divide total Type I (α) errors into two parts, both of which are α/2. Similarly, we can divide the Type II (β) error into two parts. The first is the first Type II error (No. 1) of the upper LOA limit and the second Type II error (2) of the lower LOA limit (Figure 1).  Sample size for the Bland-Altman method, with an un centralized t distribution for different standardized limits (μ/σ), different standardized tuning limits (δ/σ) and different Type II errors (β). (α=0.05). 4. JM Bland, DG Altman.