# Sample Size Calculator For Agreement Studies

If μ>0, we first calculate with equation (6) to get an initial value (n1), and then calculate with equation (5) to reach power. If the estimated power is close enough to the predefined power, n is the sample size we want to estimate. Otherwise, we will make n1 equal n1+1 and evaluate whether the estimated performance is sufficiently close to the pre-established performance. Repeat the process above until it comes closest to the predefined performance, but is larger. Table 1 summarizes reasonable sample size estimates using equations (5) and (6) for different standardized differences (μ/σ), different standardized compliance limits (δ/σ), and different Type II errors (β) assuming the data are well educated. Sample size(s) for the Bland Altman method with non-centralized t-distribution for different standardised difference limits (μ/σ), different standardised conformity limits (δ/σ) and Type II errors (β). (α=0.05). Bland indicated the sample size for a study on the concordance between two measurement methods available on its website . In the 1986 Lancet paper, they indicated a confidence interval formula for 95% compliance limits. The standard error of the 95% compliance limit is approximately the root 3s2/n, s being the standard deviation of the differences between the measurements with the two methods and n the sample size. The confidence interval is the estimate of the limit value, plus or minus 1.96s, plus or minus 1.96 standard error, and then the sample size can be released.

We show a clinically worked example from a set of prostate antigen (FPSA) measurement data that is often used to assess the presence of prostate cancer and other prostate diseases. The AIA 1800 and I2000 methods were used to measure fpsa. The same random sequence of samples was used in both instruments . Through preliminary experiment, we obtain the mean and standard deviation of the differences between AIA-1800 and I2000 methods of 0.001167 mmol /l and 0.001129 mmol / l. If we define α=0.05, β=0.20, (− δ.δ)=(− 0.004.0.004) mmol/l, we can calculate that a sampling size of 83 would be required to provide 80% power to assess conformity between two measurement methods. The Monte Carlo simulation is used to obtain the corresponding power, which corresponds to 80.51%, close to the predefined power (80%). 6. Chhapola V, Kanwal SK, Brar R. Reporting standards for Bland-Altman agreement analysis in laboratory research: a cross-sectional survey of current practice. Ann Clin Biochem 2015;52:382-386.

Given the symmetry of the confidence interval estimate of LOA with μ and μ symmetry (μ ≥ 0) and the sample size estimates of these two situations, we will only discuss the situation if μ ≥ 0. According to the principle of statistical inference of the Bland Altman conformity limits, we can separate the total Type I error (α) into two parts, both α/2. In the same way, we can separate the total error of type II (β) into two parts….

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