Ceiling – 1.8799 – 1.96 × ($0.03618) – 0.1943 – 1.96 × 0.106 (8) × average glucose – 1.8090 – 0.0150 × average glucose compliance limits can be deduced using the parametric method assuming the normality of the differences. or the use of non-parametric percentiles, if these assumptions are not included. Gross lower value – 0.3625 s 1.96 × 1.2357 – 2.06 mmol/L Gross ceiling – 0.3625 – 1.96 1.96 × 1.2357 – 2.78 mmol/L We could use these regression equations to estimate the 95% limit of the agreement, as is currently the case, the boundaries of the agreement include both systematic errors (bias) and random errors (precision) and provide a useful measure to compare the likely differences between the different results measured using two methods. If one method is a reference method, compliance limits can be used as a measure of the total error of a measurement method (Krouwer, 2002). We can see that the limit values do not match the data well. They are too wide at the lower end of glucose and too narrow at the high end of glucose. They are right because they probably have 95% of the differences (here 84/88 – 94.5%). but all the differences outside the borders are at one end and one of them is far away. Lower limit – 1.8799 – 0.1943 × average glucose – 1.96 × (0.03618 – 0.1068 × average glucose) – 1.8799 – 1.96 × (0.03618) -01 1.96 ×.1068) × average glucose – 1.9508 to 0.4036 × average glucose If these limits do not exceed the maximum allowable difference between methods (average differences ± 1.96 SD are not clinically important), both methods can be considered consistent and exchangeable.
The simple 95% limits of the agreement method are based on the assumption that the average value and the standard deviation of the differences are constant, i.e. they do not depend on the size of the measurement. In our original documents, we described the usual situation where the standard deviation is proportional to size, and described a method using a logarithmic transformation of the data. In our 1999 review paper (Bland and Altman 1999), we described a method to avoid any relationship between the average and the SD of the differences and the size of the measurement. (It was Doug Altman`s idea, I can`t take recognition.) Especially for small sample sizes, the sample average and sample SD may not be close to the actual population average and SD.