AMHconverter: an online tool for converting results between the different anti-Müllerian hormone assays of Roche Elecsys^®, Beckman Access, and Kangrun

Blood samples

For sample selection, we drew upon the previously reported distribution of AMH data from the Reproductive Centre of Peking University Third Hospital, as presented in Table 1. The samples were collected in reproductive endocrinology lab in our reproductive center. From November 2021 to February 2022, we randomly selected 300 serum AMH samples. The samples were obtained from women undergoing standard IVF at the hospital’s IVF centre, and subsequently stored at −80 °C. All patients provided their written informed consent for the anonymous donation of their residual serum for research purposes after the initial blood testing. Ethical approval for this study was granted by the Institutional Review Board of Peking University Third Hospital, approval number S2021543. The same sample was put through testing on three separate platforms: the Beckman and Kangrun platforms, both of which are located in the Reproductive Center laboratory, and the Roche platform, situated in the large laboratory of the hospital. All AMH assay results are reported in ng/mL.

Assay performance

Prior to the commencement of the study, the precision and accuracy for each assay were carefully evaluated in compliance with the Clinical and Laboratory Standards Institute EP15-A3 (Clinical and Laboratory Standards Institute (CLSI) (2014)). Quality control sera supplied by the manufacturers (control 1 and 2 for Kangrun; PreciControl AMH 1 and 2 for Elecsys^®; and controls 1, 2 and 3 for Access) were used for this purpose and each control for each assay was tested consecutively four times a day for a period of five days.

For each sample, two tubes of serum were frozen; one of which was thawed and tested on the Roche platform, while the other was thawed and tested on the same day using the Kangrun and Beckman platforms. When results exceeded the upper measurement range of any of the methods, the serum samples were automatically diluted with reagents provided by the manufactures and analysed again. The Roche Elecsys^® AMH immunoassay was run on the Roche Cobas e801, the Beckman Access AMH assay on the Beckman Coulter DxI 800, and the Kangrun AMH assay on the Kaeser6600. Respectively, these three AMH assays had linear detection ranges of 0.02–24 ng/ml, 0.01–23 ng/ml, and 0.06–18 ng/ml.

Statistical analysis

Assuming a global relationship between the Beckman, Kangrun, and Roche assays, which means that there is an algorithm that fit the full detection range of AMH concentration, a Passing–Bablok regression was employed in order to determine the conversion equation between the respective pairs. This nonparametric method was used to calculate the parameters ‘a’ and ‘b’ for the linear equation y = a+bx. The 95% confidence interval of the intercept ‘a’ and the slope ‘b’ were then checked to assess for any systematic or proportional differences between the two AMH assays.

In case of a local relationship, a spline regression was performed to obtain the conversion formula. This piecewise polynomial function is smoothly connected at the nodes, and, as per the relationship established between the independent and dependent variables in this study, a linear spline regression was used, resulting in a linear regression with smooth connections at the nodes. Quality controls provided with the AMH kits were used to evaluate the detection values, with deviations from the target value expressed as bias. The acceptable criteria for the total error, bias, and coefficient of variance were set at ±25%, ±12%, and ≤8%, respectively.

To evaluate systemic bias and heterogeneity of variance across different ranges of values, a Bland–Altman plot was created. Model fitting effects were then assessed using the squared coefficient of determination (r²), adjusted r², root mean square error (RMSE), Akaike information criterion (AIC), and corrected AIC (AICc). The higher the r² and adjusted r², the better the model performance, while the lower the RMSE, AIC, and AICc, the better the fitting effect. All statistical analyses were conducted using JMP PRO v. 16.0 (Cary. NC, USA).

Passing–Bablok regression among the three AMH assays

Assuming that the Roche and Kangrun AMH assays fit a global relationship, Passing–Bablok regression was utilized to construct a linear relationship between the two assays. Figure 1A shows the fitting results. In Fig. 1A, the dashed line illustrates the ideal perfect agreement between the two AMH assays, and the blue line is the Passing–Bablok regression. As seen in Fig. 1A, the blue line diverges from the dotted line; this disparity needs to be statistically assessed.

The Bland–Altman plot was used to explore the agreement between two AMH assays. As shown in Fig. 1B, the horizontal axis denotes the mean of Kangrun and Roche measurements, while the vertical axis reflects the difference between Kangrun and Roche measurements. The grey solid line in Fig. 1B is the reference line, denoting 0 value (representing the mean difference value of 0 between two AMH platforms); the red solid line and red dotted line indicate the mean and 95% CI of Kangrun minus Roche AMH measurements. The grey dotted line stands for the 95% distribution range of the difference (mean ± 1.96× standard deviation), commonly known as the limit of agreement. Generally speaking, the closer the red solid line to the reference line, the more consistent the two measurements. If 95% of the points are located within the dashed grey line and follow a normal distribution around the red solid line, then it can be concluded that these two AMH assays are consistent. In this study, 8.5% of observations exceeded the grey line. The points exceeding the consistency limit showed that Kangrun measurements were greater than Roche measurements, and the distribution was evidently non-normal, particularly the high-value part. Consequently, it cannot be assumed that these two AMH assays are consistent.

Figure 1C shows a mountain plot, with the abscissa indicating the value of Kangrun minus Roche and the ordinate indicating the percentile of the cumulative distribution. When the cumulative distribution probability is below 50%, this is the cumulative distribution probability, whereas when it is above 50%, it is 1 −cumulative distribution probability. If the two AMH assays are consistent, they should centered around 0 and display a symmetrical distribution. As can be seen in Fig. 1C, ‘Kangrun −Roche’ shows a right- skewed tail, indicating that the difference between Kangrun and Roche is mostly greater than 0, and the right tail is long, suggesting that some points of ‘Kangrun −Roche’ are very high. Nevertheless, when the cumulative distribution was less than 50%, there was only a small difference between the two AMH assays.

The intercept converting AMH from Roche to Kangrun was −0.0124, with its 95% CI including 0, indicating that there is no systematic difference in AMH values between Kangrun and Roche assays. The slope was 1.1517, and the 95% CI did not include 1, suggesting a possible proportional difference between the two AMH assays. Using Passing–Bablok regression, we performed other pairwise transformations among the three AMH assays. The results of the pairwise transformation between the three AMH assays are depicted in Figs. 1D–Figs. 1I and summarized in Table 3, while the converted data of the 6 selected samples can be found in Table 4 (with details in Table S1).

Spline regression

Passing–Bablok regression supposes that the correlation between two AMH assays is not a local relationship. However, as Table 3 demonstrates, in the four conversions with 95% CI of intercepts that do not include 0, the fitting effect of the low-value part appears to be unsatisfactory, implying a potential local relationship between each pair. Therefore, spline regression was conducted.

Taking the Roche to Beckman AMH assay for an example. The value obtained from Roche measurement was taken the independent variable x, while the value obtained from Beckman measurement was taken as the dependent variable y. Based on the relationship between the independent and the dependent variable in our data, linear spline regression was used to construct a linear regression with smooth connections at the nodes. A selection of nodes was based on the principal that the smaller the variation, the better the formula, as indicated by the scatter plot and the actual distribution of AMH values in our data. Therefore, two nodes of ‘1 ng/mL’ and ‘9 ng/mL’ were chosen. Table 5 shows a comparison of the fitting effects between spline regression and Passing–Bablok regression. It was evident that the RMSE, AIC, and AICc of spline regression were lower than those in Passing–Bablok regression, while the r² and adjusted r² were higher than those in Passing–Bablok regression.

Table 6 reveals the transformed values of AMH platforms with intercepts not containing 0, including the results of spline regression and Passing–Bablok regression; all converted data are presented in Table S2. It is evident that, while the overall difference between spline regression and Passing–Bablok regression is small, the lower-value is evidently better when using spline regression. For the mutual conversion between Roche and Kangrun with the intercept including 0, both spline regression and Passing–Bablok regression have satisfactory fitting outcomes in the low-value part. The formula based on Passing–Bablok regression for the Roche–Kangrun conversion is preferred due to its simplicity. Table S2 shows the converted values using spline regression and Passing–Bablok regression among the three platforms. We have also set up an online tool for AMH assay conversions (http://121.43.113.123:8006/). Therefore, for conversions with intercepts not including 0, the spline regression formula was adopted, and for conversions between Roche and Kangrun with intercepts containing 0, the Passing–Bablok regression formula was utilized.

Limitations

Although we proposed novel concepts for platform conversion in this study, this research has some restrictions. First, all our sample tests were completed within 2–3 days. Reagents with the same calibration and the same batch number were utilized; yet, when reagents with disparate calibrations and different batch numbers are taken into consideration, bias may occur. In the future, the parameter estimates of the formula should be further defined using bigger validation datasets, thus making the formula have a more extensive applicability. Moreover, we also used different quality control products provided within each individual AMH kit. If distinct commercially available AMH assays used the same third-party AMH quality control products, this could aid in the comparability among the different AMH assays.