Objectives: Patient serum for anti-HLA antibodies are tested with purified antigens covalently affixed to beads as targets. Serologic nomenclature from the World Health Organization (WHO) is currently used to specify the reactivity of antibodies, although target antigens are defined at a finer allelic level. We investigated whether different reactivity patterns could be present at the allele level of a single WHO serologic antigen.
Materials and Methods: We analyzed 2389 serum samples from 1215 patients waiting for solid-organ transplant by using class II single antigen beads for detection of HLA antibodies. We used principal component analysis to identify unique antibody reactivity patterns against the beads. We particularly focused on patterns within a WHO antigen that suggested the presence of new serologic class II HLA specificities. We used the HLA DQ7 data to illustrate the principle of the discovery methodology. Four assay target beads representing different DQA1 alleles were classified as DQ7.
Results: Two principal components accounted for about 98.6% of the DQ7 data variance. The dominant principal component, which accounted for 83.9% of the variance, represented a reaction pattern in which sera reacted equally with all 4 beads. The second principal component (14.7% of the variance) represented sera that reacted selectively with DQA1*03:01, DQB1*03:01. Four of 10 DR and 6 of 7 DQ WHO serologic specificities that were studied showed more than 5% nonconcordant patterns revealed by principal component analysis.
Conclusions: Principal component analysis revealed differential reactivity patterns of the alleles of single WHO serological specificity. This method could be a powerful tool for identifying patterns of reactivity, which may represent new serological specificities.

Key words : Antigen beads, HLA antibody testing, Solid-organ transplant

Introduction
Transplant candidate and recipient sera are often tested for antibodies against HLA antigens representing a single allele bound to beads as targets. World Health Organization (WHO) serologic nomenclature is used to specify antibodies. Advances in high-resolution molecular HLA typing techniques and identification of antibodies against these antigens using solid-phase single antigen assays^1-3 might permit analysis of patterns of serologic reactivity against allelic variants within currently defined WHO serologic specificities. The identification of such patterns involves inspection of large data sets whose patterns cannot be readily appreciated by traditional analytic techniques. Here, we explored a statistical method, principal component analysis (PCA), to systematically search for unique patterns of serologic reactivity that could represent new candidates for serologically defined antigens. The aim of our study was to look for unique serological reactivity patterns among serum samples from transplant candidate tested with HLA class II single antigen beads. We applied PCA to analyze these data. The findings of the sera reactive with DQ7 single antigen beads were used to demonstrate the methodology, although all 2389 sera were analyzed for other class II HLA antibodies in the same manner.

Materials and Methods
This study was approved by the Mass General Brigham Institutional Review Board (Protocol No. 2025P002064). We performed a retrospective analysis of 2389 serum samples derived from 1215 patients who were waiting for solid-organ transplant between 2009 and 2010 and who underwent screening for HLA antibodies for routine clinical purposes. HLA antibodies were detected with the use of LabScreen Single Antigen Class II assay (One Lambda), consisting of beads coated with class II HLA antigens, and analyzed on a solid-phase antigen detection system (Luminex). The assay is an enzyme-linked immunosorbent assay in which the beads are incubated with the patient serum, washed, and then incubated with a fluorescent anti-human immunoglobulin to quantitate anti-HLA antibody bound to the beads. We evaluated baseline normalized median fluorescence intensities (MFI) consisting of the raw data minus a normal serum control by using JMP 11 Pro software (SAS Institute). For the WHO HLA-DQ7 antigen, 5 individual beads were used to represent 5 distinct HLA-DQ7 heterodimers in the assay lots. However, 1 bead was subsequently removed from the kit by the manufacturer because of spurious results. We omitted this bead from our analysis. The remaining 4 analyzed beads had a common DQB1*03:01 but differed in the DQA1 as follows: DQA1*05:05, DQAl*06:01, DQAl*05:03, and DQA1*03:01. We will subsequently refer to the 4 DQ7 beads by the shorthand of their DQA1 designation. Principal components (PCs) are constructed as a new set of ordered variables that have the following characteristics: they account for all of the variance of the original data so that information is not lost. The PCs are mutually uncorrelated or orthogonal. In consequence, original variables that are correlated are collapsed into one of the PCs. The order of the PCs is based on the percent of the data variance accounted for, with the first PC (PC1) accounting for the most variance. In the present study, we used this method to identify heterogeneous patterns of serological reactivity between the allelic variants of WHO class II antigens.^4-6 The methodology consisted of the following steps. First, MFI data for all sera were downloaded into a CSV file, which were then imported into a JMP data table for analysis. The “multivariate” platform was used to generate n × n correlations between MFI for the individual beads. The PC platform, accessed through a graphic user interface, allowed menu-driven analysis of Eigenvalues, Eigenvectors, and loading plots. Second, we used generation and inspection of scatterplots of the MFI of sera against the beads to subjectively determine whether heterogeneity was present in the data. Third, we conducted computation of the PCs and the associated Eigenvalue or proportion of variance that each one encompassed. The PCs that cumulatively accounted for 98% of the data were retained. Fourth, we conducted generation and inspection of the Eigenvectors for each PC for which component coefficients revealed which combinations of original variables were the dominant contributors to each PC. Fifth, we labeled each serum as belonging to one of the PCs by cluster analysis constrained to the chosen number of PCs, which were mapped onto the original scatterplots.

Results

Inspection of scatterplot correlation matrices
The first step was to generate a set of scatterplots displaying the MFI of each bead against the others for all sera tested. This step permitted a visual display of the correlation between beads and a subjective assessment of variability of reactivity between the beads and sera. Any substantial heterogeneity of the data could represent differential antibody reactivity with the allelic variants. Figure 1 shows the MFI of all sera with each DQ7 bead versus the other beads. Closely correlated reactivity of sera with any 2 beads yielded a cluster of points on the diagonal (corresponding to a line of fit of r² = 1) that dominated the scatterplots, particularly as shown with DQAl*05:03, DQA1*05:05, and DQA1*06:01 compared with each other (Figure 1, boxes 1-3). Clusters of sera were shown that reacted selectively with one or more beads. An example is seen in Figure 1, boxes 4 to 6 (DQA1*03:0l vs the other 3 beads), where there appears to be a distinct subset of sera that reacted selectively with DQA1*03:0l but not with the other DQA1 beads within the broader DQ7 WHO specificity. This pattern was unlikely to be just variance from the diagonal, as it is spatially separated from the sera on the diagonal in the 2-dimensional plot.

Computation of the principal components and the associated proportion of variance
An important aspect of PCs is that they are uncorrelated or “orthogonal” to each other in multidimensional space. This aspect maximizes the likelihood that PCs represent distinct “features” of the data. Although the number of PCs is, by default, equal to the number of original variables (4 for DQ7), those PCs that account for only a small percent of the variance can be eliminated, thereby simplifying subsequent analysis and pattern recognition. Each PC is associated with an “Eigenvalue,” a number that is proportional to the percent of data variance accounted for by that PC. Table l shows the 4 Eigenvalues associated with the 4 original PCs derived from the DQ7 data. The first and second principal components (PC1 and PC2) accounted for almost 99% of the observed variance. The first PC explained 83.9% of the variability of data, the second PC explained 14.7% of the variance, and the third accounted for just 1.1% of the variance. Principal component 4 was excluded from further analysis because it accounted for only 0.02% of the variance. Determining patterns of serological reactivity within DQ7 Because the PCs are constructed to be “orthogonal” to each other in multidimensional space, the PCs represent unique patterns in the data. An explanation of how the original variables relate to these patterns can be discerned by inspecting the Eigenvectors (Table 2). Eigenvectors are a series of coefficients used to convert the original data, which is the MFI of sera versus the beads, into new variables representing the reactivity of the sera versus PCs via a linear transformation equation. The magnitude and sign of these coefficients can be inspected to discover which original variables (beads) contributed most to the unique features represented by each PC. It is possible to scan down the column representing each PC Eigenvector and to see, by the magnitude and sign of the coefficients, which combination of original variables contributed most to that PC. Table 2 shows the Eigenvectors that are associated with each of the 3 most important PCs. One can readily appreciate that the dominant PC1 represented sera where each of the 4 beads is weighted similarly. Principal component 1 showed the classic WHO DQ7 specificity expressed on all of the beads. The second, PC2, represented sera that reacted differentially with DQAl*03:01, with noted positive weight of 0.91387 versus the negative weights of the other alleles in the PC2 column. The third, PC3, represented only 1.1% of the variance, and there was a minor effect possibly attributable to reactivity with DQA1*06:01.

Graphic illustration of bead weights by principal component
Figure 2 shows the “loading plots” of the original bead variables (MFI vs the different DQ7 variants) projected onto the 3 PCs that accounted for virtually all of the data. The vectors represented the 4 original variables or reactivities with the 4 DQ7 beads. The projection of a given vector onto a particular PC axis was a function of the weight of that original variable contribution to the PC. Boxes 1 and 2 in Figure 2 show that the contribution of the original variables to PC1 was proportional to the x-axis component of the vectors; that is, all 4 beads contributed equally to PC1 (x-axis). Boxes 1 and 3 in Figure 2 show the contributions of the original variables to PC2. In box 1, the DQA1*0301 is clearly different from the other 3 alleles (y-axis projection). The same is true for box 3, where the DQA1*0301 diverges from the other alleles and where it contributes more to PC2.

Cluster analysis of sera in the original scatterplot
Because the values of the PCs reflect the unique pattern for a given serum and are uncorrelated, the PCs can be used to classify each serum as dominant for a particular PC. An easy way to do this is to cluster the sera based on similarity of the PC data, to constrain the number of clusters to equal the number of PCs, one wants to visualize in the primary data (3 in the case of DQ7) and to label each serum as belonging to 1 of the 3 clusters. This can then be represented on the original data matrix by color or marker to confirm the original subjective impression of distinct groups of serological reactivities (Figure 3). We applied the same methodology described for DQ7 to all the other class II WHO specificities (Table 3).

Bias analysis and validation
We noted that, because a number of patients had multiple samples obtained over time for antibody testing, our results could be biased. Therefore, we repeated our analysis using just the first sample obtained for each of the patients. No significant differences in the results of the analysis were shown with this subset of data. We also performed the same analysis using a completely new dataset of 2386 samples, with just 1 sample tested per patient, in a period of 18 months following our initial analysis (validation cohort). The results of the analysis with the confirmatory dataset were concordant with the initial dataset analysis.

Discussion
Our results identified a subset of patient sera that reacted selectively with one or more alleles within a WHO serologic specificity, as previously described by others.^1,2,7,8 The extremely large amount of data generated by single antigen bead multiplex assays defies classical analytic techniques such as χ2 analysis, which is routinely used in “tail” or “split” analysis of serum specificity.⁹ The clinical implications include donor selection, definition of unacceptable HLA antigens, need for desensitization, and wait time for transplant.^1,2,10 The large amount of data generated with the single antigen multiplex assay calls for novel methods of exploratory data analysis to identify candidates for further study. Multivariate statistical methods, including PCA, factor analysis, and cluster analysis, allow not only the measurement of simple associations between 2 parameters but also allow exploration of arbitrary relationships in multivariate data.^11-13 These methods have been used in several fields in immunology and infectious diseases such as the study of cytokines and antibody response to some parasites, genetic analysis,^14-16 microarray experiments,¹⁸ and genome-wide association studies.¹⁸ Principal component analysis is an exploratory multivariate statistical technique that permits reducing the number of variables to those that account for most of the variance. The PCs are a new set of calculated variables that are linear functions of the original variables.^4-5,18 Because these PCs are constructed so that they are not correlated with each other, each represents a unique feature of the data. The nature of these unique features can be appreciated by inspecting the respective Eigenvectors of the PCs that contain informative sets of coefficients. Visualization of the data is crucial as an initial stage in identifying the patterns of reactivity of the different alleles within a single WHO antigen.¹¹ Principal component analysis of antibody reactivities against DQ7 alleles revealed at least 3 distinct reactivity patterns, with PC1 capturing variance attributable to antibodies broadly reactive against all DQ7 alleles and PC2 distinguishing antibodies preferentially targeting DQA1*03-bearing alleles (positive loadings) from those preferentially targeting DQA1*05-bearing alleles (negative loadings). Using the same methodology, we analyzed the patterns of reactivity of antibodies against other HLA class II alleles where there were several analyte target beads with different alleles represented. The PCA showed several distinct patterns of reactivity within single serologically defined WHO antigens. These patterns may correspond to different specificities within the same antigen.

Conclusions
Principal component analysis is a powerful tool to analyze a large number of serological reactions and can be used to detect potentially new serological specificities that may yield new WHO antigen definitions. Such polymorphism of antibody reactivity could account for some of the false positive and false negative reactions noted in solid-state screening versus cell-based crossmatch in the clinical setting and may have important clinical implications. The serological reactions from solid phase bead reactions would need to be validated using antigens naturally expressed on the cell surface or by tests in which selective absorption with beads or cells are performed. Discordant reactivity among multiple beads representing WHO specificity could be either due to random variation or due to true biologic phenomenon of selective activity with specific alleles. This methodology demonstrates the likelihood that there is real biological variability in serum reactivity with different alleles.