## Material and Methods
### Luminex Multiplex SAB Assay
#### 2.2.4 Modifications in the Assay Protocol for Comparing the Different SABs  
To remove the protocol differences between the vendors as a confounding variable, we used the LS vendor protocol (using 2 \(\mathrm{\SIUnitSymbolMicro L}\) of beads instead of 5 \(\mathrm{\SIUnitSymbolMicro L}\)/test, a standard procedure at Terasaki Foundation Laboratory (TFL) and Terasaki Research Institute (TRI)). To keep the number of beads consistent, the LC-SABs were spun down to remove 835 \(\mathrm{\SIUnitSymbolMicro L}\) of the fluid volume from the stock to concentrate their beads (the initial volume of LC beads is 960 \(\mathrm{\SIUnitSymbolMicro L}\)). The final volume of the SABs from both vendors is therefore maintained at 125 \(\mathrm{\SIUnitSymbolMicro L}\). Our standard operating procedure (SOP) was extensively used at TFL and we had obtained concordant results when performing proficiency testing for the UCLA serum exchange program. While designing the assay, we kept the antibody-to-bead ratio consistent between the vendors. For the assay, neat sera were avoided. The sera (20 \(\mathrm{\SIUnitSymbolMicro L}\)) were diluted (1/10) and then incubated with 2 \(\mathrm{\SIUnitSymbolMicro L}\) of beads (for both LS and LC) for 30 min at room temperature (RT) on a shaker. The beads were then washed (3\(\times\)) with LS wash buffer. The Ab binding to beads was assessed with two PE-conjugated secondary Abs (see below) by incubating the detection Ab (50 \(\mathrm{\SIUnitSymbolMicro L}\) at 5 \(\mathrm{\SIUnitSymbolMicro L}\)/mL) for 30 min at RT on a shaker. After washing, the beads were suspended in 1\(\times\) PBS before acquisition on the Luminex platform. At least 100 beads were counted for each antigen for the SAB from different vendors. On the rare occasion that any variation occurred in the bead count, it was <5%. The assay includes a positive control bead (coated with human IgG) and a negative control bead (no antigen). In addition, we have used negative control serum (demonstrated by other methods considered to be free of anti-HLA IgG) as well as positive control serum, prepared by the vendor by pooling sera from several individuals carrying anti-HLA IgG.  
In this investigation, we have recorded MFI after normalizing the trimmed mean MFI. Since we are comparing MFIs of different SABs with potentially differing composition panels (LS with CC admixed with OC and LC with CC only), we normalized as follows:  
1. We subtracted MFI of PBS only from trimmed MFI. This is an essential step because when antibodies were tested on beads with PBS alone, differential MFI values were observed with different HLA molecules.
2. We used (trim mean MFI-PBS MFI) to subtract the following:  
1. Negative control MFI (NC MFI);
2. Negative sera value obtained with LS-SABs (NGS-LS);
3. Negative sera value obtained with LC-SABs (NGS-LC);
4. B and C were added and divided by 2 for correction.  
The following formula explains the steps used:  
Normalized MFI = [(Trim. Mean MFI \(-\) PBS MFI) \(-\) (NC MFI)] \(-\) (NGS-LS-SABS+ NGS-LC)/2).  
These steps are critical for comparing the two different kinds of SABs and very useful for considering the diverse composition of the panels and the different frequencies of the target epitopes on the beads. In the above protocol, no background noise was observed for any secondary antibody, whether _IgHPolyFab_ or _FcMonolgG_. Note that the protocol considers, while calculating normalized trimmed means, the factors that may cause background noise, such as PBS alone or negative controls.