Bridging Olink^® Explore 3072 to Olink^® Explore HT

Important Terminology

• Bridging samples – Overlapping samples run on two or more projects that are used as references to enable normalization. These samples are selected as described in the Introduction to Bridging tutorial to ensure samples are of high quality and span the range of the data. In the case of data containing LOD, samples are also filtered for high detectability. Bridging samples are selected from the project that is run first to run with the second project.

• Project – A set of plates that run at the same time and have been normalized together. If two projects are not randomized or are run at different times then additional normalization is required.

• Project effect/correction – As NPX is a relative quantification, overall NPX values may shift across projects. This can result in separation of projects that are part of the same study which can be corrected for using normalization or accounted for within a statistical model.

• Within-product bridging – Normalization of two or more projects run on the same Olink product using bridging samples

• Between-product bridging - Normalization of two or more projects from different Olink products (in this case, Olink Explore 3072 and Olink Explore HT) using bridging samples

• Reference data – The project data which is being normalized to is known as the reference data. In the case of between-product bridging, the reference project is the Explore HT NPX data. The reference data set is not altered during bridging and the other data set is adjusted to the reference data set using the bridging samples.

Within- and between-product bridging

The joint analysis of two or more NPX projects run on the same Olink product often requires a project correction step to remove technical variation. One such method of normalizing two projects is referred to as bridge sample reference normalization, bridge normalization, or just simply bridging. For more information on within-product bridging, see the Introduction to Bridging tutorial. Bridging makes certain assumptions on the distributions of the assays, namely that we are measuring the same true biological range no matter the setting. If an assay displays different distributions between projects, then both bridging and downstream statistical analysis will be affected. Within a product, we assume the variance and shape of the distribution remains constant within assays.

In the case where a study consists of separate projects run on Olink Explore 3072 and Olink Explore HT, an additional project correction step is required to allow data from these two products to be analyzed together, which is referred to as between-product bridging, or Olink Explore 3072 to Olink Explore HT bridging. Olink Explore 3072 and Olink Explore HT are both products that use PEA technology combined with next generation sequencing to calculate NPX for thousands of proteins. However, assays may vary more between products then within a product, and fewer assumptions can be made regarding the similarity of assay distributions and variance between products.

Since many of the assays profiled in Olink Explore 3072 are also found on Olink Explore HT, bridging data across products enables increased power in studies consisting of both Explore 3072 and Explore HT data sets, rather than limiting these studies to meta-analysis. However, differences between products, such as the number of assays being measured and the reagents being used, can sometimes lead to signal in one product and noise in another product. Bridging signal to noise can have detrimental effects on downstream statistical analysis. This means that while some assays will be able to be bridged using the same method as in within-product bridging, others will require a different normalization method, and some will not be bridgeable at all.This normalization strategy combines median-centering (as is used in within-product bridging) and quantile smoothing to normalize assays across products based on the assumption that assays can be bridged provided they have signal in both products or noise in both products.

Considerations for between-product bridging

Product bridging allows the NPX values of an Olink Explore 3072 project to be normalized and made comparable to the NPX values of an Olink Explore HT project. This process is one-directional, and normalizing Olink Explore HT NPX values to Olink Explore 3072 is not supported.

The product bridging normalization uses the ~2900 assays that are overlapping between Olink Explore 3072 and Olink Explore HT. Each overlapping assay undergoes a series of checks that evaluate the number of counts, correlation, and difference of NPX ranges between the two data sets. If an assay has enough counts and comparable metrics between the two data sets, it is determined to be suitable for bridging (referred to as a “bridgeable assay”). Assays that are not suitable for bridging can either be excluded from downstream analysis in one or both products or results can be integrated across products using meta-analysis. The set of bridgeable assays across products will vary from data set to data set, based on the samples present within the studies. Depending on the NPX distribution of each bridgeable assay in the two data sets, the assay is normalized using either median normalization or quantile smoothing.

Bridging an Explore 3072 data set to an Explore HT NPX data set requires 40 - 64 bridging samples. Bridging samples are shared samples among data sets and, as such, are analyzed in both data sets. Olink NPX data sets without shared samples cannot be combined using the bridging approach described below. More information on bridge sample selection can be found in the selecting bridging samples section of the Introduction to Bridging tutorial.

Determining bridging recommendations

For an assay to be bridgeable across products, it must either have signal in both products or be primarily background signal in both products. Bridging noise into signal or signal into noise can negatively impact downstream statistical analysis. To determine if an assay is bridgeable, the bridge samples from both products are used to assess the following criteria:

• Is there a linear relationship between products?
  • Assessing linearity across products: To determine if there is a linear relationship between products for an assay, the linear coefficient of determination (R²) is calculated using Pearson correlation. R² is a measure of how much of the variation in the data is explained by the linear function compared to just using the mean. In this correlation, counts below 10 are excluded due to lack of signal. The R² value is calculated and an assay is considered to have a linear relationship across products if the R² value is above the cutoff. A higher R² value indicates, that for both products, the assay is in the linear range. Conversely, a low R² means that either one or both assays are in background. The default cutoff is set to R² > 0.8 indicating that at least 80% of the variation in the data is explained by the linear function.
• Are the NPX ranges in the two products similar?
  • Assessing similarity of NPX ranges: To determine if the NPX ranges are similar across products, the difference in NPX values from the 10% to 90% quantile is calculated for each product, excluding data points with counts less than 10. If the difference in range of NPX between products is greater than the cutoff then the ranges are not considered similar across products. Since the NPX values are calculated on the same samples, it is expected that an increase in 1 NPX in one product would correspond to an increase of 1 NPX in the other product. If the ranges are not similar, this suggests that 1 NPX is not equivalent across products. By default, the cutoff is set to a difference of less than 1 NPX between products.
• Are there sufficient counts in both products?
  • Assessing if there are sufficient counts: An assay’s absolute level of counts is important to consider as the instruments used to generate NPX values have an inherent noise level. To determine if there are sufficient counts in an assay for bridging, the median number of counts in both products is calculated, excluding data points with less than 10 counts. If the median number of counts is less than the cutoff then the assay does not have sufficient counts to be used for bridging. The default cutoff is set to 150 counts, which is based on the count quality control metrics for Explore products.

For assays that are bridgeable, the shape of the NPX distribution is compared between the two products:

• Assessing similarity of NPX distribution across products: If the three criteria outlined above are met then the assay is considered bridgeable. Otherwise, bridging is not recommended for that assay. If an assay is bridgeable, the similarity of the NPX distribution is used to determine which method is recommended for bridging. The Kolmogorov-Smirnov test, or KS test, is used to assess the similarity of two distributions by calculating the KS statistic, which is based on the empirical cumulative distribution function (ECDF). Counts below 10 are excluded and the largest difference seen in the ECDF becomes the KS statistic. If the KS statistic is above the cutoff, the distributions are considered to have different shapes. In this case, a median shift is not sufficient to normalize the data, and quantile smoothing is recommended. If the distance is less than the cutoff, then normalization using the median of paired differences is recommended. By default this cutoff difference is set to 0.2.

An overview of these criteria is visualized below.

Criteria to determine the bridging recommendation for an assay. The assessment of linearity ensures bridging between signal in both platforms or noise in both platforms (but not between signal and noise). Similar NPX ranges and sufficient counts provide additional insight into an assay’s bridgeability. Distribution shape is assessed to determine recommended bridging method.

Prior to assessment, outlier bridging samples are excluded. A sample is considered an outlier if the NPX value is more than 3 times the interquartile range above or below the median on either product.

After assessment, an assay is considered bridgeable if it meets the first three criteria. The fourth criteria determines which normalization method is recommended for bridging. If all four criteria are met then the recommended method is normalization using the median of paired differences. If only the first three criteria are met then quantile smoothing is recommended. If any of the first three criteria are not met then bridging is not recommended for that assay. Note that bridgeable assays will differ between projects based on the expression of bridge samples in the studies.

Normalization using the median of paired differences

If it is expected that both the kind of distribution and the variance per test between runs are the same, then normalization using the median of paired differences will be preferred. Normalization using the median of paired differences based on the bridging samples is performed in the following steps:

1. For each assay in the Explore 3072 project, the pairwise difference is calculated for each of the bridging samples with the Explore HT project.

2. The normalization factor is estimated for each assay by finding the median of the pairwise differences.

3. The assay-specific normalization factor for each assay is used to normalize each data point from Explore 3072 to Explore HT.

Quantile smoothing

Since Explore HT and Explore 3072 are two distinct products with different workflows involved in generating NPX data, some of the assays exist in corresponding but distinct NPX spaces. For those assays, the median of paired differences is insufficient for bridging as it only considers one anchor point (the median/50% quantile). Instead, quantile smoothing (QS) using multiple anchor points (5%, 10%, 25%, 50%, 75%, 90% and 95% quantiles) is favored to map the Explore 3072 data to the Explore HT distribution. The normalization using QS uses bridging samples to perform the following steps:

1. Each data point of the samples from Explore 3072 is mapped to the equivalent space in Explore HT using an empirical cumulative distribution function. An empirical cumulative distribution function is a probability model which uses the observed data, in this case the NPX values of the bridging samples for an assay, to create a step function which interpolates linearly between the available data points.

2. The empirical distribution function is used to map the data points from Explore 3072 to the Explore HT space using the specified quantiles. At this point all data points from the bridging samples have NPX values that are normalized to the data points in Explore HT.

3. To normalize the remaining data, a spline regression model is constructed using the sorted Explore 3072 data (prior to mapping) and the mapped Explore 3072 data, along with the anchor points of the spline function. A spline regression model divides a data set at the quantiles and uses the quantile as an anchor point or knot. Then a model is generated to fit the points between each anchor point.

4. The spline regression model is then used to predict all the data points from Explore 3072 to Explore HT. The spline regression model results in a combination of linear regression models within intervals. The Explore 3072 NPX values are input as the x value within the corresponding interval, which results in a y value equivalent to the Explore HT NPX value.

Function Output

The output from olink_normalization() function when used for between product bridging is a dataframe with concatenated data from the two products and additional columns including adjusted NPX values, bridging recommendations, mapping information, and project names. The adjusted NPX values are notated in the columns MedianCenteredNPX and QSNormalizedNPX. For each assay a recommendation is listed in the BridgingRecommendation column and lists what method, if any should be used for that assay. Additional columns including OlinkID and OlinkID_E3072 map the assays across products and the Project column lists the name of the project based on the df1_project_nr and df2_project_nr arguments. The resulting data set will contain the newly bridged Explore 3072 data set. The reference Explore HT data will be concatenated to the Explore 3072 data. As the reference data is not altered during normalization, the normalized NPX values in the Explore HT data will be the same as the values in the NPX column which contains the non-normalized data.

Overlapping Assays within products

Both the Explore 3072 and Explore HT products contain assays that appear multiple times in the product, known as overlapping assays or correlation assays. In Explore 3072, these present as overlapping assays across panels. In Explore HT, these are overlapping assays across blocks. These assays are included for QC purposes and allow users to evaluate data performance across panels in Explore 3072 and across blocks in Explore HT. Within each product, the assays contain unique OlinkID values for each of their corresponding panels and blocks in Explore 3072 and Explore HT, respectively.

IL6, IL8 (CXCL8), and TNF are included in the Cardiometabolic, Oncology, Neurology and Inflammation panels, while IDO1, LMOD1, and SCRIB are included in the Cardiometabolic II, Oncology II, Neurology II and Inflammation II panels. Each correlation assay is measured four times in an Olink Explore 3072 run. In Explore HT, GBP1 and MAPK1 serve as overlapping assays and are measured three times in a run.

Downstream Analysis

Olink Analyze statistical analysis functions default to use the data in the NPX column. This means that if the resulting data from the olink_normalization() function is used in a downstream analysis function, then the non-normalized NPX data will be used. To use the recommended normalized data, dplyr::mutate() can be used to reassign the NPX data. Additionally, to ensure that overlapping assays within products are analyzed individually, OlinkID can be temporarily assigned to the concatenated version of the OlinkIDs. This dataframe can then be used in any downstream analysis function within Olink Analyze.

Assays which are not recommended for bridging should be analyzed separately and can be combined using a meta-analysis. Depending on the study design these assays can either be excluded from the downstream analysis or the assays can be treated as non-overlapping assays.

# Option 1: Exclude non bridgeable assays from both products
npx_recommended <- npx_after_br_final |> 
  dplyr::mutate(NPX_original = NPX) |> 
  dplyr::filter(BridgingRecommendation != "NotBridgeable") |>
  dplyr::mutate(NPX = case_when(
    BridgingRecommendation == "MedianCentering" ~ MedianCenteredNPX,
    BridgingRecommendation == "QuantileSmoothing" ~ QSNormalizedNPX,
    .default = NPX)) |> 
  dplyr::mutate(OlinkID_HT = OlinkID) |> 
  dplyr::mutate(OlinkID = paste0(OlinkID, "_", OlinkID_E3072))

# Option 2: Analyze non bridgeable assays separately
npx_recommended <- npx_after_br_final |> 
  dplyr::mutate(NPX_original = NPX) |> 
  dplyr::mutate(NPX = case_when(
    BridgingRecommendation == "MedianCentering" ~ MedianCenteredNPX,
    BridgingRecommendation == "QuantileSmoothing" ~ QSNormalizedNPX,
    .default = NPX)) |> 
  dplyr::mutate(OlinkID_HT = OlinkID) |> 
  dplyr::mutate(OlinkID = ifelse(BridgingRecommendation != "NotBridgeable",
                                 paste0(OlinkID, "_", OlinkID_E3072), 
                                 # Concatenated OlinkID for bridgeable Assays
                                 ifelse(Project == "Explore HT", 
                                        # replace with HT project name as set in function
                                        OlinkID, 
                                        OlinkID_E3072))