15  Coefficients of Variation

15.1 Overview

This protocol can be used to calculate the inter- and intra-assay variation. It can be performed repeatedly on different days or by different operators to provide a measure of variation.

This protocol measures how consistent an assay’s results are:

  • Intra-assay variation is variation within the same run

    • (e.g., running the same samples multiple times in one experiment).

    • This tells you the precision of the assay in a single test session.

  • Inter-assay variation is variation between different runs

    • (e.g., same samples tested on different days or by different people).

    • This tells you the reproducibility across time and operators.

By performing the assay repeatedly under these conditions, you can quantify both types of variation, usually as a coefficient of variation (CV%) to confirm reliability. CV measures percentage variation in the estimate of the analyte concentration compared to the mean of all results.

\[ \mathrm{CV\%} = \frac{\sigma}{\mu} \times 100\quad\text{where}\quad\sigma = \sqrt{\frac{\sum_{i=1}^n (x_i - \mu)^2}{n - 1}}, \;\mu = \frac{\sum_{i=1}^n x_i}{n} \]

The protocol was run here using anonymous DBS samples and recombinant protein standards.

15.2 Reagents, consumables & equipment

  1. General Assay Buffers as per buffers & reagents section.

  2. Capture and detection antibodies and recombinant protein standards as per the respective protocols.

  3. Coupled and confirmed beads as per the respective protocols.

Table 1. Lab worksheet to record batch dates and reagents. Supplier is bio-techne unless specified.

Antibody on bead Bead Ab conc (µg/millionbeads) Bead region Date beads coupled Antigen Detection Ab Detection Ab (µg/mL)
CRP MAB17071 5 12 n/a 1707-CR BAM17072 1
IL8 M801 (Thermo) 5 22 208-IL BAF208 1.5
sTNF-R1 MAB225 6 20 636-R1 BAF225 1.5
IL6 MAB206 5 21 206-IL BAF206 1
Ang2 NB110-85467 5 15 623-AN BAF623 1
Ang1 MAB9231 5 18 923-AN BAF923 1.5
TRAIL MAB375 6 25 375-TL BAF375 1
IL10 MAB2172 4 26 1064-IL BAF217 1.5
sTREM1 H00054210-M04 6 14 1278-TR BAF1278 2
IP-10 MAB266 5 29 266-IP BAF266 1
Azu NBP2-12045 7 27 2200-SE AF2200+B 1.5
MxA MA5-24914 (Thermo) 6 28 TP307418 (OriGene) AF7946+B 1
CHI3L1 MAB25991 4.5 30 2599-CH BAF2599 1

15.2.1 Samples

  • DBS samples 1-4 from 4 different individuals

    • DBS1, DBS2, DBS3, DBS4

  • Spiked DBS made with healthy human blood spiked with the recombinant protein antigens at high, medium, low and zero levels

    • High DBS, Med DBS, Low DBS, Blank DBS

      • spiked analyte activity identical to standards 1, 3, 6 and 8, respectively.

  • Recombinant protein standards 1-8 in PBS-TBN

    • Std1, Std2, Std3, Std4, Std5, Std6, Std7, Std8

15.2.2 Experimental Design : Intra-assay CV

  • Twelve within-plate repeats of pooled DBS eluate (DBS1-DBS4) were run on plate 1

  • Twelve within-plate repeats of the spiked DBS (High DBS, Med DBS etc) were run on plate 1

  • Twelve within-plate repeats of the protein standards (Std1-Std8) were run on plate 2

    N.B. This protocol was carried out when the CRP assay was still part of the multiplex. It has since been removed.

    15.2.2.1 Plate 1 Layout (Intra-assay)

1 2 3 4 5 6 7 8 9 10 11 12
A DBS1 DBS1 DBS1 DBS1 DBS1 DBS1 DBS1 DBS1 DBS1 DBS1 DBS1 DBS1
B DBS2 DBS2 DBS2 DBS2 DBS2 DBS2 DBS2 DBS2 DBS2 DBS2 DBS2 DBS2
C DBS3 DBS3 DBS3 DBS3 DBS3 DBS3 DBS3 DBS3 DBS3 DBS3 DBS3 DBS3
D DBS4 DBS4 DBS4 DBS4 DBS4 DBS4 DBS4 DBS4 DBS4 DBS4 DBS4 DBS4
E High DBS High DBS High DBS High DBS High DBS High DBS High DBS High DBS High DBS High DBS High DBS High DBS
F Med DBS Med DBS Med DBS Med DBS Med DBS Med DBS Med DBS Med DBS Med DBS Med DBS Med DBS Med DBS
G Low DBS Low DBS Low DBS Low DBS Low DBS Low DBS Low DBS Low DBS Low DBS Low DBS Low DBS Low DBS
H Blank DBS Blank DBS Blank DBS Blank DBS Blank DBS Blank DBS Blank DBS Blank DBS Blank DBS Blank DBS Blank DBS Blank DBS

15.2.2.2 Plate 2 Layout (Intra-assay)

1 2 3 4 5 6 7 8 9 10 11 12
A Std1 Std1 Std1 Std1 Std1 Std1 Std1 Std1 Std1 Std1 Std1 Std1
B Std2 Std2 Std2 Std2 Std2 Std2 Std2 Std2 Std2 Std2 Std2 Std2
C Std3 Std3 Std3 Std3 Std3 Std3 Std3 Std3 Std3 Std3 Std3 Std3
D Std4 Std4 Std4 Std4 Std4 Std4 Std4 Std4 Std4 Std4 Std4 Std4
E Std5 Std5 Std5 Std5 Std5 Std5 Std5 Std5 Std5 Std5 Std5 Std5
F Std6 Std6 Std6 Std6 Std6 Std6 Std6 Std6 Std6 Std6 Std6 Std6
G Std7 Std7 Std7 Std7 Std7 Std7 Std7 Std7 Std7 Std7 Std7 Std7
H Std8 Std8 Std8 Std8 Std8 Std8 Std8 Std8 Std8 Std8 Std8 Std8

15.3 Experimental Design : Inter-assay CV

  • On each of six plates, single replicates of all specimens (Pooled DBS, Spiked DBS, Standards)

15.3.0.1 Plate 3-8 Layout (Interassay)

1 2 3 4 5 6 7 8 9 10 11 12
A DBS1 Std1
B DBS2 Std2
C DBS3 Std3
D DBS4 Std4
E High DBS Std5
F Med DBS Std6
G Low DBS Std7
H Blank DBS Std8

15.4 Protocol

⌚ Timing: 1-2 hours to prepare prior to assay day, about 6-7 hours on assay day, including incubations.

  1. Eluting DBS samples: The day before assay day, prepare elution buffer with 1 mL of 25X protease inhibitor plus 24 mL PBS-TBN. In 8 x 5 mL tubes, add 20 DBS to each tube of the individual donor and spiked DBS. Add 1 mL elution buffer to each tube and incubate overnight at 4C.

  1. On assay day, get coupled beads from fridge, vortex and sonicate for 30 sec of each.

  2. Dilute beads: add 14.183 mL of PBS-TBN to a universal. Total final volume after addition of beads, will be 14.7 mL. (14.7 mL minus 517.4 µL) (288 wells, 3 plates’ worth x 50 ul = 14.4 mL)

  3. Vortex bead stocks again immediately before pipetting and add ____ µL of each bead to the tube (to get 20k beads/mL [ie 1000 beads/well] based on stock of ____x106 beads/mL). Tick as you add the beads:

    €Ang1

    €Ang2

    €Azu

    €IL-6

    €IL-8

    €IL-10

    €IP-10

    €CHI3L1

    €MxA

    €sTREM1

    €sTNFR1

    €TRAIL

  4. Label 8 black plates with plate number, date, etc.

  5. Add 50 µL of diluted beads to all required wells, as per plate layouts:

  6. Wash the beads once: put plate on magnet, wait 60 sec, flick out liquid, remove from magnet, add 100 µL PBST to each well, back on magnet 60 sec, flick out liquid, bang gently on tissue.

  7. Vortex the eluted DBS samples.

  8. Thaw, vortex & pool the buffer standards. Mix again before dispensing.

  9. Add 30 µL/well of standards and RBC-DBS eluate to respective wells.

  10. Add 30 µL/well of PBS-TBN+pi as standard 8.

  11. Cover and incubate on gentle shaker for 120 mins. Record start time:______________

  12. During the incubation, prepare biotin detection antibodies for 3 plates. The excess can be stored frozen for future use.

  13. Wash the plates 3 times with PBST as before.

  14. Add 30 µL per well of the detection antibody mix to all used wells.

  15. Cover and incubate, shaking, for 1 hour.

  16. During incubation, prepare SA-PE at 3 µg/mL by adding ___TBC___ µL of SA-PE stock (1 mg/mL) into ___ TBC__mL PBS-TBN.

  17. Wash plates 3 times with PBST as before.

  18. Add 30 µL per well of the diluted SA-PE to all used wells.

  19. Cover and incubate, shaking, for 45 minutes.

  20. Wash plates 3 times with PBST as before.

  21. Add 100 µL PBS-TBN to each well, cover and refrigerate overnight.

  22. Read plates on MagPix first thing the next day.

    Example data analysis using real data is given below.

15.5 Analysis & interpretation of results

15.5.1 Libraries

library(readxl)
library(dplyr)
library(reshape2)
library(flextable)
library(tidyverse)
library(kableExtra)

15.5.2 Intra-assay CV Estimation

# Helper function to calculate CV table for a given data frame
calc_cv <- function(data, keep = NULL) {
  if (!is.null(keep)) data <- data[keep, ]
  
  data %>%
    group_by(Sample, Assay) %>%
    summarise(
      n = n(),
      mean = mean(MFI, na.rm = TRUE),
      sd = sd(MFI, na.rm = TRUE),
      CV = 100 * (sd / mean),
      .groups = "drop"
    ) %>%
    group_by(Assay) %>%
    summarise(CV = mean(CV, na.rm = TRUE), .groups = "drop")
}

# Read and reshape a plate CSV
read_plate <- function(file, assay_cols) {
  read_csv(file, skip = 41, show_col_types = FALSE,name_repair = "universal") %>%
    slice(1:96) %>%
    mutate(across(3:16, as.numeric)) %>%
    pivot_longer(
      cols = {{ assay_cols }},
      names_to = "Assay",
      values_to = "MFI"
    )
}

# Process plates
p1 <- read_plate("data/cv/INTRAASSAY_CV_plate_01.csv", CRP:CH3L1)
p2 <- read_plate("data/cv/INTRAASSAY_CV_plate_02.csv", Ang.1:TRAIL)

# Calculate CVs
# Works without NSE issues:
pooled_dbs_results <- calc_cv(p1, str_starts(p1$Sample, "DBS")) %>% rename("Intra_CV_Pooled_DBS"=CV )
spiked_dbs_results <- calc_cv(p1, !str_starts(p1$Sample, "DBS")) %>% rename("Intra_CV_Spiked_DBS"=CV )
recombinant_results <- calc_cv(p2)  %>% rename("Intra_CV_Standards"=CV ) # no filter

# Combine into one table
CV_table_intra_assay <- pooled_dbs_results %>%
  left_join(spiked_dbs_results, by = "Assay") %>%
  left_join(recombinant_results, by = "Assay")

# Display
kable(CV_table_intra_assay,digits = 2)
Assay Intra_CV_Pooled_DBS Intra_CV_Spiked_DBS Intra_CV_Standards
Ang.1 6.82 5.48 12.59
Ang.2 5.53 6.32 9.38
Azu 3.75 4.31 7.50
CH3L1 5.41 2.62 4.21
CRP 4.72 1.75 8.96
IL.10 5.84 4.60 8.06
IL.6 4.28 6.33 6.41
IL.8 5.55 8.32 7.89
IP.10 6.38 6.80 7.56
MxA 4.50 5.18 5.84
TRAIL 5.87 5.87 11.20
sTNF.R1 3.36 5.26 12.38
sTREM1 6.94 6.26 25.28

15.5.3 interpretation

1. All CVs are comfortably low

  • Generally, intra-assay CVs under 10% are considered very good for immunoassays, and under 15% is acceptable for most biomarker work.

  • The pooled DBS and spiked DBS samples are all well under 10%, which suggests that the assay reproducibility is strong.

  • The recombinant standards are a little higher for a few assays (12–25%), but still mostly within acceptable bounds except for sTREM1.

2. sTREM1 might be the one to watch

  • 25% CV in recombinant standards is high.

  • This might be due to:

    • Low signal strength near the detection limit.

    • Pipetting or bead-count variability.

    • Poor stability in recombinant form.

  • Worth checking raw MFI values to see if it’s just noise from low readings.

  • Also worth remembering this when looking at clinical data.

3. Recombinant standards tend to have higher CVs than DBS

  • For example, Ang.1 is 6.8% (pooled DBS) vs. 12.6% (standards).

  • This pattern might be due to:

    • Matrix mismatch. The recombinant standards are in buffer rather than a complex matrix like DBS.

    • Bead performance differences when analytes are spiked into clean buffer.

  • This isn’t unusual, but it’s worth noting if you ever compare results directly between recombinant standards and real samples.

5. No obvious systematic matrix-specific instability

  • There’s no assay where the pooled DBS CV is high but standards are low, meaning that the DBS format doesn’t seem to be introducing extra noise.

  • That’s a good sign for assay robustness in the intended sample type.

15.5.4 Inter-assay CV

# Vector of plate numbers
plates <- sprintf("P%d", 1:6)

# Read and combine without ...17 column that R creates on read
df2 <- map_dfr(plates, function(plate) {
  file <- sprintf("data/cv/INTERASSAY_CV_plate_%02d.csv", as.integer(sub("P", "", plate)))
  
  read_csv(file, skip = 41, show_col_types = FALSE) %>%
    slice(1:16) %>%
    select(-starts_with("...")) %>%  # drop those unnamed columns
    mutate(plate = plate)
})


# Convert assay columns to numeric
df2_num <- df2 %>%
  mutate(across(
    c(`CRP`:`CH3L1`), # all your assay columns in order
    as.numeric
  ))

# Pivot longer like p1/p2
df2 <- df2_num %>%
  pivot_longer(
    cols = CRP:CH3L1,  # all assay columns
    names_to = "Assay",
    values_to = "MFI"
  )

# 1. Pooled DBS
inter_pooled_dbs <- calc_cv(
  df2, 
  str_starts(df2$Sample, "DBS")
) %>%
  rename(inter_CV_pooled_DBS = CV)

# 2. Spiked DBS (but not starting with "DBS")
inter_spiked_dbs <- calc_cv(
  df2, 
  !str_starts(df2$Sample, "DBS")
) %>%
  rename(inter_CV_spiked_DBS = CV)

# 3. Recombinant standards
#    If recombinant standards are in a separate pattern like "Rec" or "Std", filter accordingly
#    Here, I'll assume they're *everything* in df2_long (same as your recombinant p2 case)
inter_recombinant <- calc_cv(
  df2,str_starts(df2$Sample,"Std")
) %>%
  rename(inter_CV_recombinant = CV)

# ---- Join into one table ----
inter_assay_table <- inter_pooled_dbs %>%
  left_join(inter_spiked_dbs, by = "Assay") %>%
  left_join(inter_recombinant, by = "Assay")

kable(inter_assay_table,digits = 2)
Assay inter_CV_pooled_DBS inter_CV_spiked_DBS inter_CV_recombinant
Ang-1 4.19 5.92 7.12
Ang-2 5.42 6.22 6.41
Azu 3.29 4.53 5.46
CH3L1 2.82 2.96 3.45
CRP 2.42 4.09 4.82
IL-10 4.69 5.41 6.23
IL-6 5.26 4.14 3.90
IL-8 3.81 7.16 6.75
IP-10 3.97 5.65 5.66
MxA 4.62 4.14 3.89
TRAIL 3.70 6.17 7.04
sTNF-R1 2.89 6.37 7.27
sTREM1 3.47 6.07 6.52

15.5.5 Interpretation

1. All inter-assay CVs are comfortably low

  • Everything is below ~8%, which is excellent for inter-assay reproducibility.

  • In biomarker assays, inter-assay CVs under 10% are considered very strong; you’re well under that threshold across the board.

2. Pooled DBS vs. Spiked DBS vs. Recombinant

  • Pooled DBS CVs are consistently lowest for most analytes.

    • Suggests that the pooled DBS specimens are very stable and reproducible across plates.

  • Spiked DBS sometimes slightly higher

    • e.g., IL-8 jumps to 7.16% from 3.81% in pooled DBS.

    • This could be due to pipetting variability or how spikes integrate into the DBS matrix.

  • Recombinant CVs are generally a little higher than pooled DBS but not alarmingly so (e.g., CRP: 2.42% → 4.82%).

    • This is common because recombinant standards are often in a clean buffer and don’t always mimic real sample matrix behavior.

3. No major outliers

  • The worst CV is IL-8 in spiked DBS (7.16%), but this is still well within the “good” range.

  • No single assay looks unstable across all sample types.

  • Some analytes (e.g., MxA, IL-6) have slightly higher pooled DBS CVs than recombinants, but the differences are small (<1–2%).

15.6 Summary

The intra- and inter-assay precision results indicate that the multiplex immunoassay is performing with strong reproducibility across sample types.

  • Reliable performance in DBS format – Both pooled and spiked DBS specimens showed consistently low intra- and inter-assay CVs, all well below the commonly accepted 10% threshold for high-quality immunoassays. This supports the use of DBS as a stable and reproducible matrix for these analytes.

  • Recombinant standards less precise but acceptable – CVs for recombinant standards were generally higher than for DBS, particularly for a few analytes such as sTREM1. This is likely due to matrix differences (buffer vs. DBS), lower signal levels, or inherent instability of some recombinant proteins. While still mostly within acceptable limits, this should be considered when interpreting calibration and QC data.

  • sTREM1 warrants monitoring – Elevated CV (~25%) in recombinant standards suggests potential instability or variability in this assay. This should be monitored in future runs, and raw signal data reviewed to confirm whether variability is due to low-level signal noise or other technical factors.

  • No evidence of matrix-specific instability – The lack of any assay showing high CVs in DBS but low CVs in standards suggests the DBS format itself is not introducing additional variability.

Overall, these findings provide confidence in the robustness of the assay system for use with DBS samples, while highlighting the importance of monitoring recombinant standard performance, particularly for sTREM1.