Cortisol Concentration Values, Test4
Paloma Contreras
2025-04-24
Last updated: 2025-04-24
Checks: 6 1
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HairCort-Evaluation-Nist2020/
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| Rmd | dd200fc | Paloma | 2025-04-23 | corrected figures |
| html | dd200fc | Paloma | 2025-04-23 | corrected figures |
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| Rmd | 16ce91c | Paloma | 2025-04-10 | recalc_evaluations |
| html | 16ce91c | Paloma | 2025-04-10 | recalc_evaluations |
| html | bbb70a9 | Paloma | 2025-04-09 | comparing methods |
| Rmd | ccad031 | Paloma | 2025-04-09 | new_calc |
| html | ccad031 | Paloma | 2025-04-09 | new_calc |
| html | 77c2ab5 | Paloma | 2025-04-08 | cleaning test3 |
| Rmd | ced6eed | Paloma | 2025-04-03 | upd |
| html | ced6eed | Paloma | 2025-04-03 | upd |
| Rmd | ca6c804 | Paloma | 2025-04-03 | new calc final vals |
| html | ca6c804 | Paloma | 2025-04-03 | new calc final vals |
| Rmd | 528855b | Paloma | 2025-04-03 | new_calc |
| html | 528855b | Paloma | 2025-04-03 | new_calc |
Summary
Cortisol value calculations (includes bad quality samples, n = 41)
| Min. | 1st Qu. | Median | Mean | 3rd Qu. | Max. | NA’s | |
|---|---|---|---|---|---|---|---|
| A) Standard Method (mult. by sample dilution) | 17.13 | 29.01 | 32.27 | 35.28 | 39.47 | 82.94 | 4 |
| B) Spike-Corrected Method (Nist 2020) | -45.870 | -35.833 | -5.960 | -3.488 | 23.109 | 50.963 | 4 |
| C) Spike-Corrected (Sam’s Method) | 7.472 | 18.533 | 24.559 | 27.009 | 31.196 | 80.804 | 4 |
Cortisol value calculations (removed bad quality samples)
| Min. | 1st Qu. | Median | Mean | 3rd Qu. | Max. | |
|---|---|---|---|---|---|---|
| A) Standard Method (mult. by sample dilution) | 18.27 | 29.27 | 31.54 | 34.13 | 37.73 | 69.17 |
| B) Spike-Corrected Method (Nist 2020) | -39.371 | -34.855 | -20.577 | -14.325 | -6.825 | 40.400 |
| C) Spike-Corrected (Sam’s Method) | ** 11.80** | 18.45 | 24.09 | 24.05 | 30.32 | 40.40 |
Results:
Intra-assay CV: 14.5%
Intra-assay CV after removing low quality samples: 10%
Inter-assay CV: 21% (Bindings for 20mg sample diluted in 250 uL, no spike: 64.8% and 48% in test3 and test4, respectively)
Conclusions:
Concerns: Overall quality of the plate is not great, but serial dilusions show clear parallelism and standards have values within the expected
Explanation of each variable used in calculations
Ave_Conc_pg/ml: average ELISA reading per sample in pg/mL
Weight_mg: hair weight in mg
Buffer_nl: assay buffer volume in nL → we convert to mL
Spike: binary indicator (1 = spiked sample)
SpikeVol_uL: volume of spike added in µL
Dilution: dilution factor (already present)
Vol_in_well.tube_uL: total volume in well/tube in µL (for spike correction)
std: standard reading value
extraction: methanol volume ratio = vol added / vol recovered (e.g. 1/0.75 ml)
Cortisol concentration calculations
#practice
Ave_Conc_pg.ml <- 4617
Spike_contribution <- 0
Weight_mg <- 50
Extraction_ratio <- 1.3/1
Buffer_ml <- 0.25
((Ave_Conc_pg.ml - Spike_contribution) / # (A - spike)
Weight_mg) * # / B *
Extraction_ratio * # C / D *
Buffer_ml [1] 30.0105# 31.19476
Ave_Conc_pg.ml / Weight_mg * Extraction_ratio * Buffer_ml [1] 30.0105# 31.19476((A/B) * (C/D) * E * 10,000 * SLd) = F
Parameters and unit transformations:
# Volume of methanol used for cortisol extraction varies, so it is included in file
# as Extraction_ratio (vol added / vol recovered) in mL
# Reading of spike standard and conversion to ug/dl
std <- (3191 + 3228) / 2 # test 4 backfit
std.r <- std / 10000 # std in ul/dl
# Creating variables in indicated units
df$Buffer_ml <- c(df$Buffer_nl/1000) # dilution (buffer)
df$Ave_Conc_ug.dl <- c(df$Ave_Conc_pg.ml/10000) # Transform to μg/dl from assay outputIdentify and flag bad quality samples
ABOVE 80% binding HIGH CV HIGH CV;ABOVE 80% binding
4 2 7
HIGH CV;UNDER 20% binding OK UNDER 20% binding
1 60 8 (A) Standard Calculation
Formula:
((A/B) * (C/D) * E * 10,000) = F
- A = μg/dl from assay output;
- B = weight (in mg) of hair subjected to extraction;
- C = vol. (in ml) of methanol added to the powdered hair;
- D = vol. (in ml) of methanol recovered from the extract and subsequently dried down;
- E = vol. (in ml) of assay buffer used to reconstitute the dried extract;
- F = final value of hair CORT Concentration in pg/mg
##################################
##### Calculate final values #####
##################################
data$Final_pg.mg_A <- c(
((data$Ave_Conc_ug.dl) / data$Weight_mg) * # A/B *
data$Extraction_ratio * # C/D *
data$Buffer_ml * 10000) # E * 10000 Summary of all samples (n = 37 ): Min. 1st Qu. Median Mean 3rd Qu. Max.
0.4198 1.9653 7.6554 16.0868 30.5653 69.1712 Summary for good quality samples only (n = 18 ): Min. 1st Qu. Median Mean 3rd Qu. Max.
2.077 4.696 7.861 16.287 17.877 69.171 (B) Accounting for Spike
We followed the procedure described in Nist et al. 2020:
“Thus, after pipetting 25μL of standards and samples into the appropriate wells of the 96-well assay plate, we added 25μL of the 0.333ug/dL standard to all samples, resulting in a 1:2 dilution of samples. The remainder of the manufacturer’s protocol was unchanged. We analyzed the assay plate in a Powerwave plate reader (BioTek, Winooski, VT) at 450nm and subtracted background values from all assay wells. In the calculations, we subtracted the 0.333ug/dL standard reading from the sample readings. Samples that resulted in a negative number were considered nondetectable. We converted cortisol levels from ug/dL, as measured by the assay, to pg/mg—based on the mass of hair collected and analyzed using the following formula:
A/B * C/D * E * 10,000 * 2 = F
where
- A = μg/dl from assay output;
- B = weight (in mg) of collected hair;
- C = vol. (in ml) of methanol added to the powdered hair;
- D = vol. (in ml) of methanol recovered from the extract and subsequently dried down;
- E = vol. (in ml) of assay buffer used to reconstitute the dried extract; 10,000 accounts for changes in metrics; 2 accounts for the dilution factor after addition of the spike; and
- F = final value of hair cortisol concentration in pg/mg”
- SPd = sample dilution factor (if serially diluted)
##################################
##### Calculate final values #####
##################################
# spike is already divided by 10000 (unit is ug/dL)
data$Final_pg.mg_B <-
ifelse(
data$Spike == 1, ## Only spiked samples
((data$Ave_Conc_ug.dl - (std.r)) / # (A-spike)
data$Weight_mg) # / B
* data$Extraction_ratio * # C / D
data$Buffer_ml * 10000 * 2, # E * 10000 * 2
data$Final_pg.mg_A
)Summary all samples: Min. 1st Qu. Median Mean 3rd Qu. Max.
-45.870 -35.833 -5.960 -10.952 7.547 31.196 Summary good quality samples only: Min. 1st Qu. Median Mean 3rd Qu. Max.
-39.371 -34.855 -20.577 -19.549 -6.825 7.655 (C) Sam’s calculation
Simplifies unnecessary unit transformations and accounts for spike considering dilution of both sample and the spike
- Step 1: Calculate contribution of the spike
- Step 2: Substract spike from plate reading values and calculate final values accounting for dilution of the sample, weight, and reconstitution
Step 1: Calculate contribution of spike
X * Y / Z / SPd = SP
- SP = final value of spike contribution in pg/mL
- X = volume of spike added (mL)
- Y = concentration of the spike added (pg/mL)
- SPd = if serially diluted, dilution factor for the spike (i.e: 1, 2, 4, 8, etc.)
- Z = total volume (mL) in the well or tube, if spike is added before loading the plate (sample + spike)
# Transforming units
data$SpikeVol_ml <- data$SpikeVol_ul/1000 # X to mL
data$Vol_in_well.tube_ml <- data$Vol_in_well.tube_ul/1000 # Z to mL
# Calculate spike contribution to each sample
## ( Spike vol. x Spike Conc.)
## ------------------------ / dilution = Spike contribution
## Total vol.
# Calculate cort contribution of spike to each sample
data$Spike_contribution <- ((data$SpikeVol_ml * std / # X * Y
data$Vol_in_well.tube_ml) / # Z /
data$Dilution_spike) # SPThe reading for standard 1 in this plate is 3209.5The total contribution of the Spike to each sample is can be any of the following numbers (in pg/ml) [1] 0.000000 291.772727 160.475000 80.237500 40.118750 20.059375
[7] 10.029688 5.014844 1604.750000 802.375000 401.187500 200.593750
[13] 100.296875 50.148438 25.074219 1604.750000Step 2 : Substract spike and calculate final values
((A - SP)/B) * (C/D) * E * SLd = F
- A = pg/ml from assay output;
- SP = spike contribution (in pg/ml)
- B = weight (in mg) of hair subjected to extraction;
- C = vol. (in ml) of methanol added to the powdered hair;
- D = vol. (in ml) of methanol recovered from the extract and subsequently dried down;
- E = vol. (in ml) of assay buffer used to reconstitute the dried extract;
- F = final value of hair CORT Concentration in pg/mg.
##################################
##### Calculate final values #####
##################################
data$Final_pg.mg_C <-
(((data$Ave_Conc_pg.ml - data$Spike_contribution)) / # (A - spike)
data$Weight_mg) * # / B *
data$Extraction_ratio * # C / D *
data$Buffer_ml # E
head(data) Wells Sample Category Binding.Perc Ave_Conc_ug.dl Ave_Conc_pg.ml Weight_mg
1 C3 TA1 A 14.0 0.46170 4617.0 50
2 E3 TA2 A 22.4 0.29210 2921.0 50
3 G3 TA3 A 44.3 0.11330 1133.0 50
4 A4 TA4 A 55.2 0.07474 747.4 50
5 C4 TA5 A 74.1 0.03524 352.4 50
6 E4 TA6 A 84.2 0.02260 226.0 50
Buffer_ml Spike SpikeVol_ul Dilution_sample Dilution_spike Extraction_ratio
1 0.25 0 0 1 1 1.351351
2 0.25 0 0 2 1 1.351351
3 0.25 0 0 4 1 1.351351
4 0.25 0 0 8 1 1.351351
5 0.25 0 0 16 1 1.351351
6 0.25 0 0 32 1 1.351351
Vol_in_well.tube_ul Failed_samples Final_pg.mg_A Final_pg.mg_B
1 50 Out of curve 31.195946 31.195946
2 50 High CV 19.736486 19.736486
3 50 OK 7.655405 7.655405
4 50 OK 5.050000 5.050000
5 50 OK 2.381081 2.381081
6 50 High CV & Out of curve 1.527027 1.527027
SpikeVol_ml Vol_in_well.tube_ml Spike_contribution Final_pg.mg_C
1 0 0.05 0 31.195946
2 0 0.05 0 19.736486
3 0 0.05 0 7.655405
4 0 0.05 0 5.050000
5 0 0.05 0 2.381081
6 0 0.05 0 1.527027Summary for all samples: Min. 1st Qu. Median Mean 3rd Qu. Max.
0.2335 1.5270 6.7184 10.3434 18.0378 32.2815 Summary for good quality samples only: Min. 1st Qu. Median Mean 3rd Qu. Max.
1.943 3.461 7.069 9.283 13.188 29.414 | Sample | Final_pg.mg_A | Final_pg.mg_B | Final_pg.mg_C | Spike_contribution | Binding.Perc | SpikeVol_ul | Dilution_sample | Dilution_spike | Extraction_ratio | |
|---|---|---|---|---|---|---|---|---|---|---|
| 32 | TP2A | 33.71556 | 10.373333 | 19.45111 | 1604.75 | 17.3 | 25 | 1 | 1 | 1.333333 |
| 33 | TP2B | 27.56444 | -1.928889 | 13.30000 | 1604.75 | 21.1 | 25 | 1 | 1 | 1.333333 |
| 34 | TP2C | 32.30222 | 7.546667 | 18.03778 | 1604.75 | 18.1 | 25 | 1 | 1 | 1.333333 |
| 35 | TP3A | 69.17117 | -20.686937 | 29.41385 | 1604.75 | 23.2 | 25 | 1 | 1 | 1.351351 |
| 36 | TP3B | 28.06667 | 13.340000 | 17.36833 | 1604.75 | 15.5 | 25 | 1 | 1 | 1.333333 |
| 37 | TP3C | 31.07333 | 19.353333 | 20.37500 | 1604.75 | 13.9 | 25 | 1 | 1 | 1.333333 |
Plots
(A) Standard Calculation
Final cortisol concentrations not accounting for spike. Tags are sample numbers.
Expected results: a straight horizontal line showing that I obtained same cortisol concentration value in the Y axis, across different sample weights.
(B) Accounting for Spike
Final cortisol concentrations accounting for Spike as instructed in Nist et al. 2020.
Expected results: lower values than in the previous plot for the spiked samples, but not as low as negative samples (for all of them). Spiked and non-spiked samples should be aligned (same concentration across different weights)
(C) Sam’s calculation
Final cortisol concentration values using new method.
Expected results: one unique horizontal line, regardless of the spiking status and dilution.
Evaluation using C
1 2 3 4 5 6
23.7864361 12.3269767 0.2458956 -2.3595098 -5.0284287 -5.8824828
7 8 9 10 11 12
-6.9897125 24.8720053 8.2073235 -0.6910931 -4.3396348 -5.4665723
13 14 15 16 17 18
-6.2837077 -6.1469421 8.7032848 5.4440255 -1.5041226 -4.9930115
19 20 21 22 23 24
-6.3391394 -6.6873617 -6.6132135 5.7631276 -5.6154558 -8.4007474
25 26 27 28 29 30
-10.6543266 -11.8042162 -12.8005343 -12.5818967 2.7578472 13.8778472
31 32 33 34 35 36
-3.8578935 4.3547446 -1.7963665 2.9414113 14.8799378 2.8344198
37
5.8410864 8 9 10 11 12 13 14
24.561297 7.896615 -1.001802 -4.650343 -5.777281 -6.594416 -6.457651
15 16 17 18 22 23 24
8.392576 5.133317 -1.814831 -5.303720 5.703641 -5.674942 -8.460234
25 26 27 28 29 30 31
-10.713813 -11.863702 -12.860021 -12.641383 2.815598 13.935598 -3.800143
32 33 34 35 36 37
4.387373 -1.763738 2.974040 14.887444 2.841926 5.848593 1 2 3 4 5 6 7
24.1404901 12.6810307 0.5999496 -2.0054558 -4.6743747 -5.5284288 -6.6356585
19 20 21
-5.9850854 -6.3333077 -6.2591595 Warning: Removed 15 rows containing missing values or values outside the scale range
(`geom_smooth()`).
| Version | Author | Date |
|---|---|---|
| dd200fc | Paloma | 2025-04-23 |
| Version | Author | Date |
|---|---|---|
| dd200fc | Paloma | 2025-04-23 |
Optimal dilution (using method C results)
Error using spiked samples only
Mean Absolute Error (MAE) ALL: 7.361 Standard Deviation of Residuals ALL: 9.123 Error using non-spiked samples only
Mean Absolute Error (MAE) ALL: 7.484 Standard Deviation of Residuals ALL: 10.325 Error using all samples
Mean Absolute Error (MAE) ALL: 7.397 Standard Deviation of Residuals ALL: 9.318
sessionInfo()R version 4.5.0 (2025-04-11)
Platform: aarch64-apple-darwin20
Running under: macOS Sequoia 15.4.1
Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/lib/libRlapack.dylib; LAPACK version 3.12.1
locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
time zone: America/Detroit
tzcode source: internal
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] dplyr_1.1.4 paletteer_1.6.0 broom_1.0.8 ggplot2_3.5.2
[5] knitr_1.50
loaded via a namespace (and not attached):
[1] sass_0.4.10 generics_0.1.3 tidyr_1.3.1 prismatic_1.1.2
[5] lattice_0.22-6 stringi_1.8.7 digest_0.6.37 magrittr_2.0.3
[9] evaluate_1.0.3 grid_4.5.0 fastmap_1.2.0 Matrix_1.7-3
[13] rprojroot_2.0.4 workflowr_1.7.1 jsonlite_2.0.0 whisker_0.4.1
[17] backports_1.5.0 rematch2_2.1.2 promises_1.3.2 mgcv_1.9-1
[21] purrr_1.0.4 scales_1.3.0 jquerylib_0.1.4 cli_3.6.4
[25] rlang_1.1.6 splines_4.5.0 munsell_0.5.1 withr_3.0.2
[29] cachem_1.1.0 yaml_2.3.10 tools_4.5.0 colorspace_2.1-1
[33] httpuv_1.6.16 vctrs_0.6.5 R6_2.6.1 lifecycle_1.0.4
[37] git2r_0.36.2 stringr_1.5.1 fs_1.6.6 pkgconfig_2.0.3
[41] pillar_1.10.2 bslib_0.9.0 later_1.4.2 gtable_0.3.6
[45] glue_1.8.0 Rcpp_1.0.14 xfun_0.52 tibble_3.2.1
[49] tidyselect_1.2.1 rstudioapi_0.17.1 farver_2.1.2 nlme_3.1-168
[53] htmltools_0.5.8.1 rmarkdown_2.29 labeling_0.4.3 compiler_4.5.0