Last updated: 2025-04-03

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Summary

Cortisol value calculations

Min. 1st Qu. Median Mean 3rd Qu. Max. NA’s
A) Standard Method 0.4142 1.9653 7.5533 14.1906 28.0667 50.933 3
B) Spike-Corrected Method -45.870 -31.922 -1.929 -9.444 7.553 30.780 3
C) Standard, but simplified equation 0.4142 1.9653 7.5533 14.1906 28.0667 50.9333 3
D) Spike-Corrected (divided by two) 0.2335 1.5067 6.7184 9.7699 17.3683 32.2815 3

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

Cortisol concentration calculations

# define volume of methanol used for cortisol extraction
# vol added / vol recovered (mL)
extraction <- 1/0.750

# set reading value of spike (std1, 0.333 ug/dL), 
# and transforming to ug.dL

std <- (3191+3228)/2
std.r <- (std/10000)
std
[1] 3209.5
std.r
[1] 0.32095
# according to chatgpt, the spike's contribution is
# 1600 pg/mL, which is very similar to half of the reading for std 1 :]

Loading files and transforming units, including low quality data

df <- read.csv(file.path(data_path,"Data_QC_flagged.csv"))
kable(tail(df))
Wells Sample Category Weight_mg Buffer_nl Spike SpikeVol_uL Dilution Vol_in_well.tube_uL Raw.OD Binding.Perc Conc_pg.ml Ave_Conc_pg.ml CV.Perc SD SEM CV_categ Binding.Perc_categ Failed_samples
77 G11 TP3A P 12 220 1 25 1 50 0.258 23.2 2800 2792 0.391 10.9 7.71 NA NA NA
78 H11 TP3A P 12 220 1 25 1 50 0.259 NA 2785 NA NA NA NA NA NA NA
79 A12 TP3B P 12 60 1 25 1 50 0.195 15.5 4084 4210 4.230 178.0 126.00 NA UNDER 20% binding UNDER 20% binding
80 B12 TP3B P 12 60 1 25 1 50 0.186 NA 4336 NA NA NA NA NA NA NA
81 C12 TP3C P 12 60 1 25 1 50 0.186 13.9 4336 4661 9.870 460.0 325.00 NA UNDER 20% binding UNDER 20% binding
82 D12 TP3C P 12 60 1 25 1 50 0.166 NA 4986 NA NA NA NA NA NA NA 
# remove outlier
#df<- df[(df$Sample != "TP3A"),]

# Creating variables in indicated units
# dilution (buffer)
df$Buffer_ml <- c(df$Buffer_nl/1000)

# remove unnecessary information 
data <- df %>%
    dplyr::select(Wells, Sample, Category, Binding.Perc, Ave_Conc_pg.ml, Weight_mg, Buffer_ml, Spike, SpikeVol_uL, Dilution, Vol_in_well.tube_uL, Failed_samples) 

kable(tail(data, 10))
Wells Sample Category Binding.Perc Ave_Conc_pg.ml Weight_mg Buffer_ml Spike SpikeVol_uL Dilution Vol_in_well.tube_uL Failed_samples
73 C11 TP2B P 21.1 3101 9 0.06 1 25 1 50 NA
74 D11 TP2B P NA NA 9 0.06 1 25 1 50 NA
75 E11 TP2C P 18.1 3634 9 0.06 1 25 1 50 UNDER 20% binding
76 F11 TP2C P NA NA 9 0.06 1 25 1 50 NA
77 G11 TP3A P 23.2 2792 12 0.22 1 25 1 50 NA
78 H11 TP3A P NA NA 12 0.22 1 25 1 50 NA
79 A12 TP3B P 15.5 4210 12 0.06 1 25 1 50 UNDER 20% binding
80 B12 TP3B P NA NA 12 0.06 1 25 1 50 NA
81 C12 TP3C P 13.9 4661 12 0.06 1 25 1 50 UNDER 20% binding
82 D12 TP3C P NA NA 12 0.06 1 25 1 50 NA 
dim(data)
[1] 82 12
# remove duplicates
data.og <- data[!is.na(data$Binding.Perc), ]

(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 #####
##################################

# Transform to μg/dl from assay output
data$Ave_Conc_ug.dL <- c(data$Ave_Conc_pg.ml/10000)

data$Final_conc_pg.mg <- c(
    ((data$Ave_Conc_ug.dL) / data$Weight_mg) * # A/B *
      extraction *                                  # C/D  *     
      data$Buffer_ml * 10000 )                 # E * 10000
data <- data[order(data$Sample),]
write.csv(data, file.path(data_path, "Data_cort_values_methodA.csv"), row.names = F)

# summary for all samples
summary(data$Final_conc_pg.mg)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
 0.4142  1.9932  7.5643 15.6132 29.4367 68.2489      44 
kable(tail(data, 7))
Wells Sample Category Binding.Perc Ave_Conc_pg.ml Weight_mg Buffer_ml Spike SpikeVol_uL Dilution Vol_in_well.tube_uL Failed_samples Ave_Conc_ug.dL Final_conc_pg.mg
76 F11 TP2C P NA NA 9 0.06 1 25 1 50 NA NA NA
77 G11 TP3A P 23.2 2792 12 0.22 1 25 1 50 NA 0.2792 68.24889
78 H11 TP3A P NA NA 12 0.22 1 25 1 50 NA NA NA
79 A12 TP3B P 15.5 4210 12 0.06 1 25 1 50 UNDER 20% binding 0.4210 28.06667
80 B12 TP3B P NA NA 12 0.06 1 25 1 50 NA NA NA
81 C12 TP3C P 13.9 4661 12 0.06 1 25 1 50 UNDER 20% binding 0.4661 31.07333
82 D12 TP3C P NA NA 12 0.06 1 25 1 50 NA NA NA 
dim(data)
[1] 82 14

(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”

dSpike <- data

##################################
##### Calculate final values #####
##################################

dSpike$Final_conc_pg.mg <- 
  ifelse(
    dSpike$Spike == 1,    ## Only spiked samples
      ((dSpike$Ave_Conc_ug.dL - (std.r)) / # (A-spike) / B
        dSpike$Weight_mg) 
        * extraction *                  # C / D
        dSpike$Buffer_ml * 10000 * 2,    # E * 10000 * 2
        dSpike$Final_conc_pg.mg  
    )


write.csv(dSpike, file.path(data_path, "Data_cort_values_methodB.csv"), row.names = F)

# summary for all samples
summary(dSpike$Final_conc_pg.mg)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
-45.870 -31.013  -3.944  -9.733   7.552  30.780      44 
dSpikeSub <- data[c(data$Spike == 0), ]
summary(dSpikeSub$Final_conc_pg.mg)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
 0.4142  0.8400  2.3493  7.7984 11.9733 30.7800      17 
kable(tail(dSpike, 10))
Wells Sample Category Binding.Perc Ave_Conc_pg.ml Weight_mg Buffer_ml Spike SpikeVol_uL Dilution Vol_in_well.tube_uL Failed_samples Ave_Conc_ug.dL Final_conc_pg.mg
73 C11 TP2B P 21.1 3101 9 0.06 1 25 1 50 NA 0.3101 -1.928889
74 D11 TP2B P NA NA 9 0.06 1 25 1 50 NA NA NA
75 E11 TP2C P 18.1 3634 9 0.06 1 25 1 50 UNDER 20% binding 0.3634 7.546667
76 F11 TP2C P NA NA 9 0.06 1 25 1 50 NA NA NA
77 G11 TP3A P 23.2 2792 12 0.22 1 25 1 50 NA 0.2792 -20.411111
78 H11 TP3A P NA NA 12 0.22 1 25 1 50 NA NA NA
79 A12 TP3B P 15.5 4210 12 0.06 1 25 1 50 UNDER 20% binding 0.4210 13.340000
80 B12 TP3B P NA NA 12 0.06 1 25 1 50 NA NA NA
81 C12 TP3C P 13.9 4661 12 0.06 1 25 1 50 UNDER 20% binding 0.4661 19.353333
82 D12 TP3C P NA NA 12 0.06 1 25 1 50 NA NA NA

(C) Skip unit transformation

##################################
##### Calculate final values #####
################################## 
datac <- data
datac$Final_conc_pg.mg <- c(
    (datac$Ave_Conc_pg.ml / datac$Weight_mg) * # A/B *
      extraction *                                  # C/D  *     
      datac$Buffer_ml)                 # E 
datac <- datac[order(datac$Sample),]
write.csv(datac, file.path(data_path, "Data_cort_values_methodC.csv"), row.names = F)

# summary for all samples
summary(datac$Final_conc_pg.mg)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
 0.4142  1.9932  7.5643 15.6132 29.4367 68.2489      44

(D) Account for Spike contribution (uses vol. of spike, conc. of spike, and total reconstit. vol.)

Spike contribution (pg/mL) = (Vol. spike (mL) x Conc. spike (pg/mL) ) / Vol. reconstitution (mL) or total vol. in well (50uL) (depending on where the spike was added)

# Calculate contribution of spike according to the different volumes in which it was added
# Consider that contribution of spike in serial dilutions gets smaller 

# Vol. of spike transformed to mL
data$SpikeVol_ml <- data$SpikeVol_uL/1000
# Concentration of the spike:
std
[1] 3209.5
# Vol. reconstitution (mL) is the total volume in tube or well (sample + spike), after adding spike.
# transform to mL
data$Vol_in_well.tube_ml <- data$Vol_in_well.tube_uL/1000


  ##( Spike vol. x Spike Conc.)
  ## ------------------------  / dilution = Spike contribution
  ##      Total vol. 
  
# Cortisol added by spike in wells: 0.0025 mL x 3200 pg/mL = 80 pg
# Calculate cort contribution of spike to each sample
data$Spike.cont_pg.mL <- (((data$SpikeVol_ml * std ) / # Volume of spike * Spike concentration
                            data$Vol_in_well.tube_ml) / # divided by the total volume (spike + sample)
                              data$Dilution) # resulting number changes depending on the dilution

dSpiked <- data
                          
##################################
##### Calculate final values #####
##################################


dSpiked$Final_conc_pg.mg <- 
  ifelse(
    dSpiked$Spike == 1,           ## Only spiked samples
      ((dSpiked$Ave_Conc_pg.ml - dSpiked$Spike.cont_pg.mL) / # (A - spike) / B
      dSpiked$Weight_mg) 
    * extraction *      # C / D
      dSpiked$Buffer_ml,    # E * 
    dSpiked$Final_conc_pg.mg  
)

write.csv(dSpiked, file.path(data_path, "Data_cort_values_methodD.csv"), row.names = F)

# summary for all samples
summary(dSpiked$Final_conc_pg.mg)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
 0.2335  1.6157  7.0685 10.2765 17.8704 32.2815      44 
kable(tail(dSpiked[!is.na(dSpiked$Final_conc_pg.mg) , c("Sample", "Final_conc_pg.mg", "Ave_Conc_pg.ml", "Spike.cont_pg.mL", "Binding.Perc", "Weight_mg", "Buffer_ml", "SpikeVol_uL", "Dilution", "Vol_in_well.tube_uL")],20))
Sample Final_conc_pg.mg Ave_Conc_pg.ml Spike.cont_pg.mL Binding.Perc Weight_mg Buffer_ml SpikeVol_uL Dilution Vol_in_well.tube_uL
43 TC4 2.1748485 618.00 291.77273 60.2 50 0.25 25 1 275
45 TC5 0.9633333 144.50 291.77273 92.0 50 0.25 25 1 275
47 TC6 0.6499333 97.49 291.77273 97.7 50 0.25 25 1 275
49 TC7 0.7166667 107.50 291.77273 96.4 50 0.25 25 1 275
51 TD1 18.7971667 4168.00 1604.75000 15.7 20 0.11 110 1 220
53 TD2 7.4185833 1814.00 802.37500 32.7 20 0.11 110 2 220
55 TD3 4.6332917 1033.00 401.18750 46.7 20 0.11 110 4 220
57 TD4 2.3797125 525.10 200.59375 64.3 20 0.11 110 8 220
59 TD5 1.2298229 268.00 100.29688 80.2 20 0.11 110 16 220
61 TD6 0.2335048 81.99 50.14844 99.7 20 0.11 110 32 220
63 TD7 0.4521424 86.73 25.07422 99.0 20 0.11 110 64 220
65 TP1A 18.4166667 2986.00 1604.75000 21.8 6 0.06 25 1 50
67 TP1B 29.5366667 3820.00 1604.75000 18.1 6 0.06 25 1 50
69 TP1C 8.4966667 2242.00 1604.75000 27.8 6 0.06 25 1 50
71 TP2A 19.4511111 3793.00 1604.75000 17.3 9 0.06 25 1 50
73 TP2B 13.3000000 3101.00 1604.75000 21.1 9 0.06 25 1 50
75 TP2C 18.0377778 3634.00 1604.75000 18.1 9 0.06 25 1 50
77 TP3A 29.0216667 2792.00 1604.75000 23.2 12 0.22 25 1 50
79 TP3B 17.3683333 4210.00 1604.75000 15.5 12 0.06 25 1 50
81 TP3C 20.3750000 4661.00 1604.75000 13.9 12 0.06 25 1 50

Plots

(A) Standard Calculation

(B) Accounting for Spike

(C) Simplified Standard Calculation

(D) New calculation (substract half of the spike from A)


sessionInfo()
R version 4.4.3 (2025-02-28)
Platform: aarch64-apple-darwin20
Running under: macOS Sequoia 15.3.2

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRblas.0.dylib 
LAPACK: /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRlapack.dylib;  LAPACK version 3.12.0

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_1.0.7     ggplot2_3.5.1  
[5] knitr_1.49     

loaded via a namespace (and not attached):
 [1] sass_0.4.9        utf8_1.2.4        generics_0.1.3    tidyr_1.3.1      
 [5] prismatic_1.1.2   stringi_1.8.4     digest_0.6.37     magrittr_2.0.3   
 [9] evaluate_1.0.1    grid_4.4.3        fastmap_1.2.0     rprojroot_2.0.4  
[13] workflowr_1.7.1   jsonlite_1.8.9    whisker_0.4.1     backports_1.5.0  
[17] rematch2_2.1.2    promises_1.3.0    purrr_1.0.2       fansi_1.0.6      
[21] scales_1.3.0      jquerylib_0.1.4   cli_3.6.3         rlang_1.1.4      
[25] munsell_0.5.1     withr_3.0.2       cachem_1.1.0      yaml_2.3.10      
[29] tools_4.4.3       colorspace_2.1-1  httpuv_1.6.15     vctrs_0.6.5      
[33] R6_2.5.1          lifecycle_1.0.4   git2r_0.35.0      stringr_1.5.1    
[37] fs_1.6.5          pkgconfig_2.0.3   pillar_1.9.0      bslib_0.8.0      
[41] later_1.3.2       gtable_0.3.6      glue_1.8.0        Rcpp_1.0.13-1    
[45] xfun_0.49         tibble_3.2.1      tidyselect_1.2.1  rstudioapi_0.17.1
[49] farver_2.1.2      htmltools_0.5.8.1 rmarkdown_2.29    labeling_0.4.3   
[53] compiler_4.4.3