# Ring et al. 2017 Vignette 4: Generating Figure 3

#### Caroline Ring

#### 2019-04-25

This vignette contains code to generate Figure 3 from the paper: a plot of HTTK-Pop predicted median Css vs. literature median Css.

First, load some packages.

    library('data.table')
    library('ggplot2')
    library('httk')

Next, load in the model-predicted median Css values for the Age 20-50 non-obese sub-population.

    poormetab <- TRUE
    fup.censor <- TRUE
    grp <- 'Age.20.50.nonobese'
    model <- '3compartmentss'
    popmethod <- 'dr'

    m.dat <- readRDS(paste0('data/',
                            paste('allchems',
                                  grp,
                                  popmethod,
                                  'poormetab',
                                  poormetab,
                                  'fup.censor',
                                  fup.censor,
                                  model,
                                  "FuptoFub",
                                  sep='_'),
                            '.Rdata'))

And read in the literature values of median Css. Start with data from Obach et al. 2008.

    #Convert clearance in mL/min/kg to Css in mg/L for a dose of 1 mg/kg/day
    Obach2008[,"Css (mg/L)"] <- 1/
      (24*60*
         as.numeric(Obach2008[,
                              "CL (mL/min/kg)"])/
         1000) # 1 mg/kg/day / L/day/kg -> mg/L
    literature.Css <- Obach2008[,c("Name","CAS","Css (mg/L)")]
    Obach2008.dt <- as.data.table(literature.Css)

Then add in some data from Wetmore et al. 2012.

    Wetmore2012 <- Wetmore2012[c(1:2,13,3:12),]
    Wetmore2012.Css <- Wetmore2012[,c("Chemical","CAS","Literature.Css")]
    Wetmore2012.Css[, 'Literature.Css'] <- gsub(x=Wetmore2012.Css[,
                                                                  'Literature.Css'],
                                                pattern=',',
                                                replacement='')
    #strip commas from Css values for proper conversion
    Wetmore2012.Css[, "Literature.Css"] <- as.numeric(Wetmore2012.Css[,
                                                                      "Literature.Css"])
    colnames(Wetmore2012.Css) <- c("Name","CAS","Css (mg/L)")
    Wetmore2012.Css <- Wetmore2012.Css[!is.na(Wetmore2012.Css[,"Css (mg/L)"]),]
    Wetmore2012.dt <- as.data.table(Wetmore2012.Css)

Combine the Wetmore and Obach data

    litCss.dt <- rbind(Obach2008.dt, Wetmore2012.dt)
    setnames(litCss.dt, c('Name', 'Css (mg/L)'), c('Compound', 'litcss'))

Convert literature in vivo Css from mg/L to umol/L (uM), using Css/(MW/1000), where MW is molecular weight in grams per mole of substance.

    #MW = weight in grams per mole of substance
    #MW*1000 = weight in mg per mole of substance
    #MW*1000/10^6 = MW/1000 = weight in mg per umol of substance
    #Css in mg/L divided by MW in mg/umol = umol/L = uM

    #get MW from HTTK cheminfo
    chemlist <- as.data.table(httk::get_cheminfo(info=c('CAS', 'Compound', 'MW'),
                                                 species='Human',
                                                 model=model,
                                                 exclude.fub.zero=FALSE))
    setnames(chemlist, 'CAS', 'chemcas')
    litCss.dt <- merge(litCss.dt,
                       chemlist[, .(Compound, MW)],
                       by='Compound')
    #Now merge with litcss
    setnames(litCss.dt,
             'CAS',
             'chemcas')
    litCss.dt[, litcss:=litcss/(MW/1000)]

Next, make a data table with the literature Css values in one column and the model-predicted Css values in another.

    tmp.med <- merge(m.dat[, .(chemcas, css50)],
                     litCss.dt,
                     by=c('chemcas')
                     )

Do a linear regression on the log10-scaled data, to assess the correlation between model-predicted and literature Css.

    mymodel <- lm(log10(css50)~log10(litcss), data=tmp.med)
    summary(mymodel)

Plot the data, along with the identity line and linear regression.

    p <- ggplot(data=tmp.med)+
      geom_point(aes(y=css50, #Plot data points
                     x=litcss),
                 shape=21, #As open circles
                 size=4) +
      stat_smooth(data=tmp.med, #Plot best-fit line
                  mapping=aes(x=litcss, y=css50), #data will be log10-transformed before this is done, so this is the same as the linear regression above
                  method="lm",
                  linetype=2, #dashed line
                  size=1,
                  color="black",
                  alpha=0.25, #shading for confidence interval
                  level=0.99) + #99% CI
      geom_abline(slope=1,intercept=0, #identity line
                  linetype=1, size=1, color="black")+
      scale_x_log10() + #scale x data as log10
      scale_y_log10() + #scale y data as log10
      labs(x='Literature median Css (uM)',
           y='HTTK-Pop median Css (uM)') +
      theme_bw()+
      theme(axis.text.x=element_text(size=rel(2), angle=45, hjust=1),
            axis.text.y=element_text(size=rel(2)),
            axis.title.x=element_text(size=rel(2)),
            axis.title.y=element_text(size=rel(2)))
    print(p)

The two chemicals with the highest literature Css values look very influential. What are they?

    #First find the chemicals with the two highest literature Css values
    setorder(tmp.med, litcss) #sort ascending by literature Css
    knitr::kable(tmp.med[(nrow(tmp.med)-1):nrow(tmp.med),
                         .(Compound, chemcas, css50, litcss, MW)],
                 format="markdown",
                 col.names=c("Compound", "CASRN", "Predicted median Css", "Literature median Css", "MW (g/mol)"))

Let’s see what the regression looks like without PFOS and PFOA.

    tmp.med2 <- tmp.med[1:(nrow(tmp.med)-2), ] #remove the highest two lit Css chemicals
    mymodel2 <- lm(log10(css50)~log10(litcss), data=tmp.med2) #re-do regression
    summary(mymodel2)

And re-do the plot with the new regression, excluding PFOS and PFOA.

    p2 <- p + stat_smooth(data=tmp.med2,#Add new best-fit line
                          mapping=aes(x=litcss, y=css50),
                          method="lm",
                          color="black",
                          linetype=3, #dotted
                          size=1.2, #slightly increase thickness
                          level=0.99, #plot 99% CI shading
                          alpha=0.25)
    print(p2)
    ggsave(filename="pdf_figures/Figure3_FuptoFub.pdf",
           plot=p2,
           height=11, width=14)

The intercept and slope of the best-fit line don’t change all that much when we exclude PFOS and PFOA; the correlation (R^2) decreases somewhat, from 0.32 to 0.22.

To check whether the slopes of the regressions are significantly different from 1, check whether each model is significantly different from a corresponding model with a slope of 1.

    offset.model <- lm(log10(css50)~offset(log10(litcss)), data=tmp.med) #forces slope of 1
    summary(offset.model)
    anova(mymodel, offset.model) #Compare original regression to offset model

    offset.model2 <- lm(log10(css50)~offset(log10(litcss)), data=tmp.med2) #forces slope of 1
    summary(offset.model2)
    anova(mymodel2, offset.model2) #Compare second regression to offset model

Both p-values indicate that the slope is significantly different from 1.

Finally, to generate a table of the predicted values, literature values, and the difference between them, just add a column to the data table. Sort by the ratio between predicted and literature values to see which chemicals are underpredicted or overpredicted, and by how much.

    tmp.med[, predicted.over.lit:=css50/litcss]
    setorder(tmp.med, predicted.over.lit)

How many are within 10-fold?

    tmp.med[, sum(predicted.over.lit<=10 & predicted.over.lit>=0.1)]

How many are within 5-fold?

    tmp.med[, sum(predicted.over.lit<=5 & predicted.over.lit>=0.2)]

How many are within 2-fold?

    tmp.med[, sum(predicted.over.lit<=2 & predicted.over.lit>=0.5)]

How many are overpredicted?

    tmp.med[, sum(predicted.over.lit>1)]

Compared to the total:

    nrow(tmp.med)