# Plotting Howgate/Johnson data

#### Caroline Ring

#### 2017-07-14

This vignette plots HTTK-Pop-predicted Css against in vivo Css from Howgate 2006 and Johnson 2006.

First load some packages.

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

Then, we need to read in the study data.

    jhchem <- readRDS(file="data/jhchem.Rdata")
    #Get Funbound.plasma measured values from HTTK
    chem.dt <- as.data.table(httk::get_cheminfo(model='3compartmentss',
                                                species='Human',
                                                info=c('CAS', "MW", "Funbound.plasma"),
                                                exclude.fub.zero=FALSE))
    #Get CLint measured values from HTTK
    chem.dt[, Clint:=sapply(CAS,
                            function(x) parameterize_steadystate(chem.cas=x,
                                                                 species='Human')$Clint)]
    setnames(chem.dt, 'Human.Funbound.plasma', 'Funbound.plasma')
    chem.dt[, fup.zero:=Funbound.plasma==0.005]
    chem.dt[, Clint.zero:=Clint==0]

    jhchem <- merge(jhchem,chem.dt,by='CAS')

Define a function to plot the confidence intervals as ellipses. This function takes the confidence interval bounds in two dimensions and returns points along the circumference of an ellipse with major and minor axes defined by the confidence intervals in each dimension. By default it returns 100 points; this seems to be plenty to draw a smooth-looking ellipse.

    ellipse_fun <- function(x.CI.max,
                            x.CI.min,
                            y.CI.max,
                            y.CI.min,
                            npts=100){
      #Compute length of axes
      a <- (x.CI.max - x.CI.min)/2
      b <- (y.CI.max - y.CI.min)/2
      #Compute center point
      x0 <- mean(c(x.CI.min,x.CI.max))
      y0 <- mean(c(y.CI.min,y.CI.max))
      #get x and y coordinates of ellipse circumference
      ellipse.x <- a*cos(seq(from=0,
                             to=2*pi,
                             length.out=npts)) + x0
      ellipse.y <- b*sin(seq(from=0,
                             to=2*pi,
                             length.out=npts)) + y0
      return(data.table(ellipse.x=ellipse.x,
                        ellipse.y=ellipse.y))

      }

Next, define a function to actually do the plotting – one that can be called with arguments for poormetab and fup.censor.

    plot_virtstudy_innerfunction <- function(model,
                                                  fup.censor,
                                                  poormetab,
                                             fuptofub,
                                                  jhchem){

      if (fuptofub){
      overall.dt <- readRDS(paste0('data/',
                                   paste('virtstudypop', 'overallstats', model,
                                         'poormetab', poormetab,
                                         'fup.censor', fup.censor,
                                         "FuptoFub", sep='_'),
                                   '.Rdata'))
      }else{
        overall.dt <- readRDS(paste0('data/',
                                   paste('virtstudypop', 'overallstats', model,
                                         'poormetab', poormetab,
                                         'fup.censor', fup.censor, sep='_'),
                                   '.Rdata'))
      }
      overall.dt <- merge(overall.dt,
                          jhchem[, .(Study.id,
                                     Compound,
                                     Total.subjects,
                                     Clearance.median,
                                     Clearance.95CI.min,
                                     Clearance.95CI.max,
                                     Clearance.units,
                                     src,
                                     MW,
                                     fup.zero,
                                     Clint.zero)],
                          by='Study.id')
      overall.dt[Clearance.units=='1/h',
                 Clearance.units:='L/h'] #correct typo/misreading of "1" for lowercase "L"
      #For clearances given as L/h/kg:
      #1 mg/kg/day over L/day/kg = Css in mg/L
      #Css in mg/L divided by MW in mg/umol = umol/L = uM
      overall.dt[Clearance.units=='L/h/kg',
                 css.median.invivo:=1/(24*Clearance.median*(MW/1000))]
      overall.dt[Clearance.units=='L/h/kg',
                 css.95CImax.invivo:=1/(24*Clearance.95CI.min*(MW/1000))]
      overall.dt[Clearance.units=='L/h/kg',
                 css.95CImin.invivo:=1/(24*Clearance.95CI.max*(MW/1000))]
      #For clearances given as L/h:
      #1 mg/kg/day over L/day = mg/L/kg = Css/kg BW
      #mg/L/kg divided by MW in mg/umol = uM/kg = Css/kg BW
      overall.dt[Clearance.units=='L/h',
                 css.bw.median.invivo:=1/(24*Clearance.median*(MW/1000))]
      overall.dt[Clearance.units=='L/h',
                 css.bw.95CImax.invivo:=1/(24*Clearance.95CI.min*(MW/1000))]
      overall.dt[Clearance.units=='L/h',
                 css.bw.95CImin.invivo:=1/(24*Clearance.95CI.max*(MW/1000))]
      #Get overall bounds on Css and clearance
      overall.dt[, mean.css.95CI.max:=mean.css.95CI.max.fold*median.css.median]
      overall.dt[, mean.css.95CI.min:=mean.css.95CI.min.fold*median.css.median]
      overall.dt[, mean.css.bw.95CI.max:=mean.css.bw.95CI.max.fold*median.css.bw.median]
      overall.dt[, mean.css.bw.95CI.min:=mean.css.bw.95CI.min.fold*median.css.bw.median]
      overall.dt[, poormetab:=poormetab]
      overall.dt[, fup.censor:=fup.censor]
      overall.dt[, fuptofub:=fuptofub]

      #Generate ellipses for Css
      overall.ellipse <- overall.dt[Clearance.units=='L/h/kg',
                                    ellipse_fun(x.CI.max=log10(css.95CImax.invivo),
                                                x.CI.min=log10(css.95CImin.invivo),
                                                y.CI.max=log10(mean.css.95CI.max),
                                                y.CI.min=log10(mean.css.95CI.min)),
                                    by=.(Study.id, Compound, Clearance.units, src)]
      #Define colors for plotting
      #from ColorBrewer2.org -- qualitative scale with 12 colors (the max), plus 3 greys
      colvect <- c(brewer.pal(12, 'Paired'),
                   c("gray75", "gray50", "black"))
      names(colvect) <- overall.dt[, unique(Compound)]
      #swap alprazolam (light blue) and omeprazole (light purple)
      #makes it easier to tell differences
      tmp <- colvect['omeprazole']
      colvect['omeprazole'] <- colvect['alprazolam']
      colvect['alprazolam'] <- tmp
      rm(tmp)
      #colvect['theophylline']<-'gray50'
      #Set up function to rescale axis labels
      labels.rescale <- function(){
        function(x) 10^x
        }

      #Generate ellipses for Css/kg BW
      overall.ellipse2 <- overall.dt[Clearance.units=='L/h',
                                     ellipse_fun(x.CI.max=log10(css.bw.95CImax.invivo),
                                                 x.CI.min=log10(css.bw.95CImin.invivo),
                                                 y.CI.max=log10(mean.css.bw.95CI.max),
                                                 y.CI.min=log10(mean.css.bw.95CI.min)),
                                     by=.(Study.id, Compound, Clearance.units, src)]

    ellipse.dt <- rbind(overall.ellipse, overall.ellipse2)

    ellipse.dt[Clearance.units=="L/h", Css.units:="Css in uM/kg"]
    ellipse.dt[Clearance.units=="L/h/kg", Css.units:="Css in uM"]

    ptest <- ggplot(data=ellipse.dt)

    for (i in ellipse.dt[, unique(Study.id)]) {
    ptest <- ptest + geom_path(data=ellipse.dt[Study.id==i,],
    aes(x=ellipse.x, y=ellipse.y,
    color=Compound))
    }

    ptest<- ptest + geom_abline(slope=1,intercept=0, linetype=2)+
    scale_color_manual(limits=ellipse.dt[, unique(Compound)],
    values=colvect)+
    scale_x_continuous(labels=labels.rescale()) + #force axes equal range
    scale_y_continuous(labels=labels.rescale()) + #force axes equal range
    facet_wrap(~Css.units, scales="free") + #, space="free") +
      coord_fixed(ratio=1) +
    labs(x=expression(paste(C[ss], ' in vivo')),
    y=expression(paste(C[ss], ' predicted'))) +
    theme_bw() +
    theme(legend.key=element_blank(),
    aspect.ratio=1,
    strip.background=element_blank(),
    legend.position="bottom")

      return(list(ptest=list(ptest), ov.dt=list(overall.dt)))
      }

Finally, let’s call the plotting function for the four combinations of poormetab and fup.censor.

    args.dt <- as.data.table(expand.grid(poormetab=c(TRUE, FALSE),
                             fup.censor=c(TRUE, FALSE),
                             fuptofub=c(TRUE, FALSE)))
    out.dt <- args.dt[, plot_virtstudy_innerfunction(model="3compartmentss",
                                           poormetab=poormetab,
                                           fup.censor=fup.censor,
                                           fuptofub=fuptofub,
                                           jhchem=jhchem),
            by=.(poormetab, fup.censor, fuptofub)]

    plotfun <- function(ptmp, poormetab, fup.censor, fuptofub){
      print(ptmp[[1]] + ggtitle(paste(c("poormetab",
                                   "fup.censor",
                                   "Fup to Fub"),
                                 c(poormetab,
                                   fup.censor,
                                   fuptofub),
                                 sep=" = ",
                                 collapse=", ")))
      ggsave(paste0(paste("pdf_figures/howgatejohnson_css_poormetab",
                   poormetab,
                   "fupcensor",
                   fup.censor,
                   "FuptoFub",
                   fuptofub,
                   sep="_"),
                   ".pdf"),
             ptmp[[1]],
             width=8.5,
             height=5.4)
    }

    out.dt[, plotfun(ptmp=ptest,
                     poormetab=poormetab,
                     fup.censor=fup.censor,
                     fuptofub=fuptofub),
           by=.(poormetab, fup.censor, fuptofub)]

    stats.dt <- rbindlist(out.dt[, ov.dt])
    #Also show a table of how many are within 2-fold, 5-fold, 10-fold
    #Compare Css medians:
    stats.dt[src=="Howgate et al. 2006",
               css.median.pred.over.lit:=median.css.bw.median/css.bw.median.invivo]
    stats.dt[src=="Johnson et al. 2006",
               css.median.pred.over.lit:=median.css.median/css.median.invivo]
    #Compare 95% CI ranges:
    stats.dt[src=="Johnson et al. 2006",
               css.95CI.range.pred.over.lit:=(mean.css.95CI.max-mean.css.95CI.min)/(css.95CImax.invivo - css.95CImin.invivo)]
    stats.dt[src=="Howgate et al. 2006",
               css.95CI.range.pred.over.lit:=(mean.css.bw.95CI.max-mean.css.bw.95CI.min)/(css.bw.95CImax.invivo - css.bw.95CImin.invivo)]

    cssmed.dt <- stats.dt[, list(sum(css.median.pred.over.lit<=2 &
                                                        css.median.pred.over.lit>=0.5),
                                                  sum(css.median.pred.over.lit<=5 &
                                                        css.median.pred.over.lit>=0.2),
                                                  sum(css.median.pred.over.lit<=10 &
                                                        css.median.pred.over.lit>=0.1),
                                          length(unique(Study.id))),
                       by=.(poormetab, fup.censor, fuptofub, src)]
    setnames(cssmed.dt, paste0("V", 1:4), c("within.2fold",
                           "within.5fold",
                           "within.10fold",
                           "Total"))
    knitr::kable(cssmed.dt,
                 format="html",
                 col.names=c("PMs included?",
                             "Funbound.plasma censored below avg LOD?",
                             "Funbound.plasma converted to Funbound.blood?",
                   "Data from",
                             "Within 2-fold",
                             "Within 5-fold",
                             "Within 10-fold",
                             "Total"),
                 caption="Css median, predicted vs. literature in vivo, number of studies")

    css95CI.dt <- stats.dt[, list(sum(css.95CI.range.pred.over.lit<=2 &
                                                        css.95CI.range.pred.over.lit>=0.5),
                                                  sum(css.95CI.range.pred.over.lit<=5 &
                                                        css.95CI.range.pred.over.lit>=0.2),
                                                  sum(css.95CI.range.pred.over.lit<=10 &
                                                        css.95CI.range.pred.over.lit>=0.1),
                                          length(unique(Study.id))),
                       by=.(poormetab, fup.censor, fuptofub, src)]
    setnames(css95CI.dt, paste0("V", 1:4), c("within.2fold",
                           "within.5fold",
                           "within.10fold",
                           "Total"))
    knitr::kable(css95CI.dt,
                 format="html",
                 col.names=c("PMs included?",
                             "Funbound.plasma censored below avg LOD?",
                             "Funbound.plasma converted to Funbound.blood?",
                   "Data from",
                             "Within 2-fold",
                             "Within 5-fold",
                             "Within 10-fold",
                             "Total"),
                 caption="Css 95% CI range, predicted vs. literature in vivo, number of studies")