Pearce et al. (2017) Figures in Partition Coefficient Evaluation

Robert Pearce

2020-03-01

This vignette generates the data and figures from “Evaluation and calibration of high-throughput predictions of chemical distribution to tissues”.

Robert G. Pearce, R. Woodrow Setzer, Jimena L. Davis & John F. Wambaugh

Journal of Pharmacokinetics and Pharmacodynamics volume 44, pages549-565 (2017)

https://dx.doi.org/10.1007%2Fs10928-017-9548-7

Abstract

Toxicokinetics (TK) provides critical information for integrating chemical toxicity and exposure assessments in order to determine potential chemical risk (i.e., the margin between toxic doses and plausible exposures). For thousands of chemicals that are present in our environment, in vivo TK data are lacking. The publicly available R package “httk” (version 1.8, named for “high throughput TK”) draws from a database of in vitro data and physico-chemical properties in order to run physiologically-based TK (PBTK) models for 553 compounds. The PBTK model parameters include tissue:plasma partition coefficients (Kp) which the httk software predicts using the model of Schmitt (Toxicol In Vitro 22 (2):457-467, 2008). In this paper we evaluated and modified httk predictions, and quantified confidence using in vivo literature data. We used 964 rat Kp measured by in vivo experiments for 143 compounds. Initially, predicted Kp were significantly larger than measured Kp for many lipophilic compounds (log10 octanol:water partition coefficient > 3). Hence the approach for predicting Kp was revised to account for possible deficiencies in the in vitro protein binding assay, and the method for predicting membrane affinity was revised. These changes yielded improvements ranging from a factor of 10 to nearly a factor of 10,000 for 83 Kp across 23 compounds with only 3 Kp worsening by more than a factor of 10. The vast majority (92%) of Kp were predicted within a factor of 10 of the measured value (overall root mean squared error of 0.59 on log10-transformed scale). After applying the adjustments, regressions were performed to calibrate and evaluate the predictions for 12 tissues. Predictions for some tissues (e.g., spleen, bone, gut, lung) were observed to be better than predictions for other tissues (e.g., skin, brain, fat), indicating that confidence in the application of in silico tools to predict chemical partitioning varies depending upon the tissues involved. Our calibrated model was then evaluated using a second data set of human in vivo measurements of volume of distribution (Vss) for 498 compounds reviewed by Obach et al. (Drug Metab Dispos 36(7):1385-1405, 2008). We found that calibration of the model improved performance: a regression of the measured values as a function of the predictions has a slope of 1.03, intercept of ??? 0.04, and R2 of 0.43. Through careful evaluation of predictive methods for chemical partitioning into tissues, we have improved and calibrated these methods and quantified confidence for TK predictions in humans and rats.

library(httk)
library(gdata)
library(ggplot2)
library(viridis)
#> Loading required package: viridisLite
#> 
#> Attaching package: 'viridis'
#> The following object is masked from 'package:scales':
#> 
#>     viridis_pal
library(CensRegMod)
library(gmodels)
library(gplots)
#> 
#> Attaching package: 'gplots'
#> The following object is masked from 'package:stats':
#> 
#>     lowess
library(scales)
library(colorspace)
# We love to give warning messages whenever assumptions are used by HTTK,
# but they will overwhelm the output of this vignette so we turn them
# off:
options(warn = -1)

We first filter the measured rat Kp data, pc.data. Then the old and new Kp predictions are made, along with error and improvement measures, and these are all consolidated into a table for analysis and plotting. Note that the final table contains log10-transformed values and error and improvements derived from subtracting these values. Only relevant rat values are used. Compounds with Funbound.plasma and partition coefficients of zero are removed as well as compounds with approximated Funbound.plasma values.

pc.table <- NULL
pc.data <- subset(httk::pc.data,fu != 0 & Exp_PC != 0 & Tissue %in% c("Adipose","Bone","Brain","Gut",
    "Heart","Kidney","Liver","Lung","Muscle","Skin","Spleen","Blood Cells") & 
    tolower(Species) == 'rat' & !CAS %in% c('10457-90-6','5786-21-0','17617-23-1','69-23-8','2898-12-6',
    '57562-99-9','59-99-4','2955-38-6','155-97-5','41903-57-5','58-55-9','77-32-7','59-05-2','60-54-8'))
cas.list <- get_cheminfo(model='schmitt',species='rat')
cas.list <-  cas.list[cas.list %in% pc.data[,'CAS']]
ma.data.list <- subset(chem.physical_and_invitro.data,!is.na(logMA))[,'CAS']
for(this.cas in cas.list){
  parameters <- parameterize_schmitt(chem.cas=this.cas,species='rat')
  init.parameters <- parameters
  charge <- calc_ionization(chem.cas=this.cas,pH=7.4)$fraction_charged
  if(!this.cas %in% ma.data.list){
    init.parameters$MA <- 10^(0.999831 - 0.016578*38.7 + 0.881721 * log10(parameters$Pow))
  }
  pcs <- predict_partitioning_schmitt(parameters=parameters,species='rat',regression=F)
  init.pcs <- predict_partitioning_schmitt(parameters=init.parameters,species='rat',regression=F)
  for(this.tissue in subset(pc.data,CAS==this.cas)[,'Tissue']){
    if(this.tissue == 'Blood Cells') this.pc <- 'rbc'
    else this.pc <- this.tissue
    pc.table <- rbind(pc.table,cbind(as.data.frame(this.cas),as.data.frame(this.tissue),
    as.data.frame(log10(init.pcs[[which(substr(names(init.pcs),2,nchar(names(init.pcs))-3)
                                  == tolower(this.pc))]] * init.parameters$Funbound.plasma)),
    as.data.frame(log10(pcs[[which(substr(names(pcs),2,nchar(names(pcs))-3)
                             == tolower(this.pc))]] * parameters$unadjusted.Funbound.plasma)),
    as.data.frame(log10(init.pcs[[which(substr(names(init.pcs),2,nchar(names(init.pcs))-3)
                                  == tolower(this.pc))]] * init.parameters$unadjusted.Funbound.plasma)),
    as.data.frame(log10(pcs[[which(substr(names(pcs),2,nchar(names(pcs))-3)
                             == tolower(this.pc))]] * parameters$Funbound.plasma)),
    as.data.frame(log10(subset(pc.data,CAS==this.cas & Tissue==this.tissue)[,'Exp_PC'])),
    as.data.frame(subset(pc.data,CAS==this.cas & Tissue==this.tissue)[,'LogP']),as.data.frame(charge),
    as.data.frame(as.character(subset(pc.data,CAS == this.cas)[1,'A.B.N'])),
    as.data.frame(subset(pc.data,CAS == this.cas)[1,'fu'])))
  }
}
colnames(pc.table) <- c('CAS','Tissue','fup.adjustment','ma.adjustment','init.Predicted',
                        'Predicted','Experimental','logP','charge','type','fup')
init.error <- pc.table[,'Experimental'] - pc.table[,'init.Predicted']
fup.error <- pc.table[,'Experimental'] - pc.table[,'fup.adjustment']
ma.error <- pc.table[,'Experimental'] - pc.table[,'ma.adjustment']
final.error <- pc.table[,'Experimental'] - pc.table[,'Predicted']
fup.improvement <- abs(init.error) - abs(fup.error)
ma.improvement <- abs(init.error) - abs(ma.error)
final.improvement <- abs(init.error) - abs(final.error)
pc.table <- cbind(pc.table,fup.improvement,ma.improvement, final.improvement,
                  final.error,init.error,ma.error,fup.error)

scientific_10 <- function(x) {                                  
  out <- gsub("1e", "10^", scientific_format()(x))              
  out <- gsub("\\+","",out)                                     
  out <- gsub("10\\^01","10",out)                               
  out <- parse(text=gsub("10\\^00","1",out))                    
}  


init.plot <- ggplot() + geom_point(data=pc.table,aes(10^(init.Predicted),10^(Experimental))) +
    geom_abline() + labs(y=expression(paste("Measured ",K[p])), x=expression(paste("Predicted ",K[p]))) +
    theme(axis.text=element_text(size=16),axis.title=element_text(size=16),
    plot.title=element_text(size=18,hjust = 0.5)) + scale_x_log10(label=scientific_10,limits=c(0.01,10^4.5)) +
    scale_y_log10(label=scientific_10,limits=c(0.01,10^4.5)) + ggtitle('(A)')
print(init.plot)


final.plot <- ggplot() + geom_point(data=pc.table,aes(10^(Predicted),10^(Experimental))) +
    geom_abline() + labs(y=expression(paste("Measured ",K[p])),x=expression(paste("Predicted ",K[p]))) +
    theme(axis.text=element_text(size=16),axis.title=element_text(size=16),
    plot.title=element_text(size=18,hjust=0.5)) + scale_x_log10(label=scientific_10,limits=c(0.01,10^4.5)) +
    scale_y_log10(label=scientific_10,limits=c(0.01,10^4.5)) + ggtitle('(B)')
print(final.plot)


fup.change.plot <-  ggplot() +
    geom_point(data=pc.table[order(pc.table[,'fup.improvement'],decreasing=F),],
    aes(10^(fup.adjustment),10^(Experimental),color=fup.improvement)) + geom_abline() +
    labs(y=expression(paste("Measured ",K[p])),x=expression(paste("Predicted ",K[p])),color='Improvement') +
    theme(axis.text=element_text(size=16),axis.title=element_text(size=16)) +
    scale_x_log10(label=scientific_10,limits=c(0.01,10^4.5)) + 
    scale_y_log10(label=scientific_10,limits=c(0.01,10^4.5)) +
    scale_color_viridis(direction=-1,option='inferno')
print(fup.change.plot)


ma.subset <- subset(pc.table,!CAS %in% ma.data.list)
ma.change.plot <- ggplot() +
    geom_point(data=ma.subset[order(ma.subset[,'ma.improvement'],decreasing=F),]
    ,aes(10^(ma.adjustment),10^(Experimental),color=ma.improvement)) + geom_abline() +
    labs(y=expression(paste("Measured ",K[p])),x=expression(paste("Predicted ",K[p])),color='Improvement') +
    theme(axis.text=element_text(size=16),axis.title=element_text(size=16)) +
    scale_x_log10(label=scientific_10,limits=c(0.01,10^4.5)) + 
    scale_y_log10(label=scientific_10,limits=c(0.01,10^4.5)) +
    scale_color_viridis(direction=-1,option='inferno')
print(ma.change.plot)

Now we calculate and plot the regressions for all tissues, together with their 95% confidence intervals.

regressions <- NULL

for(tissue in as.character(unique(pc.table[,'Tissue']))){
  fit <- lm(Experimental ~ Predicted ,data=subset(pc.table,Tissue==tissue))
  smry <- summary(fit)
  est <- estimable(fit, cm=diag(2), beta0=c(0,1), joint.test=TRUE)
  regressions <- rbind(regressions,cbind(tissue,as.data.frame(fit$coefficients[['(Intercept)']]),
      as.data.frame(fit$coefficients[['Predicted']]),
      as.data.frame(smry$coefficients[['Predicted','Pr(>|t|)']]),
      as.data.frame(smry$sigma),as.data.frame(smry$r.squared),
      as.data.frame(smry[[11]][1,1]),as.data.frame(smry[[11]][2,2]),
      as.data.frame(smry[[11]][1,2]),as.data.frame(smry$df[2]),as.data.frame(est[[3]])))
}
#>    X2.stat DF Pr(>|X^2|)
#> 1 90.01639  2          0
#>    X2.stat DF Pr(>|X^2|)
#> 1 122.3277  2          0
#>    X2.stat DF Pr(>|X^2|)
#> 1 321.9856  2          0
#>    X2.stat DF Pr(>|X^2|)
#> 1 2.136021  2  0.3436917
#>   X2.stat DF  Pr(>|X^2|)
#> 1  11.432  2 0.003292852
#>    X2.stat DF   Pr(>|X^2|)
#> 1 68.58971  2 1.221245e-15
#>    X2.stat DF   Pr(>|X^2|)
#> 1 39.54754  2 2.584407e-09
#>   X2.stat DF Pr(>|X^2|)
#> 1 4.50025  2   0.105386
#>    X2.stat DF  Pr(>|X^2|)
#> 1 9.747334  2 0.007645278
#>    X2.stat DF   Pr(>|X^2|)
#> 1 55.63481  2 8.300027e-13
#>    X2.stat DF Pr(>|X^2|)
#> 1 2.434562  2  0.2960341
#>   X2.stat DF Pr(>|X^2|)
#> 1 4.30141  2  0.1164021
colnames(regressions) <- c('Tissue','Intercept','Slope','P-value','SE','R-squared',
                           'Int Var','Slp Var','Cov','df','estimable')
x.cf <- seq(-2,3.5,.01)
for(tissue in  as.character(unique(pc.table[,'Tissue']))){
  conf <- qt(0.975,df=subset(regressions,Tissue==tissue)[['df']]+1) *
      subset(regressions,Tissue==tissue)[['SE']] *
      sqrt(subset(regressions,Tissue==tissue)[['Int Var']] +
      x.cf^2 * subset(regressions,Tissue==tissue)[['Slp Var']] +
      2 * x.cf * subset(regressions,Tissue==tissue)[['Cov']] + 1)
  line <- subset(regressions,Tissue==tissue)[['Intercept']] +
      x.cf * subset(regressions,Tissue==tissue)[['Slope']]
  y.cf <- line + conf
  y.ncf <- line - conf

  cf <- cbind(as.data.frame(x.cf),as.data.frame(y.cf),as.data.frame(y.ncf))
  if(tissue == 'Blood Cells'){
    eval(parse(text= paste('Blood <- ggplot() + labs(y=expression(paste("Inferred ",K[p])),
                               x=expression(paste("Predicted ",K[p]))) + geom_abline(linetype = "dashed") +
                               geom_point(data=subset(pc.table,Tissue == \'',tissue,'\'),aes(10^(Predicted),
                               10^(Experimental)))  +  theme(axis.text=element_text(size=14),
                               axis.title=element_text(size=14),plot.title=element_text(size=14,hjust=0.5)) +
                               scale_x_log10(label=scientific_10,limits=c(0.01,1000)) + 
                               scale_y_log10(label=scientific_10,limits=c(0.01,1000)) +
                               geom_line(data=cf,aes(10^(x.cf),10^(y.cf))) +
                               geom_line(data=cf,aes(10^(x.cf),10^(y.ncf))) +
                               geom_abline(intercept=subset(regressions,Tissue==tissue)[[\'Intercept\']],
                               slope=subset(regressions,Tissue==tissue)[[\'Slope\']]) +
                               ggtitle(\'Red Blood Cells\')',sep='')))
  }else{
    eval(parse(text= paste(tissue,' <- ggplot() + labs(y=expression(paste("Measured ",K[p]))
                               ,x=expression(paste("Predicted ",K[p]))) + geom_abline(linetype = "dashed") +
                               geom_point(data=subset(pc.table,Tissue == \'',tissue,'\'),
                               aes(10^(Predicted),10^(Experimental))) + theme(axis.text=element_text(size=14),
                               axis.title=element_text(size=14),plot.title=element_text(size=14,hjust=0.5)) +
                               scale_x_log10(label=scientific_10,limits=c(0.01,1000)) + 
                               scale_y_log10(label=scientific_10,limits=c(0.01,1000)) +
                               geom_line(data=cf,aes(10^(x.cf),10^(y.cf))) +
                               geom_line(data=cf,aes(10^(x.cf),10^(y.ncf))) +
                               geom_abline(intercept=subset(regressions,Tissue==tissue)[[\'Intercept\']],
                               slope=subset(regressions,Tissue==tissue)[[\'Slope\']]) +
                               ggtitle(\'',tissue,'\')',sep='')))
  }
}

In vivo volume of distribution data are compared with the predictions, and errors are calculated. Regressions and improvements are calculated and plotted.

obach <- subset(Obach2008,CAS %in% get_cheminfo(model='schmitt'))
vd.table <- NULL

for(this.cas in obach[,'CAS']){
  parameters <- parameterize_schmitt(chem.cas=this.cas)
  init.parameters <- parameters
  if(!this.cas %in% ma.data.list){
    init.parameters$MA <- 10^(0.999831 - 0.016578*37 + 0.881721 * log10(parameters$Pow))
  }
  pcs <- predict_partitioning_schmitt(parameters=parameters,regression=F)
  init.pcs <- predict_partitioning_schmitt(parameters=init.parameters,regression=F)
  reg.pcs <- predict_partitioning_schmitt(parameters=parameters,regression=T)
  vdist <- calc_vdist(parameters=c(pcs,
    Funbound.plasma=parameters$Funbound.plasma),
    suppress.messages = TRUE)
  init.vdist <- calc_vdist(parameters=c(init.pcs,
    Funbound.plasma=parameters$unadjusted.Funbound.plasma),
    suppress.messages = TRUE)
  reg.vdist <- calc_vdist(parameters=c(reg.pcs,
    Funbound.plasma=parameters$Funbound.plasma),
    suppress.messages = TRUE)
  vd.table <- rbind(vd.table,cbind(as.data.frame(this.cas),as.data.frame(log10(init.vdist)),
                    as.data.frame(log10(vdist)),as.data.frame(log10(reg.vdist)),
                    as.data.frame(log10(subset(obach,CAS==this.cas)[['VDss (L/kg)']]))))
}
colnames(vd.table) <- c('CAS','init.vdist','adjusted.vdist','calibrated.vdist','Experimental')
init.error <- vd.table[,'Experimental'] - vd.table[,'init.vdist']
adjustment.error <- vd.table[,'Experimental'] - vd.table[,'adjusted.vdist']
calibration.error <- vd.table[,'Experimental'] - vd.table[,'calibrated.vdist']
adjustment.improvement <- abs(init.error) - abs(adjustment.error)
calibration.improvement <- abs(adjustment.error) - abs(calibration.error)
vd.table <- cbind(vd.table,adjustment.improvement,calibration.improvement,
                  init.error,adjustment.error,calibration.error)
fit <- lm(Experimental ~ calibrated.vdist,data=vd.table)
smry <- summary(fit)
calibrated.reg <- cbind(as.data.frame(fit$coefficients['(Intercept)']),
                        as.data.frame(fit$coefficients['calibrated.vdist']),
                        as.data.frame(smry$coefficients['calibrated.vdist','Pr(>|t|)']),
                        as.data.frame(smry$sigma),as.data.frame(smry$r.squared))
fit <- lm(Experimental ~ init.vdist,data=vd.table)
smry <- summary(fit)
init.reg <- cbind(as.data.frame(fit$coefficients['(Intercept)']),
                  as.data.frame(fit$coefficients['init.vdist']),
                  as.data.frame(smry$coefficients['init.vdist','Pr(>|t|)']),
                  as.data.frame(smry$sigma),as.data.frame(smry$r.squared))
fit <- lm(Experimental ~ adjusted.vdist,data=vd.table)
smry <- summary(fit)
adjustment.reg <- cbind(as.data.frame(fit$coefficients['(Intercept)']),
                       as.data.frame(fit$coefficients['adjusted.vdist']),
                       as.data.frame(smry$coefficients['adjusted.vdist','Pr(>|t|)']),
                       as.data.frame(smry$sigma),as.data.frame(smry$r.squared))
colnames(init.reg) <- colnames(adjustment.reg) <-
colnames(calibrated.reg) <- c('Intercept','Slope','P-value','Std Err','R-squared')

init.vd.plot <- ggplot(vd.table,aes(10^(init.vdist),10^(Experimental))) + geom_point() +
    geom_abline(intercept = init.reg[['Intercept']], slope = init.reg[["Slope"]]) +
    geom_abline(linetype = "dashed") + xlab("Predicted Volume of Distribution") +
    ylab("Measured Volume of Distribution") + theme(axis.text=element_text(size=16),
    axis.title=element_text(size=16),plot.title=element_text(size=18,hjust = 0.5)) +
    scale_x_log10(label=scientific_10,limits=c(10^(-1.5),10^(8.5))) + 
    scale_y_log10(label=scientific_10,limits=c(10^(-1.5),10^(8.5))) +
    ggtitle('(A)')
print(init.vd.plot)


adjustment.plot <- ggplot() +
    geom_point(data=vd.table[order(vd.table[,'adjustment.improvement'],decreasing=F),],
    aes(10^(adjusted.vdist),10^(Experimental),color=adjustment.improvement)) +
    geom_abline(intercept = adjustment.reg[['Intercept']],slope = adjustment.reg[["Slope"]]) +
    geom_abline(linetype = "dashed") + xlab("Predicted Volume of Distribution") +
    ylab("Measured Volume of Distribution") + theme(legend.position = c(.95, .95),
    legend.justification = c("right", "top"),legend.box.just = "right",
    legend.margin = margin(6, 6, 6, 6),axis.text=element_text(size=16),
    axis.title=element_text(size=16),plot.title=element_text(size=18,hjust = 0.5)) +
    scale_x_log10(limits=c(10^(-1.5),10^(3))) + scale_y_log10(limits=c(10^(-1.5),10^(3))) +
    ggtitle('(B)') + scale_color_viridis(direction=-1,option='inferno')
print(adjustment.plot)


calibration.plot <- ggplot() +
    geom_point(data=vd.table[order(vd.table[,'calibration.improvement'],decreasing=F),],
    aes(10^(calibrated.vdist),10^(Experimental),color=calibration.improvement)) +
    geom_abline(intercept = calibrated.reg[['Intercept']],slope = calibrated.reg[["Slope"]]) +
    geom_abline(linetype = "dashed") + xlab("Predicted Volume of Distribution") +
    ylab("Measured Volume of Distribution") + theme(legend.position = c(.95, .95),
    legend.justification = c("right", "top"),legend.box.just = "right",
    legend.margin = margin(6, 6, 6, 6),axis.text=element_text(size=16),
    axis.title=element_text(size=16),plot.title=element_text(size=18,hjust = 0.5)) +
    scale_x_log10(limits=c(10^(-1.5),10^(3))) + scale_y_log10(limits=c(10^(-1.5),10^(3))) +
    ggtitle('(C)') + scale_color_viridis(direction=-1,option='inferno')
print(calibration.plot)

Now we pull in the in vivo blood to plasma ratios, use these to calculate the inferred red blood cell to plasma ratios, and then make predictions for these values. A censored regressions is performed, and predictions are plotted against errors.

rb2p.data <- subset(chem.physical_and_invitro.data,!is.na(Human.Rblood2plasma))
measured.rb2p <- NULL
measured.krbc <- NULL
predicted.rb2p <- NULL
predicted.krbc <- NULL
cas <- NULL
charge <- NULL
fup <- NULL
logP <- NULL
pka_donor <- NULL
pka_accept <- NULL
for(this.cas in rb2p.data[rb2p.data[,'CAS'] %in% get_cheminfo(model='schmitt'),'CAS']){
  rb2p <- get_rblood2plasma(chem.cas=this.cas)
  krbc <- (rb2p + .44 - 1) / 0.44
  measured.rb2p <- c(measured.rb2p,rb2p)
  measured.krbc <- c(measured.krbc,krbc)
  parameters <- parameterize_schmitt(chem.cas=this.cas)
  pcs <- predict_partitioning_schmitt(parameters=parameters)
  predicted.krbc <- c(predicted.krbc,pcs[['Krbc2pu']] * parameters$Funbound.plasma)
  cas <- c(cas,this.cas)
  charge <- c(charge,calc_ionization(chem.cas=this.cas,pH=7.4)$fraction_charged)
  fup <- c(fup,parameters$unadjusted.Funbound.plasma)
  logP <-  c(logP,log10(parameters$Pow))
  pka_donor <- c(pka_donor,paste(parameters$pKa_Donor,collapse=','))
  pka_accept <- c(pka_accept,paste(parameters$pKa_Accept,collapse=','))
}
predicted.rb2p <-  1 - 0.44 + 0.44 * predicted.krbc
rb2p.table <- cbind(as.data.frame(cas),as.data.frame(predicted.rb2p),as.data.frame(measured.rb2p))
colnames(rb2p.table) <- c('cas','predicted.rb2p','measured.rb2p')
error <- log10(rb2p.table[,'measured.rb2p']) - log10(rb2p.table[,'predicted.rb2p'])
rb2p.table <- cbind(rb2p.table,error,charge,fup,logP)

error <- log10(measured.krbc) -  log10(predicted.krbc)
krbc.table <- cbind(as.data.frame(cas),as.data.frame(predicted.krbc),as.data.frame(measured.krbc),
                    as.data.frame(error),charge,fup,logP,pka_donor,pka_accept)

pdta <- data.frame(x = predicted.krbc,
                   y = measured.krbc)
pdta$y[pdta$y <= 0.1] <- 0.1
pdta$Censoring <- factor(c("Not Censored","Censored")[as.numeric(pdta$y <= 0.1) + 1])
y <- measured.krbc
x <- cbind(rep(1, length(y)),-1 * log10(predicted.krbc))
colnames(x) <- c("Intercept","Predicted")
cc <- as.numeric(y <= 0.1)
y[y < 0.1] <- 0.1
y <- -log10(y)

out <- em.cens(cc, x, y, dist="Normal")
#> 
#> -------------------------------------------
#>          EM estimates and SE 
#> -------------------------------------------
#>           Estimates      SE
#> Intercept   0.17831 0.03817
#> Predicted   0.29792 0.03803
#> sigma^2     0.16431 0.01517
#> ------------------------------------------
#> 
 
#> 
#> Model selection criteria
#> -------------------------------------------
#>         Loglik     AIC     BIC     EDC
#> Value -183.154 372.308 383.459 376.769
#> -------------------------------------------
#> 

censored.regression <- ggplot() +
    geom_point(data=pdta,aes(x=x,y=y, color=Censoring)) +
    scale_x_log10(limits=c(.0009,40)) + scale_y_log10(limits=c(.1,4),breaks=c(.1,.5,2.5)) +
    labs(y=expression(paste("Inferred ",K[p])),x=expression(paste("Predicted ",K[p]))) +
    geom_abline(intercept=0, slope=1, linetype='dashed') +
    theme(axis.text=element_text(size=16),axis.title=element_text(size=16),
    plot.title=element_text(size=18,hjust=0.5),legend.position = c(0.11, .8)) +
    geom_abline(slope=out$betas[2],intercept=-out$betas[1]) + ggtitle('(B)')

rb2p.plot <- ggplot(rb2p.table,aes(predicted.rb2p,measured.rb2p)) +
    geom_point()  + scale_x_log10(lim=c(.52,18)) + 
    scale_y_log10(lim=c(.52,2.5),breaks=c(0.5,1,2)) + geom_abline(linetype='dashed') +
    labs(y="Measured B:P Ratio ",
    x="Predicted B:P Ratio") +
    theme(axis.text=element_text(size=16),axis.title=element_text(size=16),
    plot.title=element_text(size=18,hjust=0.5)) + ggtitle('(A)')
print(rb2p.plot)

Lastly, we make the heatmap.

heatmap.table <- NULL
for(this.cas in get_cheminfo(model='schmitt')){
    parms <- parameterize_schmitt(chem.cas=this.cas)
    pcs <- predict_partitioning_schmitt(parameters=parms)
    heatmap.table <- cbind(heatmap.table,log10(unlist(pcs)[1:11]*parms$Funbound.plasma))
}
rownames(heatmap.table) <-  c('Adipose','Bone','Brain','Gut','Heart',
                              'Kidney','Liver','Lung','Muscle','Skin','Spleen')
colnames(heatmap.table) <- rep("",dim(heatmap.table)[2])

pal <- function (n, h = c(260, -328), c = 80, l = c(30, 100), power = 1.5,
    fixup = TRUE, gamma = NULL, alpha = 1, ...)
{
    if (!is.null(gamma))
        warning("'gamma' is deprecated and has no effect")
    if (n < 1L)
        return(character(0L))
   h <- rep(h, length.out = 2L)
    c <- c[1L]
    l <- rep(l, length.out = 2L)
    power <- rep(power, length.out = 2L)
    rval <- seq(1, -1, length = n)
    rval <- hex(polarLUV(L = l[2L] - diff(l) * abs(rval)^power[2L],
        C = c * abs(rval)^power[1L], H = ifelse(rval > 0, h[1L],
            h[2L])), fixup = fixup, ...)
    if (!missing(alpha)) {
        alpha <- pmax(pmin(alpha, 1), 0)
        alpha <- format(as.hexmode(round(alpha * 255 + 1e-04)),
            width = 2L, upper.case = TRUE)
        rval <- paste(rval, alpha, sep = "")
    }
    return(rval)
}

hclust.ave <- function(x) hclust(x, method="ward.D2")
par(cex.main=1.5,cex.lab=2)
lhei <- c(1,4)
lwid <- c(1.25,2)
lmat <- rbind(c(2,3),c(4,1))
heatmap.2(heatmap.table,dendrogram='column',col=pal,trace="none",
          hclustfun=hclust.ave,key.xlab=expression(paste(log[10],K[p]," Value")),
          key.ylab=expression(paste("Number of ",K[p])),
          key.title="Partition Coefficients",xlab="Chemicals",cex.lab=2,
          lmat=lmat,margins=c(2,5),lwid=lwid,lhei=lhei)