# Ring et al. 2017 Vignette 2: Evaluating HTTK models for subpopulations

#### Caroline Ring

#### 2019-04-25

Once you have generated virtual population data for each subpopulation, you probably want to do something with that data – like run an HTTK model over each population. This vignette describes how to do that.

Before running the code in this vignette, you need to generate the virtual subpopulations by running the code in the Generating subpopulations vignette.

To use the code in this vignette, you’ll first need to load a few packages (if you haven’t already).

    library(httk)
    library(data.table)
    library(EnvStats)

# Running the HTTK models

The HTTK models are all general (chemical-independent) models, which means that in order to run them, you need to specify a chemical for which they can be parameterized. Let’s loop over all the chemicals in the HTTK data set. First, get a list of all of their CAS numbers.

    chemlist <- httk::get_cheminfo(info='CAS', exclude.fub.zero=FALSE)

# Things to do for each chemical

Next, we set up a function to be applied for each chemical. For each chemical, we need to draw Monte Carlo samples for `funbound.plasma` and for `Clint`, because those values are chemical-specific. Then we need to convert the physiological parameters generated by `httkpop`, along with the `Funbound.plasma` and `Clint` values, into the parameters for a specified HTTK model. Finally, we need to actually run the HTTK model for the specified chemical, and compute Css (the steady-state plasma concentration). Here, we’re using a fixed dose of 1 mg/kg/day; these Css values will be used to compute oral equivalent doses later on.

Rather than storing all 1000 Css values for each chemical, we compute several percentiles of the Css distribution for each chemical and store those instead. We also use a non-parametric method (implemented in `EnvStats::eqnpar`) to estimate the confidence intervals around each percentile of the Css distribution.

This function returns one row of a data.table: the Css percentiles, their lower and upper confidence limits, and the CAS number. When this function is applied repeatedly over many chemicals, the rows can be bound together to form one big data.table over all the chemicals.

    doforeachchem <- function(this.chemcas,
                              model,
                              species,
                              sigma.factor,
                              css.method,
                              indiv.model.bio,
                              poormetab,
                              fup.censor,
                              ExpoCast.group,
                              nsamp,
                              Clint.vary){

      indiv.model.bio <- data.table::copy(indiv.model.bio)
      #Convert to HTTK model params
      if (ExpoCast.group=="indepMC"){
        indiv.model.tmp <- cbind(indiv.model.bio,
                             httk::draw_fup_clint(this.chem=this.chemcas,
                                                     nsamp=nrow(indiv.model.bio),
                                                     poormetab=poormetab,
                                                     fup.censor=fup.censor))
        indiv.model <- httk::convert_httk(indiv.model.bio=indiv.model.tmp,
                                             model=model,
                                             this.chem=this.chemcas)
      }else{
      indiv.model <- httk::get_httk_params(indiv_dt=indiv.model.bio,
                                           model=model,
                                           chemcas=this.chemcas,
                                           poormetab=poormetab,
                                           fup.censor=fup.censor,
                                           Clint.vary=Clint.vary)
      }

      #If model is 3compartmentss, convert Funbound.plasma to Funbound.blood
      if (model=="3compartmentss"){
      #First, get the default parameters used for the Schmitt method of estimating
        #partition coefficients.
        pschmitt <- httk::parameterize_schmitt(chem.cas=this.chemcas,
                                               species='Human')
        #next, replace the single default value for Funbound.plasma with the vector
        #of Funbound.plasma values from the virtual population data.table.
        pschmitt$Funbound.plasma<-indiv.model[, Funbound.plasma]

        #Now, predict the partitioning coefficients using Schmitt's method. The
        #result will be a list of numerical vectors, one vector for each
        #tissue-to-plasma partitioning coefficient, and one element of each vector
        #for each individual. The list element names specify which partition
        #coefficient it is, e.g. Kliver2plasma, Kgut2plasma, etc.
        PCs <- httk::predict_partitioning_schmitt(parameters=pschmitt,
                                                  chem.cas=this.chemcas,
                                                  species='Human')
        Rb2p <- 1 - indiv.model.bio$hematocrit + indiv.model.bio$hematocrit *
          PCs[["Krbc2pu"]] *
          indiv.model$Funbound.plasma

      indiv.model[, Funbound.plasma:=Funbound.plasma/Rb2p]
      }

      #Evaluate model
      if (tolower(css.method)=='analytic') {
        #Css
        css <- httk::calc_analytic_css(chem.cas=this.chemcas,
                                       parameters=indiv.model,
                                       daily.dose=1,
                                       output.units="uM",
                                       model=model,
                                       species=species,
                                       suppress.messages=TRUE,
                                       recalc.blood2plasma=TRUE)

        if (model=="3compartmentss"){ #convert from Css.blood back to Css.plasma
          css <- css/Rb2p
        }
        }
      else if (tolower(css.method)=='full'){
        #Css
        css <- apply(X=indiv.model,
                     MARGIN=1,
                     FUN=function(x) httk::calc_css(chem.cas=this.chemcas,
                                                    parameters=as.list(x),
                                                    daily.dose=1,
                                                    output.units="uM",
                                                    model=model,
                                                    species=species,
                                                    suppress.messages=TRUE)[['avg']])
        }
      #Compute percentiles
      prob.vect <- c(0.01, 0.05,0.1,0.25,0.5,0.75,0.9,0.95, 0.99)
      css.q <- quantile(css, probs=prob.vect)
      #Function to compute lower and upper CI bounds
      tmpfun <- function(x,z){
        tmp <- tryCatch(EnvStats::eqnpar(x,
                                         p=z,
                                         ci=TRUE,
                                         lb=0)$interval[['limits']],
                        error=function(err){
                          return(c(LCL='NA', UCL='NA'))
                          })
        return(tmp)
        }
      #Compute Css CI bounds
      css.cl <- sapply(prob.vect, function(z) tmpfun(z, x=css)
                       )
      #Construct list to return
      dat.chem.out <- c(as.list(css.q),
                           as.list(css.cl['LCL',]),
                           as.list(css.cl['UCL',]),
                           as.list(var(css)),
                           as.list(this.chemcas),
                           as.list(ExpoCast.group))
      names(dat.chem.out) <- c(paste0('css',100*prob.vect),
                               paste0('LCL', 'css', 100*prob.vect),
                               paste0('UCL', 'css', 100*prob.vect),
                               'var.css',
                               'chemcas',
                               'ExpoCast.group')
      return(dat.chem.out)
      }

# Looping over subpopulations and over chemicals

So now, we need to loop over each of the subpopulations and then each of the chemicals.

We also need to choose a couple of settings – like whether poor metabolizers should be included in the `Clint` distribution, and whether the `Funbound.plasma` distribution should be censored or not. Let’s try it all ways, so we can compare them later on. Let’s also evaluate the model using both the virtual-individuals and direct-resampling populations, so we can compare those and see if there is a difference between the two ways of generating populations. (Spoiler alert: There isn’t.)

Warning: the following code may take a while to run!

Also note: This code was written for a machine where 10 processors were available. If you want to run on your own machine, you’ll need to change `numcluster` to a reasonable number of processors for your machine!

    numcluster <- 40 #The number of processors to use in parallel
    #Note: This will depend on how many your machine has available!
    cluster <- parallel::makeCluster(numcluster, outfile='subpoprun_parallel_out.txt')
    parallel::clusterEvalQ(cl=cluster,
                           {library(httk)})
    #Set seeds on all workers for reproducibility
    parallel::clusterSetRNGStream(cluster,
                                  TeachingDemos::char2seed("Caroline Ring"))
    #List subpopulations
    ExpoCast.groups<-list("Total",
                          "Age.6.11",
                          "Age.12.19",
                          "Age.20.65",
                          "Age.GT65",
                          "BMIgt30",
                          "BMIle30",
                          "Females",
                          "Males",
                          "ReproAgeFemale",
                          "Age.20.50.nonobese")
    #Evaluate model
    model <- '3compartmentss'
    popmethod <- "dr"
      for (grp in ExpoCast.groups){
        for (poormetab in c(TRUE, FALSE)){
          for (fup.censor in c(TRUE, FALSE)) {
            #First read in population data.table
            grp.dt <- readRDS(file=paste0('data/',paste('httkpop',
                                                        popmethod,
                                                        grp, sep='_'),
                                          '.Rdata'))
            nsamp <- nrow(grp.dt)
            #Next, loop over chemicals and rbind the result.
            allchems.dt <- data.table::rbindlist(parallel::parLapply(cl = cluster,
                                                                     X = chemlist,
                                                                     fun = doforeachchem,
                                                                     model = model,
                                                                     species = 'Human',
                                                                     sigma.factor = 0.3,
                                                                     css.method = 'analytic',
                                                                     indiv.model.bio = grp.dt,
                                                                     ExpoCast.group = grp,
                                                                     poormetab = poormetab,
                                                                     fup.censor = fup.censor,
                                                                     nsamp = nsamp,
                                                                     Clint.vary = TRUE))
            #Now, save the result. Put some metadata in the filename,
            #like the group, the method used to generate this population,
            #and the values of poormetab and fup.censor.
            #Also put which HTTK model was used.
            saveRDS(object = allchems.dt,
                    file = paste0('data/',
                                  paste('allchems', grp, popmethod,
                                        'poormetab', poormetab,
                                        'fup.censor', fup.censor,
                                        model,
                                        "FuptoFub", sep='_'),
                                  '.Rdata'))
            }
          }
        }
    parallel::stopCluster(cluster)

There – now we have Css and total clearance percentile data for each chemical, in each of the subpopulations of interest.

We also would like to evaluate Css and total clearance for a “virtual population” generated using independent Monte Carlo, for comparison purposes. First, we need to generate the independent-MC parameters.

    indep_gen <- function(nsamp=1000, sigma.factor=0.3){

      COmean <- physiology.data[physiology.data$Parameter=='Cardiac Output',
                                   'Human']
      indep.bio <- data.table(Qcardiacc=truncnorm::rtruncnorm(n=nsamp,
                                                              mean=COmean,
                                                              sd=sigma.factor*COmean,
                                                              a=0)/1000*60)
      indep.bio[, BW:=truncnorm::rtruncnorm(n=nsamp,
                                            mean=physiology.data[physiology.data$Parameter=='Average BW',
                                                                    'Human'],
                                            sd=sigma.factor*physiology.data[physiology.data$Parameter=='Average BW',
                                                                               'Human'],
                                            a=0)]
      indep.bio[, plasma.vol:=truncnorm::rtruncnorm(n=nsamp,
                                                    mean=physiology.data[physiology.data$Parameter=='Plasma Volume',
                                                                            'Human'],
                                                    sd=sigma.factor*physiology.data[physiology.data$Parameter=='Plasma Volume',
                                                                                       'Human'],
                                                    a=0)/1000] #convert mL/kg to L/kg
      indep.bio[, hematocrit:=truncnorm::rtruncnorm(n=nsamp,
                                                    mean=physiology.data[physiology.data$Parameter=='Hematocrit',
                                                                            'Human'],
                                                    sd=sigma.factor*physiology.data[physiology.data$Parameter=='Hematocrit',
                                                                                       'Human'],
                                                    a=0,
                                                    b=1)]
      indep.bio[, million.cells.per.gliver:=truncnorm::rtruncnorm(n=nsamp,
                                                                  mean=110,
                                                                  sd=sigma.factor*110,
                                                                  a=0)]

      all.tissues <- tissue.data$Tissue[tissue.data$Tissue!='red blood cells']
      for (tissue in all.tissues){
        vol.mean <- tissue.data[tissue.data$Tissue==tissue,
                                'Human Vol (L/kg)']
        flow.mean <- tissue.data[tissue.data$Tissue==tissue,
                                 'Human Flow (mL/min/kg^(3/4))']/
          1000*60
        if (tissue=='liver'){ #subtract gut flow from portal vein flow
          #to get arterial flow
          flow.mean <- (tissue.data[tissue.data$Tissue=='liver',
                                    'Human Flow (mL/min/kg^(3/4))'] -
                          tissue.data[tissue.data$Tissue=='gut',
                                      'Human Flow (mL/min/kg^(3/4))'])/
            1000*60
          }

        indep.bio[, paste0('V',
                           tissue,
                           'c'):=truncnorm::rtruncnorm(n=nsamp,
                                                       mean=vol.mean,
                                                       sd=sigma.factor*vol.mean,
                                                       a=0)]
        indep.bio[, paste0('Q',
                           tissue,
                           'f'):=truncnorm::rtruncnorm(n=nsamp,
                                                       mean=flow.mean,
                                                       sd=sigma.factor*flow.mean,
                                                       a=0)/Qcardiacc]
        }

      indep.bio[, Qtotal.liverc:=(Qliverf+Qgutf)*Qcardiacc]
      indep.bio[, liver.density:=1.05]
      gfr.mean<-physiology.data[physiology.data$Parameter=='GFR',
                                   'Human']*60/1000 #convert from ml/min/kg^(3/4) to L/hr/kg(3/4)
      indep.bio[, Qgfrc:=truncnorm::rtruncnorm(n=nsamp,
                                               mean=gfr.mean,
                                               sd=sigma.factor*gfr.mean,
                                               a=0)]
      indep.bio[,
                Vartc:= plasma.vol/
                  (1-hematocrit)/2] #L/kgBW
      indep.bio[,
                Vvenc:= plasma.vol/
                  (1-hematocrit)/2] #L/kgBW
      return(indep.bio)
      }

Next, we just call `doforeachchem()` on this independent-MC virtual population.

    model <- '3compartmentss'
    popmethod <- 'indepMC'
    TeachingDemos::char2seed("Caroline Ring")
    indep.bio <- indep_gen()
    numcluster <- 40 #The number of processors to use in parallel
    #Note: This will depend on how many your machine has available!
    cluster <- parallel::makeCluster(numcluster, outfile='indepMC_evalmodels_parallel_out.txt')
    parallel::clusterEvalQ(cl=cluster,
                           {library(httk)})
    #Set seeds on all workers for reproducibility
    parallel::clusterSetRNGStream(cluster,
                                  TeachingDemos::char2seed("Caroline Ring"))
    for (poormetab in c(TRUE, FALSE)){
      for (fup.censor in c(TRUE, FALSE)){
    allchems.dt <- data.table::rbindlist(parallel::parLapply(cl = cluster,
                                                             X = chemlist,
                                                             fun = doforeachchem,
                                                             model = model,
                                                             species = 'Human',
                                                             sigma.factor = 0.3,
                                                             css.method = 'analytic',
                                                             indiv.model.bio = indep.bio,
                                                             ExpoCast.group = 'indepMC',
                                                             poormetab = poormetab,
                                                             fup.censor = fup.censor,
                                                             nsamp = 1000,
                                                             Clint.vary = TRUE))
    #Now, save the result. Put some metadata in the filename,
    #like the group, the method used to generate this population,
    #and the values of poormetab and fup.censor.
    #Also put which HTTK model was used.
    saveRDS(object = allchems.dt,
            file = paste0('data/',
                          paste('allchems', popmethod,
                                'poormetab', poormetab,
                                'fup.censor', fup.censor,
                                model,
                                "FuptoFub",
                                sep='_'),
                          '.Rdata'))
    }
    }

    parallel::stopCluster(cluster)