Convert linear effect to Emax-Hill effect

Convert linear effect to Emax-Hill effect

Usage

convertEmaxHill(
  ui,
  emax = "Emax",
  ec50 = "EC50",
  g = "g",
  imax = "Imax",
  ic50 = "IC50",
  ek = c("Ik", "Ek"),
  cc = c("Ec", "Cc")
)

Arguments

ui

rxode2 model

emax

Emax parameter

ec50

EC50 parameter

g

hill coefficient

imax

Imax parameter used when input model contains "Ik" instead of "Ek"

ic50

IC50 parameter used when input model contains "Ik" instead of "Ek"

ek

simulation linear constant

cc

the concentration value

Value

Model with the linear effect converted to an Emax effect

Author

Matthew L. Fidler

Examples

readModelDb("PK_2cmt_no_depot") |>
  addIndirectLin(stim="in") |>
  convertEmaxHill()
#>  
#>  
#>  ── rxode2-based free-form 3-cmt ODE model ────────────────────────────────────── 
#>  ── Initalization: ──  
#> Fixed Effects ($theta): 
#>       lcl       lvc       lvp        lq    propSd      lkin     lkout  effectSd 
#>  1.000000  3.000000  5.000000  0.100000  0.500000  0.100000  0.100000  0.100000 
#>     lEmax     lEC50       lgg 
#>  0.100000  0.100000 -2.302585 
#> 
#> States ($state or $stateDf): 
#>   Compartment Number Compartment Name
#> 1                  1          central
#> 2                  2      peripheral1
#> 3                  3                R
#>  ── Multiple Endpoint Model ($multipleEndpoint): ──  
#>     variable                   cmt                   dvid*
#> 1     Cc ~ …     cmt='Cc' or cmt=4     dvid='Cc' or dvid=1
#> 2 effect ~ … cmt='effect' or cmt=5 dvid='effect' or dvid=2
#>   * If dvids are outside this range, all dvids are re-numered sequentially, ie 1,7, 10 becomes 1,2,3 etc
#> 
#>  ── Model (Normalized Syntax): ── 
#> function() {
#>     ini({
#>         lcl <- 1
#>         label("Clearance (CL)")
#>         lvc <- 3
#>         label("Central volume of distribution (V)")
#>         lvp <- 5
#>         label("Peripheral volume of distribution (Vp)")
#>         lq <- 0.1
#>         label("Intercompartmental clearance (Q)")
#>         propSd <- c(0, 0.5)
#>         label("Proportional residual error (fraction)")
#>         lkin <- 0.1
#>         label("zero order response production(kin)")
#>         lkout <- 0.1
#>         label("first order rate response loss (kout)")
#>         effectSd <- c(0, 0.1)
#>         label("additive error for effect")
#>         lEmax <- 0.1
#>         label("Maximum effect (Emax)")
#>         lEC50 <- 0.1
#>         label("Concentration of 50% Emax (Emax)")
#>         lgg <- -2.30258509299405
#>         label("logit-constrained Hill coefficient g")
#>     })
#>     model({
#>         Emax <- exp(lEmax)
#>         EC50 <- exp(lEC50)
#>         g <- expit(lgg, 0.1, 10)
#>         kin <- exp(lkin)
#>         kout <- exp(lkout)
#>         cl <- exp(lcl)
#>         vc <- exp(lvc)
#>         vp <- exp(lvp)
#>         q <- exp(lq)
#>         kel <- cl/vc
#>         k12 <- q/vc
#>         k21 <- q/vp
#>         d/dt(central) <- kel * central - k12 * central + k21 * 
#>             peripheral1
#>         d/dt(peripheral1) <- k12 * central - k21 * peripheral1
#>         Cc <- central/vc
#>         Cc ~ prop(propSd)
#>         R(0) <- kin/kout
#>         d/dt(R) <- kin * (1 + Emax * Cc^g/(Cc^g + EC50^g)) - 
#>             kout * R
#>         effect <- R
#>         effect ~ add(effectSd)
#>     })
#> }

# can also specify as emax=1

readModelDb("PK_2cmt_no_depot") |>
  addIndirectLin(stim="in") |>
  convertEmaxHill(emax=1)
#>  
#>  
#>  ── rxode2-based free-form 3-cmt ODE model ────────────────────────────────────── 
#>  ── Initalization: ──  
#> Fixed Effects ($theta): 
#>       lcl       lvc       lvp        lq    propSd      lkin     lkout  effectSd 
#>  1.000000  3.000000  5.000000  0.100000  0.500000  0.100000  0.100000  0.100000 
#>     lEC50       lgg 
#>  0.100000 -2.302585 
#> 
#> States ($state or $stateDf): 
#>   Compartment Number Compartment Name
#> 1                  1          central
#> 2                  2      peripheral1
#> 3                  3                R
#>  ── Multiple Endpoint Model ($multipleEndpoint): ──  
#>     variable                   cmt                   dvid*
#> 1     Cc ~ …     cmt='Cc' or cmt=4     dvid='Cc' or dvid=1
#> 2 effect ~ … cmt='effect' or cmt=5 dvid='effect' or dvid=2
#>   * If dvids are outside this range, all dvids are re-numered sequentially, ie 1,7, 10 becomes 1,2,3 etc
#> 
#>  ── Model (Normalized Syntax): ── 
#> function() {
#>     ini({
#>         lcl <- 1
#>         label("Clearance (CL)")
#>         lvc <- 3
#>         label("Central volume of distribution (V)")
#>         lvp <- 5
#>         label("Peripheral volume of distribution (Vp)")
#>         lq <- 0.1
#>         label("Intercompartmental clearance (Q)")
#>         propSd <- c(0, 0.5)
#>         label("Proportional residual error (fraction)")
#>         lkin <- 0.1
#>         label("zero order response production(kin)")
#>         lkout <- 0.1
#>         label("first order rate response loss (kout)")
#>         effectSd <- c(0, 0.1)
#>         label("additive error for effect")
#>         lEC50 <- 0.1
#>         label("Concentration of 50% 1 (1)")
#>         lgg <- -2.30258509299405
#>         label("logit-constrained Hill coefficient g")
#>     })
#>     model({
#>         EC50 <- exp(lEC50)
#>         g <- expit(lgg, 0.1, 10)
#>         kin <- exp(lkin)
#>         kout <- exp(lkout)
#>         cl <- exp(lcl)
#>         vc <- exp(lvc)
#>         vp <- exp(lvp)
#>         q <- exp(lq)
#>         kel <- cl/vc
#>         k12 <- q/vc
#>         k21 <- q/vp
#>         d/dt(central) <- kel * central - k12 * central + k21 * 
#>             peripheral1
#>         d/dt(peripheral1) <- k12 * central - k21 * peripheral1
#>         Cc <- central/vc
#>         Cc ~ prop(propSd)
#>         R(0) <- kin/kout
#>         d/dt(R) <- kin * (1 + Cc^g/(Cc^g + EC50^g)) - kout * 
#>             R
#>         effect <- R
#>         effect ~ add(effectSd)
#>     })
#> }