Probability of Pharmacological Success (PoPS)

#  *** High-level settings ***
support_level <- 0L

# ggplot theme
ggplot2::theme_set(theme_pmx())
targetColor <- pmx_palettes(divName="divergentRedGreen",type="divergent")[4]
therapeuticColor <- pmx_palettes(divName="divergentRedGreen",type="divergent")[8]

# Seed number
SIMSEED <- 201110

# Nr of 'populations' (for cases with parameter uncertainty) and
# nr of 'individuals' (for cases with IIV)
n_pop <- 200L
n_ind <- 200L

# Nr of points to split graphs into (along x axes)
n_points <- 50L

# Width of CIs / PIs
CI_width <- 0.95
PI_width <- 0.90

Project details

Project name DualNP_2 |
Asset(s) ABC001, ABC002, and ABC003 |
Stage Candidate selection
Date 04 October, 2024 |
Responsible P. Pharmetheusson

Input data

Pharmacokinetic and exposure-response parameters

Range and criteria variables

Concentration - response

#  *** Actual concentration-response functions used in this report ***

emax_fnc <- function(C, EMAX, HILL, EC50) {
  return(list(value = EMAX * C**HILL / (EC50**HILL + C**HILL)))
}

conc_response_fncs <- list(
  `ABC001` = list( `T1` = emax_fnc, `T2` = emax_fnc ),
  `ABC002` = list( `T1` = emax_fnc, `T2` = emax_fnc ),
  `ABC003` = list( `T1` = emax_fnc, `T2` = emax_fnc )
)

Median response, including parameter uncertainty

Concentration-response relationships presented with the median prediction and a 95% confidence interval. This figure is based on 200 simulated populations, in which all parameters were sampled with uncertainty where specified. For each population, individual parameter values were sampled for 200 individuals using between-subject variability where specified. The target response ranges are indicated with shaded brown areas. The upper exposure limit is indicated by vertical dashed lines. The thick colored line represents the median prediction and the corresponding shaded area a 95% confidence interval.

Between-subject variability

Concentration-response relationships presented with the median prediction and a 90% prediction interval. This figure shows between-subject variability for predictions based on specified typical values and between-subject variability for all parameters. The target response ranges are indicated with shaded brown areas. The resulting therapeutic Cav intervals are indicated with shaded green areas. The upper exposure limit is indicated by vertical dashed lines. The thick colored line represents the median prediction and the corresponding shaded area a 90% prediction interval.

Dose - concentration

#  *** Actual dose-concentration functions used in this report ***

dose_conc_fncs <- list(
  `ABC001` = function(Dose, CL, F, MW, Tau) { return(list(value=F*Dose/CL/Tau/ MW * 1e6)) },
  `ABC002` = function(Dose, CL, F, MW, Tau) { return(list(value=F*Dose/CL/Tau/ MW * 1e6)) },
  `ABC003` = function(Dose, CL, F, MW, Tau) { return(list(value=F*Dose/CL/Tau/ MW * 1e6)) }
)

Median concentration, including parameter uncertainty

Figure 1: Dose-concentration relationships presented with the median prediction and a 95% confidence interval. This figure is based on 200 simulated populations, in which all parameters were sampled with uncertainty where specified. For each population, individual parameter values were sampled for 200 individuals using between-subject variability where specified. The upper exposure limit is indicated by horizontal dashed lines. The thick colored line represents the median prediction and the corresponding shaded area a 95% confidence interval.

Between-subject variability

Figure 2: Dose-concentration relationships presented with the median prediction and a 90% prediction interval. This figure shows between-subject variability for predictions based on specified typical values and between-subject variability for all parameters. The upper exposure limit is indicated by horizontal dashed lines. The thick colored line represents the median prediction and the corresponding shaded area a 90% prediction interval.

Dose - response

#  *** Actual dose-response functions used in this report ***

dose_response_fncs <- list(
  `ABC001` = list(
    `T1` = function(Dose, CL, F, Tau, MW, EMAX, HILL, EC50) {
      C    <- dose_conc_fncs$`ABC001`(Dose=Dose, CL=CL, F=F, Tau=Tau, MW)$value
      resp <- conc_response_fncs$`ABC001`$T1(C=C, EMAX=EMAX, HILL=HILL, EC50=EC50)$value
      return( list(value=resp, Conc=C) )
    },
    `T2` = function(Dose, CL, F, Tau, MW, EMAX, HILL, EC50) {
      C    <- dose_conc_fncs$`ABC001`(Dose=Dose, CL=CL, F=F, Tau=Tau, MW)$value
      resp <- conc_response_fncs$`ABC001`$T2(C=C, EMAX=EMAX, HILL=HILL, EC50=EC50)$value
      return( list(value=resp, Conc=C) )
    }
  ),
  `ABC002` = list(
    `T1` = function(Dose, CL, F, Tau, MW, EMAX, HILL, EC50) {
      C    <- dose_conc_fncs$`ABC002`(Dose=Dose, CL=CL, F=F, Tau=Tau, MW)$value
      resp <- conc_response_fncs$`ABC002`$T1(C=C, EMAX=EMAX, HILL=HILL, EC50=EC50)$value
      return( list(value=resp, Conc=C) )
    },
    `T2` = function(Dose, CL, F, Tau, MW, EMAX, HILL, EC50) {
      C    <- dose_conc_fncs$`ABC002`(Dose=Dose, CL=CL, F=F, Tau=Tau, MW)$value
      resp <- conc_response_fncs$`ABC002`$T2(C=C, EMAX=EMAX, HILL=HILL, EC50=EC50)$value
      return( list(value=resp, Conc=C) )
    }
  ),
  `ABC003` = list(
    `T1` = function(Dose, CL, F, Tau, MW, EMAX, HILL, EC50) {
      C    <- dose_conc_fncs$`ABC003`(Dose=Dose, CL=CL, F=F, Tau=Tau, MW)$value
      resp <- conc_response_fncs$`ABC003`$T1(C=C, EMAX=EMAX, HILL=HILL, EC50=EC50)$value
      return( list(value=resp, Conc=C) )
    },
    `T2` = function(Dose, CL, F, Tau, MW, EMAX, HILL, EC50) {
      C    <- dose_conc_fncs$`ABC003`(Dose=Dose, CL=CL, F=F, Tau=Tau, MW)$value
      resp <- conc_response_fncs$`ABC003`$T2(C=C, EMAX=EMAX, HILL=HILL, EC50=EC50)$value
      return( list(value=resp, Conc=C) )
    }
  )
)

Median response, including parameter uncertainty

Figure 3: Dose-response relationships presented with the median prediction and a 95% confidence interval. This figure is based on 200 simulated populations, in which all parameters were sampled with uncertainty where specified. For each population, individual parameter values were sampled for 200 individuals using between-subject variability where specified. The target response ranges are indicated with shaded brown areas. The upper exposure limit is indicated by vertical dashed lines. The thick colored line represents the median prediction and the corresponding shaded area a 95% confidence interval.

Between-subject variability

Figure 4: Concentration-response relationships presented with the median prediction and a 90% prediction interval. This figure shows between-subject variability for predictions based on specified typical values and between-subject variability for all parameters. The target response ranges are indicated with shaded brown areas. The upper exposure limit is indicated by vertical dashed lines. The thick colored line represents the median prediction and the corresponding shaded area a 90% prediction interval.

PoPS - Probability of pharmacological success

Criteria-by-criteria PoPS

For asset 'ABC001':
  - The individual exposure target is between 0 nM and 160 nM
  - The target for the population is to have between 90% and 100% meet this

  - The individual response target for endpoint T1 is between 0.85 - and 1 -
  - The target for the population is to have between 50% and 100% meet this

  - The individual response target for endpoint T2 is between 0.2 - and 0.4 -
  - The target for the population is to have between 50% and 100% meet this

 
For asset 'ABC002':
  - The individual exposure target is between 0 nM and 280 nM
  - The target for the population is to have between 90% and 100% meet this

  - The individual response target for endpoint T1 is between 0.85 - and 1 -
  - The target for the population is to have between 50% and 100% meet this

  - The individual response target for endpoint T2 is between 0.2 - and 0.4 -
  - The target for the population is to have between 50% and 100% meet this

 
For asset 'ABC003':
  - The individual exposure target is between 0 nM and 330 nM
  - The target for the population is to have between 90% and 100% meet this

  - The individual response target for endpoint T1 is between 0.85 - and 1 -
  - The target for the population is to have between 50% and 100% meet this

  - The individual response target for endpoint T2 is between 0.2 - and 0.4 -
  - The target for the population is to have between 50% and 100% meet this

Figure 5: Relationship between dose and probability of meeting each separate criterion that makes up the composite PoPS. This figure is based on 200 sampled populations of 200 individuals each, using parameter uncertainty and between-subject variability where specified.

Composite PoPS

The final PoPS results by dose are shown in Figure 6.

Figure 6: Relationship between dose and the composite probability of pharmacological success (PoPS). This figure is based on 200 sampled populations of 200 individuals each, using parameter uncertainty and between-subject variability where specified. For ABC001 (dosing every 24 h), the maximum PoPS is 47.73%, which is obtained at the dose 12.8 mg. For ABC002 (dosing every 24 h), the maximum PoPS is 43.7%, which is obtained at the dose 20.4 mg. For ABC003 (dosing every 24 h), the maximum PoPS is 28.41%, which is obtained at the dose 25 mg.

The final cumulative PoPS results considering the successive ascending dose ranges are shown in Figure 7.

Figure 7: Relationship between dose and the composite probability of pharmacological success (PoPS). This figure is based on 200 sampled populations of 200 individuals each, using parameter uncertainty and between-subject variability where specified. For ABC001 (dosing every 24 h), the PoPS over the full dose range selected (between 0 mg and 25 mg) is 98%. For ABC002 (dosing every 24 h), the PoPS over the full dose range selected (between 0 mg and 50 mg) is 87%. For ABC003 (dosing every 24 h), the PoPS over the full dose range selected (between 0 mg and 50 mg) is 63%.

For ABC001 (dosing every 24 h), the PoPS over the doses of interest (8, 13, 18mg) is 83.5%. For ABC002 (dosing every 24 h), the PoPS over the doses of interest (15, 20, 30mg) is 65%. For ABC003 (dosing every 24 h), the PoPS over the doses of interest (15, 25, 35mg) is 40.5%.