A posteriori dose selection

library(posologyr)

Introduction

Dosage individualization for a critical care patient treated with amikacin for suspected ventilator-associated pneumonia, using the population pharmacokinetic (ppk) model of Burdet et al. 2015, using the data from therapeutic drug monitoring (TDM).

mod_amikacin_Burdet2015 <- list(
  ppk_model   = rxode2::rxode({
    centr(0) = 0;
    TVCl  = THETA_Cl*(CLCREAT4H/82)^0.7;
    TVVc  = THETA_Vc*(TBW/78)^0.9*(PoverF/169)^0.4;
    TVVp  = THETA_Vp;
    TVQ   = THETA_Q;
    Cl    = TVCl*exp(ETA_Cl);
    Vc    = TVVc*exp(ETA_Vc);
    Vp    = TVVp*exp(ETA_Vp);
    Q     = TVQ *exp(ETA_Q);
    ke    = Cl/Vc;
    k12   = Q/Vc;
    k21   = Q/Vp;
    Cc    = centr/Vc;
    d/dt(centr)  = - ke*centr - k12*centr + k21*periph;
    d/dt(periph) =            + k12*centr - k21*periph;
    d/dt(AUC)    =   Cc;
  }),
  error_model = function(f,sigma){
    g <- sigma[1] + sigma[2]*f
    return(g)
  },
  theta = c(THETA_Cl=4.3, THETA_Vc=15.9, THETA_Vp=21.4,THETA_Q=12.1),
  omega = lotri::lotri({ETA_Cl + ETA_Vc + ETA_Vp + ETA_Q ~
      c(0.1,
        0.01     ,   0.05 ,
        0.01     ,   0.02 ,   0.2  ,
        -0.06    ,   0.004,   0.003,    0.08)}),
  covariates  = c("CLCREAT4H","TBW","PoverF"),
  sigma       = c(additive_a = 0.2, proportional_b = 0.1))

A posteriori dose selection

Patient record with TDM data

After the first administration, the dosage selection can be refined using the results of TDM. See vignette("patient_data_input") for more details regarding the patient record.

df_patientA <- data.frame(ID=1,TIME=c(0,1,6),
                              DV=c(NA,58,14),
                              EVID=c(1,0,0),
                              AMT=c(2000,0,0),
                              DUR=c(0.5,NA,NA),
                              CLCREAT4H=50,TBW=62,PoverF=169)
df_patientA
#>   ID TIME DV EVID  AMT DUR CLCREAT4H TBW PoverF
#> 1  1    0 NA    1 2000 0.5        50  62    169
#> 2  1    1 58    0    0  NA        50  62    169
#> 3  1    6 14    0    0  NA        50  62    169

The concentration measured 30 min after a 30 min infusion do not meet the target for a peak concentration; it is < 60 mg/L.

Estimate the MAP individual parameters

The maximum a posteriori (MAP) individual parameters are estimated.

patA_map <- poso_estim_map(dat=df_patientA,
                           prior_model=mod_amikacin_Burdet2015)

Plot the individual pharmacokinetic profile

The individual pharmacokinetic profile can be plotted using the rxode2 model provided by the poso_estim_map() function.

plot(patA_map$model,Cc)

Time required to reach the target Cmin following the first administration

With the MAP estimates of the individual parameters, the prediction of the time needed before reaching the target Cmin can be updated.

poso_time_cmin(dat=df_patientA,
               prior_model=mod_amikacin_Burdet2015,
               tdm = TRUE,
               target_cmin = 2.5)
#> $time
#> [1] 33.9
#> 
#> $type_of_estimate
#> [1] "point estimate"
#> 
#> $cmin_estimate
#> [1] 2.487865
#> 
#> $indiv_param
#>   THETA_Cl THETA_Vc THETA_Vp THETA_Q    ETA_Cl    ETA_Vc    ETA_Vp    ETA_Q
#> 3      4.3     15.9     21.4    12.1 0.4499479 0.2730561 0.7061648 -0.13884
#>   CLCREAT4H TBW PoverF
#> 3        50  62    169

The next dose (if needed) can be administered 33.9 hours following the first infusion.

Optimal dose selection a posteriori

The optimal dose to achieve a peak concentration of 80 mg/l can be determined using the MAP estimates.

map_dose <- poso_dose_conc(dat=df_patientA,
                           prior_model=mod_amikacin_Burdet2015,
                           tdm=TRUE,
                           time_c = 35,               #target concentration at t = 35 h
                           time_dose = 34,            #dosing at t = 34 h
                           duration = 0.5,
                           target_conc = 80)
map_dose
#> $dose
#> [1] 2447.917
#> 
#> $type_of_estimate
#> [1] "point estimate"
#> 
#> $conc_estimate
#> [1] 0
#> 
#> $indiv_param
#>   THETA_Cl THETA_Vc THETA_Vp THETA_Q    ETA_Cl    ETA_Vc    ETA_Vp      ETA_Q
#> 3      4.3     15.9     21.4    12.1 0.4499608 0.2730596 0.7061496 -0.1388505
#>   CLCREAT4H TBW PoverF
#> 3        50  62    169

The next dose should be 2450 mg.

Interdose interval selection a posteriori

The optimal inter-dose interval to reach a Cmin of 2.5 mg/L before each dosing can be determined using the MAP estimates.

map_interval <- poso_inter_cmin(dat=df_patientA,
                                prior_model=mod_amikacin_Burdet2015,
                                dose = map_dose$dose,
                                duration = 0.5,
                                target_cmin = 2.5)
map_interval
#> $interval
#> [1] 38.57781
#> 
#> $type_of_estimate
#> [1] "point estimate"
#> 
#> $conc_estimate
#> [1] 0
#> 
#> $indiv_param
#>   THETA_Cl THETA_Vc THETA_Vp THETA_Q   ETA_Cl    ETA_Vc    ETA_Vp      ETA_Q
#> 1      4.3     15.9     21.4    12.1 0.449952 0.2730587 0.7061588 -0.1388432
#>   CLCREAT4H TBW PoverF
#> 1        50  62    169

The interval between doses should not be less than 38.6 hours to allow adequate elimination of amikacin between each infusion.