Introduction

AUC-based dosage adjustment for a patient treated with vancomycin for methicillin-resistant Staphylococcus aureus blood stream infection, using the population pharmacokinetic (ppk) model of Goti et al. 2018, using the data from therapeutic drug monitoring (TDM).

mod_vancomycin_Goti2018 <- list(
  ppk_model   = rxode2::rxode({
    centr(0) = 0;
    TVCl  = THETA_Cl*(CLCREAT/120)^0.8*(0.7^DIAL);
    TVVc  = THETA_Vc*(WT/70)          *(0.5^DIAL);
    TVVp  = THETA_Vp;
    TVQ   = THETA_Q;
    Cl    = TVCl*exp(ETA_Cl);
    Vc    = TVVc*exp(ETA_Vc);
    Vp    = TVVp*exp(ETA_Vp);
    Q     = TVQ;
    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=4.5, THETA_Vc=58.4, THETA_Vp=38.4,THETA_Q=6.5),
  omega = lotri::lotri({ETA_Cl + ETA_Vc + ETA_Vp + ETA_Q ~
      c(0.147,
        0     ,   0.510,
        0     ,       0,   0.282,
        0     ,       0,       0,    0)}),
  covariates  = c("CLCREAT","WT","DIAL"),
  sigma       = c(additive_a = 3.4, proportional_b = 0.227))

Discontinuous intravenous infusion

Patient record with TDM data

The dosage selection can be informed using the results of TDM. See vignette("patient_data_input") for more details regarding the patient records.

df_patientB <- data.frame(ID=1,TIME=c(0.0,13.0,24.2,48),
                          DV=c(NA,12,NA,9.5),
                          AMT=c(2000,0,1000,0),
                          DUR=c(2,NA,2,NA),
                          EVID=c(1,0,1,0),
                          CLCREAT=65,WT=70,DIAL=0)
df_patientB
#>   ID TIME   DV  AMT DUR EVID CLCREAT WT DIAL
#> 1  1  0.0   NA 2000   2    1      65 70    0
#> 2  1 13.0 12.0    0  NA    0      65 70    0
#> 3  1 24.2   NA 1000   2    1      65 70    0
#> 4  1 48.0  9.5    0  NA    0      65 70    0

Estimate the MAP individual parameters

patB_map <- poso_estim_map(dat=df_patientB,
                           prior_model=mod_vancomycin_Goti2018)

Plot the individual pharmacokinetic profile

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

plot(patB_map$model,Cc)

Using ggplot2 the observed data points can be added to the plot

#Get the observations from the patient record
indiv_obs             <- df_patientB[,c("DV","TIME")]
names(indiv_obs)      <- c("value","time")

#Overlay the MAP profile and the observations
plot(patB_map$model,Cc) +
  ggplot2::ylab("Central concentration") +
  ggplot2::geom_point(data=indiv_obs, size= 3, na.rm=TRUE)

The MAP profile matches the observations.

Get the AUC24 from the MAP model

Considering a MIC of 1 mg/L, the target AUC over 24 hours (AUC24) is 400 mg.h/L. The AUC can be retrieved from the rxode2 model using the usual R data.frame syntax.

#AUC 0_24
AUC_map_first_dose <- patB_map$model$AUC[which(patB_map$model$time == 24)]
AUC_map_first_dose
#> [1] 337.8965

#AUC 24_48
AUC_map_second_dose <- patB_map$model$AUC[which(patB_map$model$time == 48)] - AUC_map_first_dose
AUC_map_second_dose
#> [1] 325.3072

The current dosage does not meet the target AUC.

Optimal dose selection a posteriori

The next dose needed to achieve an AUC24 of 400 mg.h/L can be estimated using TDM data.

poso_dose_auc(dat=df_patientB,
              prior_model=mod_vancomycin_Goti2018,
              tdm=TRUE,
              time_auc=24,            #AUC24
              time_dose = 48,         #48 h: immediately following the last observation
              duration=2,             #infused over 2 h
              target_auc=400)
#> $dose
#> [1] 1411.593
#> 
#> $type_of_estimate
#> [1] "point estimate"
#> 
#> $auc_estimate
#> [1] 400
#> 
#> $indiv_param
#>   THETA_Cl THETA_Vc THETA_Vp THETA_Q     ETA_Cl     ETA_Vc     ETA_Vp CLCREAT
#> 4      4.5     58.4     38.4     6.5 0.08208203 0.06122374 0.06285943      65
#>   WT DIAL
#> 4 70    0

The optimal dose estimated for the next infusion is 1411 mg.

Optimal maintenance dose selection a posteriori

The maintenance dose needed to reliably achieve an AUC24 of 400 mg.h/L can be estimated by simulating a multiple dose regimen over enough administrations (e.g. 11 consecutive administrations, with add_dose=10) to approximate the steady-state.

poso_dose_auc(dat=df_patientB,
              prior_model=mod_vancomycin_Goti2018,
              time_auc=24,
              starting_time=24*9,
              interdose_interval=24,
              add_dose=10,
              duration=2,
              target_auc=400)
#> $dose
#> [1] 1198.266
#> 
#> $type_of_estimate
#> [1] "point estimate"
#> 
#> $auc_estimate
#> [1] 400
#> 
#> $indiv_param
#>   THETA_Cl THETA_Vc THETA_Vp THETA_Q     ETA_Cl     ETA_Vc    ETA_Vp CLCREAT WT
#> 1      4.5     58.4     38.4     6.5 0.08208199 0.06122337 0.0628591      65 70
#>   DIAL
#> 1    0

The optimal maintenance dose is 1200 mg.

Continuous intravenous infusion

The maintenance dose for a continuous intravenous infusion can be easily determined by setting the duration of the infusion equal to the interdose_interval.

poso_dose_auc(dat=df_patientB,
              prior_model=mod_vancomycin_Goti2018,
              time_auc=24,
              starting_time=24*9,
              interdose_interval=24,
              add_dose=10,
              duration=24,
              target_auc=400)
#> $dose
#> [1] 1198.923
#> 
#> $type_of_estimate
#> [1] "point estimate"
#> 
#> $auc_estimate
#> [1] 400
#> 
#> $indiv_param
#>   THETA_Cl THETA_Vc THETA_Vp THETA_Q     ETA_Cl     ETA_Vc     ETA_Vp CLCREAT
#> 1      4.5     58.4     38.4     6.5 0.08208202 0.06122453 0.06285936      65
#>   WT DIAL
#> 1 70    0

The optimal maintenance dose is also 1200 mg / 24 h for a continuous intravenous infusion.

AUC-based dose selection