---
bibliography: export_cs.bib
csl: aa.csl
output: 
  bookdown::word_document2: 
  bookdown::pdf_document2: 
    latex_engine: xelatex
    number_sections: yes
    fig_caption: yes
    highlight: tango
    extra_dependencies: "subfig"
header-includes:
  - \usepackage{float}
  - \floatplacement{table}{H}
  - \usepackage{booktabs}
  - \usepackage{caption}
  - \captionsetup{labelfont=bf,margin=12pt}
urlcolor: blue
---


```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE, fig.pos= "H")
library(tidyverse)
library(rxode2)
library(DescTools)
library(gtsummary)
library(knitr)
library(mvtnorm)
library(flextable)
set.seed(123456) # you need a set seed so that you get same results each time you knit
## Oral sim using De Velde data

# Define the two-compartment model with Michaelis-Menten absorption and Savic transit
mod <- rxode2({
  # Parameters
  F1 = exp(logF1 + eta.F1);           # Bioavailability
  mtt = exp(logmtt+eta.mtt) ;           # mean transit time
  n= exp(logn+eta.n); # mean number of transit compartments
  Vmax = exp(logVmax + eta.Vmax);     # Maximum absorption rate (mg/h)
  Km = exp(logKm +eta.km );           # Michaelis constant (mg)
  V1 = exp(logV1 + eta.V1);           # Central volume
  Cl = exp(logCl + eta.Cl);           # Clearance
  Q = exp(logQ);              # Intercompartmental clearance
  V2 = exp(logV2);           # Peripheral volume
  
  ktr = (n+1)/mtt
  # Depot compartment (Michaelis-Menten absorption with bioavailability)
  d/dt(depot) = transit(n,mtt,F1)-Vmax * depot / (Km + depot);
  
  
  # Central compartment dynamics
  d/dt(cent) = Vmax * depot / (Km + depot) - (Cl / V1) * cent - (Q / V1) * cent + (Q / V2) * peri;
  
  # Peripheral compartment
  d/dt(peri) = (Q / V1) * cent - (Q / V2) * peri;
  
  # Plasma concentration in the central compartment
  cp = cent / V1;
})

# Population-level parameter estimates from de Velde et al.doi:10.1093/jac/dkw226
theta_dv <- c(
  logF1 = log(0.7),         # Bioavailability  
  logmtt = log(0.524),      # mean transit time
  logn = log(4.41),         #number of transit compartments
  logVmax = log(1220),     # Michaelis-Menten Vmax
  logKm = log(287),        # Michaelis-Menten Km 
  logV1 = log(27.7),      # Central volume
  logCl = log(21.3),      # Clearance from the study
  logQ = log(1.70),        # Intercompartmental clearance 
  logV2 = log(3.02)        # Peripheral volume
)

# Define variability (omega^2) on the parameters, converted from %CV from De Velde
omi_dv<-lotri(eta.F1~0.116,
              eta.mtt~0.198,
              eta.n~0.823,
              eta.Vmax~0.097,
              eta.km~0.680,
              eta.V1~0.112,
              eta.Cl~0.064
) 

# event information for De Velde oral
ev_dv <- et(amount.units="mg", time.units="hours") %>%
  et(amt=500, evid=7) %>% # evid 7 places dose in the transit compartment
  add.sampling(seq(0,12,by=0.125)) # takes samples every 7.5mins from time=0 to time=12 hours

# Simulate for 10,000 patients
sim_dvoral <- rxSolve(mod, theta_dv, ev_dv, omega=omi_dv, nSub=10000) # nsub is number of participants

# Summarize results across all patients
summary_sim_dvoral <- sim_dvoral %>%
  group_by(time) %>%
  summarise(median_Cp = median(cp),
            Cp_5th = quantile(cp, 0.05),
            Cp_95th = quantile(cp, 0.95))

## Oral sim using combined De Velde and Lonsdale with absorption estimates for CC pop

# Population-level parameter estimates from de Velde et al.doi:10.1093/jac/dkw226
# cl, v1, v2, q from Lonsdale et al https://doi.org/10.1093/jac/dkaa363 
# 20% increase in MTT, 20% decrease in F and Vmax - estimates for CC pop
theta_est <- c(
  logF1 = log(0.56),         # Bioavailability  20% reduction  
  logmtt = log(1.5),      # mean transit time logmtt = log(0.524)
  logn = log(4.41),         #number of transit compartments  logn = log(4.41),
  logVmax = log(976),     # Michaelis-Menten Vmax  logVmax = log(1220),
  logKm = log(344),        # Michaelis-Menten Km   logKm = log(287),
  logV1 = log(11.5),      # Central volume
  logCl = log(15.9),      # Clearance from the study
  logQ = log(15.4),        # Intercompartmental clearance 
  logV2 = log(17.2)        # Peripheral volume
)

# Define variability (omega^2) on the parameters, converted from %CV from De Velde
# V1, Cl from Lonsdale et al
# MTT, F and Vmax *1.5 for critical care pop
omi_est<-lotri(eta.F1~0.116,
              eta.mtt~0.198,
              eta.n~0.823,
              eta.Vmax~0.097,
              eta.km~0.680,
               eta.V1~0.06,
               eta.Cl~0.15
) 

# event information
ev_est <- et(amount.units="mg", time.units="hours") %>%
  et(amt=500, evid=7) %>% # places dose in the transit compartment
  add.sampling(seq(0,12,by=0.125)) # takes samples every 7.5mins from time=0 to time=12 hours


# Theta Population-level parameter estimates from de Velde et al.doi:10.1093/jac/dkw226
# cl, v1, v2, q from Lonsdale et al
# Simulate for 10,000 patients
sim_estoral <- rxSolve(mod, theta_est, ev_est,omega=omi_est, nSub=10000) # nsub is number of participants

# Summarize results across all patients
summary_sim_estoral <- sim_estoral %>%
  group_by(time) %>%
  summarise(median_Cp = median(cp),
            Cp_5th = quantile(cp, 0.05),
            Cp_95th = quantile(cp, 0.95))

## IV sim for combined De Velde and Lonsdale with Est variance for Crit Care pop

##2-compartment model for IV infusion
mod2 <- rxode2({
  # Parameters
  V1 = exp(logV1 + eta.V1);           # Central volume
  Cl = exp(logCl + eta.Cl);           # Clearance
  Q = exp(logQ);              # Intercompartmental clearance
  V2 = exp(logV2);           # Peripheral volume
  

  # Central compartment dynamics
  d/dt(cent) =  - (Cl / V1) * cent - (Q / V1) * cent + (Q / V2) * peri;
  
  # Peripheral compartment
  d/dt(peri) = (Q / V1) * cent - (Q / V2) * peri;
  
  # Plasma concentration in the central compartment
  cp = cent / V1;
})

#population-level parameter estimates
# cl, v1, v2, q from Lonsdale et al https://doi.org/10.1093/jac/dkaa363 
theta_iv <- c(
  logV1 = log(11.5),      # Central volume
  logCl = log(15.9),      # Clearance from the study
  logQ = log(15.4),        # Intercompartmental clearance 
  logV2 = log(17.2)        # Peripheral volume
)

# Define variability (omega^2) on the parameters
# from Lonsdale et al
omi_iv<-lotri(eta.V1~0.06,
               eta.Cl~0.15
) 

# variable rate infusion
# timings based on Molina-Molina et al 
ev_abdiv_v <- et(amount.units="mg", time.units="hours") %>%
  et(amt=2, cmt = "cent", dur=1/6) %>% #1% of dose over 10mins 
  et(time=1/6, cmt = "cent", amt = 18, dur=1/3) %>% #next 9% dose over 20 mins
  et(time=1/2, cmt = "cent", amt=180, dur=1) %>% # remainder of dose over one hour
    add.sampling(seq(0,12,by=0.125)) # takes samples every 7.5mins from time=0 to time=12 hours
# for 250mg Cmax 7.70 tmax 1.45 auc 15 

# sim for variable infusion
sim_abdiv_v <- rxSolve(mod2, theta_iv, ev_abdiv_v,omega=omi_iv, nSub=10000)

# Summarize results across all patients variable infusion
summary_sim_abdiv_v <- sim_abdiv_v %>%
  group_by(time) %>%
  summarise(median_Cp = median(cp),
            Cp_5th = quantile(cp, 0.05),
            Cp_95th = quantile(cp, 0.95))

### Combining for plots and table

sim_dvoral$condition<-"General population (oral)";sim_dvoral$dose<-500
sim_estoral$condition<-"Critical care population (oral)";sim_estoral$dose<-500
sim_abdiv_v$condition<-"Critical care population (IV variable-rate infusion)";sim_abdiv_v$dose<-200; sim_abdiv_v$F1<-1

sim_full<-sim_dvoral %>% 
  select(sim.id,time, cp, condition,dose,Cl,F1) %>% 
  bind_rows(.,select(sim_estoral,sim.id,time, cp, condition,dose,Cl,F1))%>% 
  bind_rows(.,select(sim_abdiv_v,sim.id,time, cp, condition,dose,Cl,F1))

#reorder study conditions
sim_full$condition <- factor(sim_full$condition, levels=c('General population (oral)', 'Critical care population (oral)', 'Critical care population (IV variable-rate infusion)')) 

```

# Bullet point summary

Please note that there are some differences between the text in this R markdown file and the final manuscript as the text was altered after review by the editorial panel. No changes were made to the code. 

*What is already known about this subject*

* The label of penicillin allergy is incorrect in 80-90% of patients and a label of penicillin allergy is associated with worse outcomes and increased use of healthcare services
* De-labelling services are successful in removing incorrect penicillin allergy labels. Sometimes this is done with the use of a drug provocation test where an oral dose of penicillin is given and the patient observed for a period for a reaction
* In critical illness, pharmacokinetics are altered and enteral administration of drugs is often unreliable or impossible

*What this study adds*

* Absorption of enterally administered amoxicillin in critically unwell patients is likely to lead to reduced exposure during a drug provocation test compared to the exposure in non-critically ill patients. The impact of this for drug provocation tests is unknown
* We present a protocol for an intravenous infusion penicillin drug provocation test that mirrors the plasma profile of an enteral challenge. This protocol could be considered as part of comprehensive penicillin allergy de-labeling protocols in critically unwell patients 

\newpage

# Abstract

The majority of penicillin allergy labels are incorrect and a label of penicillin allergy is associated with worse outcomes and increased use of healthcare services. Penicillin allergy assessment and de-labeling may be considered in critically ill patients. An oral penicillin challenge is a common component of most penicillin allergy protocols.  In critical illness, the enteral route may not be an option and is less reliable due to altered absorption kinetics. In this study, simulations were undertaken to determine an intravenous infusion dosing schedule for critically ill patients that matches the concentration-time profile of an oral penicillin drug provocation test in the general population. These simulations may help clinicians develop guidelines for intravenous infusion penicillin drug provocation tests for critically ill patients. 

\newpage


# Introduction

The impact of an incorrect penicillin allergy label is a challenge in critical care. The label of a penicillin allergy is associated with worse healthcare outcomes for the individual @West, including an increase in acquisition of drug resistant infections @Reddy and exposure to antibiotics with a less favorable adverse effect profile compared to $\beta$-lactams, including quinolones.

Discussions around penicillin allergy are common, with 6-10% of patients reporting penicillin hypersensitivity [@West; @NICE2014]. The incidence of true penicillin allergy is likely to be far lower, with 5-20% of people who report an allergy actually having one [@NICE2014; @Mota; @Macy2013]. Assessment of allergy history leads to over 60% patients being labelled as low-risk. This group are suitable for direct drug provocation test without skin sensitisation testing [@Savic2022]. Identifying those who _do not_ have a penicillin allergy through assessment and testing where appropriate (allergy de-labeling) is a potential strategy to optimise infection management and antimicrobial stewardship in critical care. Studies evaluating enteral penicillin provocation tests in critical care have demonstrated these to be safe in individuals assessed to be at low-risk of true penicillin allergy [@Stone2020; @Koo2022; @Alamin]. Amoxicillin is a commonly used agent for this purpose via the enteral route.

For some, the enteral route of drug administration may be an imperfect choice. Absorption kinetics are highly variable in critical illness, through mechanisms such as altered haemodynamics and ileus [@Morales; @Roberts2014]. Some pathologies and clinical situations will render the enteral route of administration unavailable. Forsberg et al. undertook a systematic review of oral drug absorption in critical illness. They found no published data on penicillin absorption in this patient group and in the small number of antibiotics that do have data, absorption was lower compared to non-critically ill populations @Forsberg2023. 

For drugs that are more well studied, the impact of critical illness on absorption kinetics is significant. For example, Heyland et al. undertook a study on the impact of critical illness on paracetamol kinetics @Heyland. In critically ill populations, they found a 55% reduction in maximum concentration ($C_{max}$), and 20% reduction in the area under the concentration-time curve compared to healthy volunteer controls. The time to maximum concentration ($T_{max}$) was 3.5 times (75 minutes) longer in critically ill patients compared with healthy individuals. Similar results were found by Tarling et al @Tarling.

A protocol for an IV penicillin infusion drug provocation test was recently published by Molina-Molina et al., with accompanying safety data from their experience over a retrospective four-year period @Molina2024. The patient population in this study were general hospital inpatients. To our knowledge there is no similarly published protocol for critically ill patients.

In this report we present a simulated pharmacokinetic study of a protocol for an IV amoxicillin drug provocation test in critical illness. We have taken published parameters from pharmacokinetic models of amoxicillin and aim to demonstrate the feasibility of providing a pharmacokinetic profile through IV infusion that mirrors that of the clinical dose used in an oral amoxicillin drug provocation test.


# Methods 

**Pharmacokinetic models**

Published pharmacokinetic models of amoxicillin from de Velde et al. @deVelde2016 and Lonsdale et al. @Lonsdale2020 provided parameters for a two compartment model. Simulations were undertaken in R, using the rxode2 package [@R; @rxode2]. The code file is provided as supplementary material. 

Three scenarios were simulated, each for a 70 kg individual:

* A reference model of enteral administration in the non-critically ill population.
* A simulated enteral model in critically ill patients to illustrate potential impact of critical illness on absorption kinetics.
* A simulated IV model in critically ill patients using a similar infusion rate strategy to that suggested by Molina-Molina et al. and amoxicillin pharmacokinetic parameters from Lonsdale et al. 

10,000 patients were simulated for each scenario. Concentrations were generated every 7.5 minutes for each simulated patient, between 0 and 12 hours after dosing. 

*Enteral amoxicillin model in non-critically ill patients*

A two-compartment oral-absorption model with Michaelis-Menten and Savic transit compartment absorption kinetics was simulated. Fixed and random effects parameters were taken from de Velde et al. @deVelde2016. Amoxicillin dose was 500 mg.

*Enteral amoxicillin model in critically ill patients*

A two-compartment oral absorption model with Michaelis-Menten and Savic transit compartment absorption kinetics was simulated. Absorption parameters were taken from de Velde et al. and distribution and elimination parameters from Lonsdale et al. To simulate the effect of critical illness on absorption, we increased mean transit time and reduced bioavailability and Vmax to provide a similar impact on kinetics to that found by Heyland et al. in their paracetamol study @Heyland. Amoxicillin dose was 500mg. 

*IV infusion model*

A two-compartment IV model was simulated. Fixed and random effects parameters were taken from Lonsdale et al. @Lonsdale2020. The IV infusion utilised incremental increases in rate, adapted from a protocol published by Molina-Molina et al. @Molina2024. 1% of the dose was delivered over the first 10 minutes, 9% over the next 20 minutes, and the remainder over an hour (total infusion time 90 minutes). Stability data is in keeping with this being an acceptable duration of time for amoxicillin to be left @ibiamox. A range of doses were tested in 50mg increments, we present results of a simulated total amoxicillin dose of 200 mg in this report as this resulted in the most similar median maximum concentration ($C_{max}$) to the enteral model in non-critically ill patients.

**Analysis of simulations** 

End points were ($C_{max}$), time to maximum concentration ($T_{max}$) and exposure (quantified as area under the time-concentration curve, $AUC_{0-\infty}$). Parameters are presented as median with 5th and 95th centile range. $AUC_{0-\infty}$ was calculated using simulated clearance:  
\begin{equation}
AUC_{0-\infty} = \frac{\text{simulated bioavailability x dose}}{\text{simulated clearance}}
\label{eq:auc}
\end{equation}

# Results

```{r res,echo=F, message=F}

res<-sim_full %>% 
  group_by(condition, sim.id) %>% 
  summarise(Cmax =max(cp),
          Tmax =time[which.max(cp)],
          AUC  =max(dose)*max(F1)/max(Cl), #note that dose and cl is identical in each row so max/mean/median all fine here
          ) %>%
  ungroup()%>% 
  group_by(condition) %>% 
  summarise(medCmax=median(Cmax),
            medTmax=median(Tmax),
            medAUC=median(AUC),
            Cmax5= quantile(Cmax, 0.05),
            Cmax95= quantile(Cmax, 0.95),
            Tmax5= quantile(Tmax, 0.05),
            Tmax95= quantile(Tmax, 0.95),
            AUC5= quantile(AUC, 0.05),
            AUC95= quantile(AUC, 0.95))%>%
  ungroup()

```

Simulations of a 200 mg variable infusion of amoxicillin in a critically ill population achieved a similar pharmacokinetic profile to a 500 mg enteral dose in a non-critically ill population (Table 1). Median $C_{max}$ was `r round(res$medCmax[res$condition == 'Critical care population (IV variable-rate infusion)'],2)` mg/L and $T_{max}$ was `r round(res$medTmax[res$condition == 'Critical care population (IV variable-rate infusion)'],2)` hours in the simulated IV scenario compared to `r round(res$medCmax[res$condition == 'General population (oral)'],2)` mg/L and `r round(res$medTmax[res$condition == 'General population (oral)'],2)` hours from the oral route in the non-critically ill. Concentration-time profiles from the three simulated scenarios are presented in Figure 1.

# Discussion

Our simulations predict that a 200 mg infusion of amoxicillin given to critically ill populations with staged infusion rates will confer a similar time-concentration profile to that expected in a healthy population given an oral 500 mg dose of amoxicillin. This, alongside studies of IV penicillin drug provocation tests in healthy patients, may provide clinicians with some assurance when considering protocols for IV amoxicillin drug provocation test in the intensive care unit. Similarly, we offer some evidence of the lower exposure expected through the use of enteral administration in this population. 

Recent hypotheses based on the law of mass action have argued that adverse drug reactions are all dose-dependent and explanations for situations where this was not felt to be the case have been proposed @Aronson2015. Based on this, it is expected that increased $C_{max}$ may lead to a higher rate of harm. For this reason, this study aimed to match the $C_{max}$ of doses used in established enteral drug provocation test protocols. 

Pharmacokinetic model-informed doses are not (to our knowledge) used in existing penicillin allergy de-labeling protocols. Molina-Molina et al. used a standard licensed dose of 1000 mg of amoxicillin @Molina2024. Immediate reactions in this study were higher in the group administered an IV provocation challenge, although interpreting this result is challenging as the study was not randomised, and the intravenous group had a higher risk of a true allergy at baseline and were preferentially chosen for the IV group for safety reasons. 

In our view, the IV route of administration in critically ill patients has a number of advantages over enteral. Principally, this is in the reliable achievement of meaningful exposure that may be lost in the setting of unreliable and lower absorption kinetics found in critical illness. Further, in the event of a reaction to the drug, the IV infusion can be stopped immediately, reducing exposure to the drug (an option not available once an oral dose is administered or with an IV bolus).

Clinicians may be concerned that the IV route may present a large and rapid drug burden at the site of administration. The IV route is associated with a risk of rapidly evolving reactions, but it is suggested that the IV route, using incremental doses, is easier to control, as symptoms are likely to occur earlier during IV than oral administration and may appear after a smaller dose. 

Further mitigation may be found from a large administration volume (with rate adjusted to deliver dose), or central administration, where the impact of cardiac output is likely to dilute drug administered at this rate to a concentration commensurate with that found in the portal venous system after an oral dose. Infusion rates for a range of reconstitution volumes are provided in Table 2.

Small dose increments with no intervals can potentially desensitize and blunt hypersensitivity reactions. We feel this is unlikely to occur with our proposed protocol as it is markedly different to desensitization protocols. The starting rate of our modelled infusion is 12 mg/h compared to 0.006 mg/h for a $\beta$-lactam desensitisation protocol [@alvarez2022]; our infusion duration is also shorter (90 minutes compared to three hours).

Guidelines on penicillin allergy assessment and testing in the general population advocate for drug provocation tests without the use of skin sensitisation testing for patients assessed to be low-risk based on their allergy history @Savic2022. Oral drug provocation tests have been shown to have an excellent safety profile in critical care populations [@Koo2022; @Stone2020]. We propose that IV drug provocation tests could also be considered for low-risk penicillin allergy in critically ill patients. This would allow more patients to benefit from allergy de-labeling as skin sensitisation testing, typically led by immunology or allergy specialist services, is not readily available at many centres. 

Our work shares the same limitations of other simulation based science, in that it is dependent on the models used and the precision of the parameter estimates within. Our work is particularly limited by the absence of pharmacokinetic data from oral administration in the critically ill population. However, we do not believe the conduct of a study to accurately determine the impact of critical illness on absorption kinetics of amoxicillin is likely to be undertaken. The drug is seldom used through this route and such a study would likely require a relatively large sample size to understand the variability in this population. Our model of IV infusion is more robust as it is based on a relatively large pharmacokinetic study. In our view, if a clinical study is felt necessary to confirm our simulations, the focus should be on confirming the pharmacometrics and safety of the IV infusion approach.

Verification of an individual's allergy status should form a key part of optimising their care, but may be limited in critical illness by the unreliability of the enteral route and access to specialist allergy services. This study used pharmacokinetic modelling to inform suggested IV infusion rates for critically ill patients which approximate the concentration-time profile of the amoxicillin dose used in penicillin drug provocation tests in the general population. This could be used to add the option of an IV route to allergy testing protocols and improve access to the benefits of penicillin allergy de-labeling. 

\newpage 

# Conflict of interest statement

None of the authors disclose any conflict of interest directly relevant or directly related to this work.

# Funding information

There are no funders to report for this submission.

# Data availability statement

R markdown file available in article supplementary material.

\newpage

# Tables

*Table 1: Summary pharmacokinetics from three simulated amoxicillin experiments. $C_{max}$ is maximum concentration, $T_{max}$ is time from administration to maximum concentration, AUC is area under the concentration curve for a single dose.*

```{r table,echo=F,message=FALSE}

sim_full %>% 
  group_by(condition, sim.id) %>% 
  summarise("Cmax (mg/L)" =max(cp),
          "Tmax (hours)" =time[which.max(cp)],
          "AUC (mg.h/L)"  =max(dose)*max(F1)/max(Cl), #note that dose and cl is identical in each row so max/mean/median all fine here
          ) %>%
  ungroup() %>% 
  select(-sim.id)  %>% 
  tbl_summary(by=condition,
            statistic = all_continuous() ~ c("{median} ({p5}, {p95})"),      
            type=everything()~"continuous") %>% 
  modify_header(label='**Pharmacokinetic parameter**') #%>%
  #as_kable_extra(booktabs=TRUE,
       #          caption="Summary pharmacokinetics from three simulated amoxicillin experiments. Cmax is maximum concentration, Tmax is time to maximum #concentration, AUC is area under the concentration curve for a single dose") %>% 
#column_spec(2:4, width = "3.5cm")
 
```

*Table 2: Step-wise infusion rate for a 200 mg intravenous amoxicillin dose. A range of potential infusion volumes are shown.*

```{r table2, echo=F, message=FALSE}

rate_50<- c(0.05, 0.23, 0.75)
rate_250<- c(0.25, 1.125, 3.75)
rate_500<- c(0.5, 2.25, 7.5)
duration <- c(10, 20, 60)
order <- c("Period 1: 10 minute infusion \n (1% of total dose)", "Period 2: 20 minute infusion (9% of total dose)", "Period 3: 60 minute infusion (90% of total dose)")
infusion_df <- data.frame(order, rate_50, rate_250,rate_500)
colnames(infusion_df) <- c("Infusion volume", "50 mL (4 mg/mL)", "250 mL (0.8 mg/mL)","500 mL (0.4 mg/mL)")

flextable(infusion_df)%>%
    add_header_row(values=c(" ", "Rate of amoxicillin infusion (ml per min)"), colwidths=c(1,3))%>%
    add_footer_lines("The above do not take into account line volume (e.g. if central line used)")%>%
  set_table_properties(layout="autofit")%>%
  theme_box()
            
#kable(infusion_df, 
       #     format = "latex",
        #    booktabs = TRUE,
      #col.names = c("Infusion volume", "50 mL (4 mg/mL)", "250 mL (0.8 mg/mL) ","500 mL (0.4 mg/mL)"), 
     # caption = "Step-wise infusion rate for a 200 mg intravenous amoxicillin dose. A range of potential infusion volumes are shown") %>%
 # add_header_above( .,header = c(" " = 1, "Rate of amoxicillin infusion (ml per min)" = 3))%>% 
 # column_spec(2:4, width = "2cm")%>%
 #  add_footnote("The above do not take into account line volume (e.g. if central line used)", notation="none")



```

# Figures

```{r pkprof,echo=F,eval=T, fig.width=6,fig.height=3, fig.align = 'center', warning=F,message=F}

sim_full%>%
  group_by(time,condition) %>%
  summarise(median_Cp = median(cp),
            Cp_5th = quantile(cp, 0.05),
            Cp_95th = quantile(cp, 0.95))%>% 
  ggplot(., aes(x = time)) +
  geom_ribbon(aes(ymin = Cp_5th, ymax = Cp_95th), fill = "lightblue", alpha = 0.5) +
  geom_line(aes(y = median_Cp), color = "blue", size = 1) +
  labs(x = "Time (hours)",
       y = "Plasma amoxicillin concentration (mg/L)")+
  theme_bw(base_size=10)+
  facet_wrap(vars(condition), labeller = labeller(condition=label_wrap_gen(width=40))) +
  theme(panel.spacing.x = unit(4, "mm"))+ scale_x_continuous(breaks=c(0,2,4,6,8,10,12))

```

*Figure 1: Concentration-time plots from three simulated scenarios of a single dose of amoxicillin. Solid line represents median concentration-time profile, shaded area the 5th to 95th centile*

\newpage 

# References







