mapbayr is a free and open source package for *maximum a
posteriori* bayesian estimation of PK parameters in R. Thanks to a
single function, `mapbayest()`

, you can estimate individual
PK parameters from:

- a population PK model (coded in mrgsolve),
- a data set with concentrations (NM-TRAN format).

It was designed to be easily wrapped in shiny apps in order to ease model-based Therapeutic Drug Monitoring, also referred to as Model-Informed Prediction Dosing (MIPD).

mapbayr is available on CRAN. You can install the development version from github by executing the following code in R console.

```
install.packages("devtools")
::install_github("FelicienLL/mapbayr") devtools
```

mapbayr relies on mrgsolve for model implementation and ordinary differential equation solving which requires C++ compilers. If you are a Windows user, you would probably need to install Rtools. Please refer to the installation guide of mrgsolve for additional information.

```
library(mapbayr)
library(mrgsolve)
```

```
<- "
code $PARAM @annotated
TVCL: 0.9 : Clearance
TVV1: 10.0 : Central volume
V2 : 10.0 : Peripheral volume of distribution
Q : 1.0 : Intercompartmental clearance
ETA1: 0 : Clearance (L/h)
ETA2: 0 : Central volume (L)
$PARAM @annotated @covariates
BW : 70 : Body weight (kg)
$OMEGA 0.3 0.3
$SIGMA
0.05 // proportional
0.1 // additive
$CMT @annotated
CENT : Central compartment (mg/L)[ADM, OBS]
PERIPH: Peripheral compartment ()
$TABLE
double DV = (CENT/V1) *(1 + EPS(1)) + EPS(2);
$MAIN
double CL = TVCL * exp(ETA1 + ETA(1)) * pow(BW / 70, 1.2) ;
double V1 = TVV1 * exp(ETA2 + ETA(2)) ;
double K12 = Q / V1 ;
double K21 = Q / V2 ;
double K10 = CL / V1 ;
$ODE
dxdt_CENT = K21 * PERIPH - (K10 + K12) * CENT ;
dxdt_PERIPH = K12 * CENT - K21 * PERIPH ;
$CAPTURE DV CL
"
<- mcode("Example_model", code) my_model
```

```
<- data.frame(ID = 1, time = c(0,6,15,24), evid = c(1, rep(0,3)), cmt = 1, amt = c(100, rep(0,3)),
my_data rate = c(20, rep(0,3)), DV = c(NA, 3.9, 1.1, 2), mdv = c(1,0,0,1), BW = 90)
my_data#> ID time evid cmt amt rate DV mdv BW
#> 1 1 0 1 1 100 20 NA 1 90
#> 2 1 6 0 1 0 0 3.9 0 90
#> 3 1 15 0 1 0 0 1.1 0 90
#> 4 1 24 0 1 0 0 2.0 1 90
```

`<- mapbayest(my_model, data = my_data) my_est `

As building dataset into a NM-TRAN format can be painful, you can use
pipe-friendly `obs_rows()`

, `adm_rows()`

and
`add_covariates()`

functions in order to pass administration
and observation information, and perform the estimation
subsequently.

```
<- my_model %>%
my_est adm_rows(time = 0, amt = 100, rate = 20) %>%
obs_rows(time = 6, DV = 3.9) %>%
obs_rows(time = 20, DV = 1.1) %>%
obs_rows(time = 24, DV = 2, mdv = 1) %>%
add_covariates(BW = 90) %>%
mapbayest()
```

The results are returned in a single object (“mapbayests” S3 class) which includes input (model and data), output (etas and tables) and internal arguments passed to the internal algorithm (useful for debugging). Additional methods are provided to ease visualization and computation of a posteriori outcomes of interest.

```
print(my_est)
#> Model: Example_model
#> ID : 1 individual(s).
#> OBS: 2 observation(s).
#> ETA: 2 parameter(s) to estimate.
#>
#> Estimates:
#> ID ETA1 ETA2
#> 1 1 0.3872104 0.1569604
#>
#> Output (4 lines):
#> ID time evid cmt amt rate mdv DV IPRED PRED CL BW ETA1 ETA2
#> 1 1 0 1 1 100 20 1 NA 0.000 0.000 1.79 90 0.387 0.157
#> 2 1 6 0 1 0 0 0 3.9 4.162 5.174 1.79 90 0.387 0.157
#> 3 1 15 0 1 0 0 0 1.1 1.087 1.647 1.79 90 0.387 0.157
#> 4 1 24 0 1 0 0 1 2.0 0.556 0.959 1.79 90 0.387 0.157
```

`plot(my_est)`

`hist(my_est) `

```
# Easily extract a posteriori parameter values to compute outcomes of interest
get_eta(my_est)
#> ETA1 ETA2
#> 0.3872104 0.1569604
get_param(my_est, "CL")
#> [1] 1.79217
# The `use_posterior()` functions updates the model object with posterior values and covariates to simulate like with a regular mrgsolve model
%>%
my_est use_posterior() %>%
data_set(expand.ev(amt = c(50, 100, 200, 500), dur = c(5, 24)) %>% mutate(rate = amt/dur)) %>%
carry_out(dur) %>%
mrgsim() %>%
plot(DV~time|factor(dur), scales = "same")
```

mapbayr is under development. Your feedback for additional feature requests or bug reporting is welcome. Contact us through the issue tracker.

mapbayr is a generalization of the “MAP Bayes estimation” tutorial available on the mrgsolve blog. Additional features are:

- a unique function to perform the estimation:
`mapbayest()`

. - accepts a large variety of structural models thanks to the flexibility of mrgsolve
- flexibility with random effects on parameters, accepting both inter-individual and inter-occasion variability.
- additive, proportional, mixed or exponential (without prior log-transformation of data) residual error models.
- estimate from both parent drug and metabolite simultaneously.
- fit multiple patients stored in a single dataset.
- functions to easily pass administration and observation information, as well as plot methods to visualize predictions and parameter distribution.
- a single output object to ease post-processing, depending on the purpose of the estimation.
- several optimization algorithm available, such as “L-BFGS-B” (the default) or “newuoa”.
- handling data below the limit of quantification.
- estimate only a subset of ETAs defined in the model.
- flatten priors to favor observed data.

Reliability of parameter estimation against NONMEM was assessed for a wide variety of models and data. The results of this validation study were published in CPT:Pharmacometrics & System Pharmacology, and materials are available in a dedicated repository. If you observe some discrepancies between mapbayr and NONMEM on your own model and data, feel free to contact us through the issue tracker.

mapbayr contains a library of example model files (.cpp), accessible
with `exmodel()`

. You are invited to perform MAP-Bayesian
estimation with your own models. These model files should be slightly
modified in order to be “read” by mapbayr with the subsequent
specifications:

`$PARAM`

block- Mandatory:
- Add as many ETA as there are parameters to estimate (i.e. the length of the OMEGA matrix diagonal).
- Name them as ETAn (n being the N° of ETA).
- Set 0 as default value.

- Strongly recommended:
- Provide a description as a plain text

```
$PARAM @annotated: 0 : CL (L/h)
ETA1 : 0 : VC (L)
ETA2 : 0 : F ()
ETA3 //do not write ETA(1)
//do not write iETA
```

- Mandatory:
- Use a
`@covariates`

tag to record covariates in the`$PARAM`

block. Otherwise, you will not be allowed to pass a dataset with covariates columns. - Set the reference value.

- Use a
- Strongly recommended
- Provide a description as a plain text
- Provide units in parentheses (or a description of 0/1 coding for categorical covariates)

```
$PARAM @annotated @covariates: 70 : Body weight (kg)
BW : 0 : Sex (0=Male, 1=Female) SEX
```

`$CMT`

block- Strongly recommended…

… yet**mandatory**if you have multiple types of DV, i.e. parent drug + metabolite:- A
`@annotated`

tag must be used to record compartments. - Write OBS in brackets to define the observation compartment(s). Also
used by
`obs_rows()`

to fill the ‘cmt’ column in your dataset. - Write ADM in brackets to define “default” administration
compartment(s). This information is not used for optimization process
and the
`mapbayest()`

function. The information is mandatory if you use`adm_rows()`

to build your dataset in order to automatically set the value of the ‘cmt’ column. Especially useful if you use a model with an absorption from several depot compartment requiring to duplicate administrations lines in the data set.

- A

```
//example: model with dual zero and first order absorption in compartment 1 & 2, respectively, and observation of parent drug + metabolite
$CMT @annotated: Depot [ADM]
DEPOT: examplinib central [ADM, OBS]
CENT_PAR: examplinib peripheral
PERIPH : methylexamplinib central [OBS] CENT_MET
```

`$OMEGA`

block- Mandatory:
- The length of the omega matrix must be the same as the number of
ETAn provided in
`$PARAM`

. - The order of the omega values must correspond to the order of the
ETAs provided in
`$PARAM`

. This cannot be checked by mapbayr !

- The length of the omega matrix must be the same as the number of
ETAn provided in

```
$OMEGA0.123 0.456 0.789
$OMEGA @block0.111
0.222 0.333
// reminder: omega values can be recorded in multiple $OMEGA blocks
```

`$SIGMA`

blockThe definition of the `$SIGMA`

block may not be as
straightforward as other blocks, but we tried to keep it as simple as
possible. Keep in mind that mapbayr always expect a **pair of
sigma values** for each type of dependent variable: the
**first** value for proportional error, the
**second** for additive.

Two situations can be distinguished:

- You only have one type of concentration to fit, and you did not use
the [OBS] assignment in
`$CMT`

.

Simply write **one pair** of sigma values to describe
proportional and additive error on your concentrations. This error model
will be automatically applied to the compartment where observations were
recorded in your dataset (i.e. value of CMT when MDV = 0).

`0.111 0 // proportional error $SIGMA `

`0 0.222 // (log) additive error $SIGMA `

`0.333 0.444 // mixed error $SIGMA `

- You have multiple types of DV (parent and metabolite), and/or you
used the [OBS] assignment in
`$CMT`

.

Write as many **pairs of sigma values** as there are
compartments assigned with [OBS] in `$CMT`

. The order of the
pair must respect the order in which compartments were assigned. To put
it more clearly, the sigma matrix will be interpreted as such whatever
the model :

N° in the SIGMA matrix diagonal | Associated error |
---|---|

1 | Proportional on concentrations in the 1st cmt with [OBS] |

2 | Additive on concentrations in the 1st cmt with [OBS] |

3 | Proportional on concentrations in the 2nd cmt with [OBS] |

4 | Additive on concentrations in the 2nd cmt with [OBS] |

```
//example: correlated proportional error between parent and metabolite
$SIGMA @block0.050 // proportional error on parent drug
0.000 0.000 // additive error on parent drug
0.100 0.000 0.200 // proportional error on metabolite
0.000 0.000 0.000 0.000 // additive error on metabolite
// reminder: sigma values can be recorded in multiple $SIGMA blocks
```

`$TABLE`

block or
`$ERROR`

block- Mandatory:
- Refer the concentration variable to fit as
`DV`

. Mind the code, especially if concentrations are observed in multiple compartments. - Express log-additive error models as exponential. This way, concentrations will automatically be log-transformed during the optimization process, with no necessity to prior log-transform your concentration.

- Refer the concentration variable to fit as

```
$TABLEdouble DV = (CENTRAL / VC) * exp(EPS(2)) ;
```

- For fitting parent drug and metabolite simultaneously, refer to them as PAR and MET, and define DV accordingly (only DV will be used during the optimization process, but PAR and MET variables are mandatory for post-processing internal functions)

```
$TABLEdouble PAR = (CENT_PAR / V) * (1 + EPS(1)) ;
double MET = (CENT_MET / V) * (1 + EPS(3)) ;
double DV = PAR ;
if(self.cmt == 4) DV = MET ;
// reminder: use "self.cmt" to internaly refer to a compartment in a mrgsolve model code.
```

Note that mapbayr does not strictly rely on this `$ERROR`

block to define the residual error internally and compute the objective
function value, but on information passed in the `$SIGMA`

block. However, we strongly advise you to properly code your
`$ERROR`

block with `EPS(1)`

, `EPS(2)`

etc…, if only to use your code as a regular mrgsolve model code and
simulate random effects.

`$MAIN`

block- Mandatory:
- Double every expression containing ETA information, with ETAn (will be used for optimization of parameters) and ETA(n) (generated for simulations with random effects like a “regular” mrgsolve model)
- Mind the attribution to the good ETAn and ETA(n) as respect to the
information you provided in
`$PARAM`

and`$OMEGA`

. This cannot be checked by mapbayr !

```
$PKdouble CL = TVCL * exp(ETA1 + ETA(1)) ;
```

`$CAPTURE`

block- Mandatory:
- DV must be captured
- For models with parent + metabolite, PAR and MET must be captured too.
- Do not capture variables called IPRED and PRED (they will be
returned by
`mapbayest()`

anyway) - Do not capture any ETAn (ETA1, ETA2 etc…) (they will be returned by
`mapbayest()`

anyway)

- Strongly recommended:
- Capture a posteriori values of parameters you are interested in (e.g. CL)

` $CAPTURE DV PAR MET CL`