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 of concentrations to fit (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.

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.

```
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
"
my_model <- mcode("Example_model", code)
```

```
my_data <- data.frame(ID = 1, time = c(0,6,15,24), evid = c(1, rep(0,3)), cmt = 1, amt = c(100, rep(0,3)),
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
```

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

, `adm_lines()`

and `add_covariates()`

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

```
my_est <- my_model %>%
adm_lines(time = 0, amt = 100, rate = 20) %>%
obs_lines(time = 6, DV = 3.9) %>%
obs_lines(time = 20, DV = 1.1) %>%
obs_lines(time = 24, DV = 2, mdv = 1) %>%
add_covariates(list(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
#> 1 1 0 1 1 100 20 1 NA 0.0000000 0.0000000 1.79217 90 0.3872104
#> 2 1 6 0 1 0 0 0 3.9 4.1621701 5.1739186 1.79217 90 0.3872104
#> 3 1 15 0 1 0 0 0 1.1 1.0867408 1.6468556 1.79217 90 0.3872104
#> 4 1 24 0 1 0 0 1 2.0 0.5559693 0.9594398 1.79217 90 0.3872104
#> ETA2
#> 1 0.1569604
#> 2 0.1569604
#> 3 0.1569604
#> 4 0.1569604
```

```
# 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()`

. - handles multiple error models such as additive, proportional, mixed or exponential error (without prior log-transformation of data).
- fit multiple patients stored in a single dataset.
- fit both parent drug and metabolite simultaneously.
- accepts any kind of models thanks to the flexibility of mrgsolve.
- 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”.

Performance, in terms of quality of parameter predictions, was validated against NONMEM for a wide variety of models and data. However predictions might differ depending on the complexity of the user’s data or model, or as function of the number of parameter to estimate. The user is invited to investigate if discrepancies come from the prediction of the concentrations (i.e. mrgsolve) or from the optimization process *per se* (i.e. mapbayr). Feel free to contact us through the issue tracker.

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

The user is invited to perform MAP-Bayesian estimation with his/her own mrgsolve 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
ETA1 : 0 : CL (L/h)
ETA2 : 0 : VC (L)
ETA3 : 0 : F ()
//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)

`$CMT`

block- Strongly recommended…

… yet**mandatory**if you use`obs_lines()`

and`adm_lines()`

to build your dataset, or 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_lines()`

to build 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_lines()`

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: Depot [ADM]
CENT_PAR: examplinib central [ADM, OBS]
PERIPH : examplinib peripheral
CENT_MET : methylexamplinib central [OBS]
```

`$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

```
$OMEGA
0.123 0.456 0.789
$OMEGA @block
0.111
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).

- You have multiple DV to fit (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 @block
0.050 // 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 log-transformed during the optimization process, with no necessity to prior log-transform your concentration.

- Refer the concentration variable to fit as

- 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)

```
$TABLE
double 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 !

`$CAPTURE`

block- Mandatory:
- DV must be captured
- For models with parent + metabolite, PAR and MET must be captured too.

- Strongly recommended:
- Capture a posteriori values of parameters you are interested in (e.g. CL)
- Do not capture covariates and ETAn (they will be returned by
`mapbayest()`

anyway)