Author: Benjamin Guiastrennec

# Visual Predictive Checks (VPC)

#### Benjamin Guiastrennec

#### 02 March, 2026

### Disclosure

The Visual predictive checks (VPC) shown below are only intended to demonstrate the various options available in xpose and should not be used as reference for modeling practice. Furthermore, the plots are only based on 20 simulations to minimize the computing time of the examples, the size of the `xpdb_ex_pk` object and of the xpose package in general.

### Introduction

VPC can be created either by:

1. Using an xpdb containing a simulation and an estimation problem
2. Using a PsN generated VPC folder

The VPC functionality in xpose is build around the vpc R package. For more details about the way the vpc package works, please check the github repository.

### Workflow

The VPC computing and plotting parts have been separated into two distinct functions: `vpc_data()` and `vpc()` respectively. This allows to:

- Optimize the speed when adjusting the graphics aesthetics
- Adjust the VPC data (e.g. remove panels or factor labels) before plotting
- Facilitate error debugging

    xpdb_ex_pk %>%
     vpc_data() %>%  # Compute the vpc data
     vpc()            # Plot the vpc

The generated VPC data is stored in the xpdb under specials datasets and can be used later on.

    xpdb_w_vpc <- vpc_data(xpdb_ex_pk) # Compute and store VPC data

    xpdb_w_vpc # The vpc data is now listed under the xpdb "special" data

    run001.lst overview:
     - Software: nonmem 7.3.0
     - Attached files (memory usage 1.7 Mb):
       + obs tabs: $prob no.1: catab001.csv, cotab001, patab001, sdtab001
       + sim tabs: $prob no.2: simtab001.zip
       + output files: run001.cor, run001.cov, run001.ext, run001.grd, run001.phi, run001.shk
       + special: vpc continuous (#3)
     - gg_theme: theme_readable
     - xp_theme: theme_xp_default
     - Options: dir = data, quiet = FALSE, manual_import = NULL

    vpc(xpdb_w_vpc) # Plot the vpc from the stored data

Multiple VPC data can be stored in an xpdb, but only one of each `vpc_type`.

    xpdb_w_multi_vpc <- xpdb_ex_pk %>%
     vpc_data(vpc_type = 'continuous', opt = vpc_opt(n_bins = 6, lloq = 0.1)) %>%
     vpc_data(vpc_type = 'censored', opt = vpc_opt(n_bins = 6, lloq = 0.1))

    vpc(xpdb_w_multi_vpc, vpc_type = 'continuous')
    vpc(xpdb_w_multi_vpc, vpc_type = 'censored')

### Common options

#### Options in `vpc_data()`

- The option `vpc_type` allows to specify the type of VPC to be computed: “continuous” (default), “categorical”, “censored”, “time-to-event”.
- The `stratify` options defines up to two stratifying variable to be used when computing the VPC data. The `stratify` variables can either be provided as a character vector (`stratify = c('SEX', 'MED1')`) or a formula (`stratify = SEX~MED1`) . The former will result in the use of `ggforce::facet_wrap_paginate()` and the latter of `ggforce::facet_grid_paginate()` when creating the plot. With “categorical” VPC the “group” variable will also be added by default.
- More advanced options (i.e. binning, pi, ci, predcorr, lloq, etc.) are accessible via the `opt` argument. The `opt` argument expects the output from the `vpc_opt()` functions argument.

    xpdb_ex_pk %>%
     vpc_data(vpc_type = 'censored', stratify = 'SEX',
              opt = vpc_opt(bins = 'jenks', n_bins = 7, lloq = 0.5)) %>%
     vpc()

#### Options in `vpc()`

- The option `vpc_type` works similarly to `vpc_data()` and is only required if several VPC data are associated with the xpdb.
- The option `smooth = TRUE/FALSE` allows to switch between smooth and squared shaded areas.
- The plot VPC function works similarly to all other xpose functions to map and customize aesthetics. However in this case the `area_fill` and `line_linetype` each require three values for the low, median and high percentiles respectively.

### Creating VPC using the xpdb data

To create VPC using the xpdb data, at least one simulation and one estimation problem need to present. Hence in the case of NONMEM the run used to generate the xpdb should contain several`$PROBLEM`. In `vpc_data()` the problem number can be specified for the observation (`obs_problem`) and the simulation (`sim_problem`). By default xpose picks the last one of each to generate the VPC.

    # View the xpdb content and data problems
    xpdb_ex_pk

    run001.lst overview:
     - Software: nonmem 7.3.0
     - Attached files (memory usage 1.5 Mb):
       + obs tabs: $prob no.1: catab001.csv, cotab001, patab001, sdtab001
       + sim tabs: $prob no.2: simtab001.zip
       + output files: run001.cor, run001.cov, run001.ext, run001.grd, run001.phi, run001.shk
       + special: <none>
     - gg_theme: theme_readable
     - xp_theme: theme_xp_default
     - Options: dir = data, quiet = FALSE, manual_import = NULL

    # Generate the vpc
    xpdb_ex_pk %>%
     vpc_data(vpc_type = 'continuous', obs_problem = 1, sim_problem = 2) %>%
     vpc()

### Creating the VPC using a PsN folder

The `vpc_data()` contains an argument `psn_folder` which can be used to point to a PsN generated VPC folder. As in most xpose function `template_titles` keywords can be used to automatize the process e.g. `psn_folder = '@dir/@run_vpc'` where `@dir` and `@run` will be automatically translated to initial (i.e. when the xpdb was generated) run directory and run number `'analysis/models/pk/run001_vpc'`.

In this case, the data will be read from the `/m1` sub-folder (or `m1.zip` if compressed). Note that PsN drops unused columns to reduce the simtab file size. Thus, in order to allow for more flexibility in R, it is recommended to use multiple stratifying variables (`-stratify_on=VAR1,VAR2`) and the prediction corrected (`-predcorr` adds the PRED column to the output) options in PsN to avoid having to rerun PsN to add these variables later on. In addition, `-dv`, `-idv`, `-lloq`, `-uloq`, `-predcorr` and `-stratify_on` PsN options are automatically applied to xpose VPC.

The PsN generated binning can also applied to xpose VPC with the `vpc_data()` option `psn_bins = TRUE` (disabled by default). However PsN and the vpc package work slightly differently so the results may not be optimal and the output should be evaluated carefully.

    xpdb_ex_pk %>%
     vpc_data(psn_folder = '@dir/run001_vpc', psn_bins = TRUE) %>%
     vpc()