Covariate Forest Plots

Simulate outcomes from model empirical Bayes estimates with mrgsolve.

pmforest
mrgsolve

1 Introduction

This page demonstrates how to use the pmforest package along with mrgsolve to create covariate forest plots. These plots are used to provide context around estimated covariate effects by simulating model parameters (e.g., clearance) after varying the values of different covariates one at a time. The simulated parameters are normalized to parameters simulated at the reference covariate levels and all simulations are performed over the uncertainty distribution of the THETAs from the estimated model.

2 Tools used

  • pmforest Create forest plots, for pharmacometrics, to visualize variables of interest.

  • mrgsolve Simulate from ODE-based population PK/PD and QSP models in R.

  • yspec Data specification, wrangling, and documentation for pharmacometrics.

3 Outline

This document is more involved than most of the other pages in this Expo.

First, we’ll load the

  • data specification object
  • relevant mrgsolve model
  • data frame of bootstrap parameter estimates

Then we’ll use the mrgsolve model to simulate clearances across the bootstrap parameter estimate set for the reference covariate set.

Next, we’ll simulate clearances (again across the bootstrap parameter set) after varying the values of the different model covariates, one at a time. This illustrates how changes in the covariate translate into changes in clearance.

Finally, we’ll summarize the simulated clearance values at each covariate level and create a forest plot from these summarized simulations.

4 Required packages and options

library(here)
library(mrgsolve)
library(tidyverse)
library(rlang)
library(yspec)
library(pmforest)

5 Load the data specification object

We load the yspec object, which will provide information about the data set, including covariates in the model:

spec <- ys_load(here("data/derived/pk.yml"))

We’ll modify the EGFR unit to be blank:

spec$EGFR$unit <- ""

Then, extract a list of units to annotate the plot:

unit <- 
  spec %>% 
  ys_get_unit() %>% 
  as_tibble() %>% 
  pivot_longer(everything(), values_to = "unit")

head(unit)
# A tibble: 6 × 2
  name  unit  
  <chr> <chr> 
1 C     ""    
2 NUM   ""    
3 ID    ""    
4 TIME  "hour"
5 SEQ   ""    
6 CMT   ""

6 Read in bootstrap parameter estimates

We’ll retain only 200 rows for now, and we’ll number the rows.

post <- read_csv(here("data/boot/boot-106.csv"))
set.seed(10101)
post <- select(post, contains("THETA")) 
post <- slice_sample(post, n = 200) 
post <- mutate(post, iter = row_number())

7 Read in the mrgsolve model

For the final model (run 106), we already have the simulation model coded up: 106.mod. This will enable us to simulate clearances from different covariate values.

mod <- mread(here("script/model/106.mod"), end = -1, outvars = "CL")

mod <- zero_re(mod)

Note that we called zero_re() on the model object; this suppresses the simulation of random effects. In this task, we are only interested in simulated typical parameters.

8 Simulate

8.1 Simulate the reference

Simulate a dataframe of clearances at the reference covariate combination:

ref <- mrgsim(mod, idata = post) %>% select(iter = ID, ref = CL)

head(ref)
# A tibble: 6 × 2
   iter   ref
  <dbl> <dbl>
1     1  3.23
2     2  3.15
3     3  3.07
4     4  3.41
5     5  3.23
6     6  3.15

Note that this simulation produces clearances at the reference covariate levels because we coded the default covariates to be the reference values in the mrgsolve model.

8.2 Simulate different covariate levels

Now, we have to simulate clearances after perturbing each covariate across levels of interest, one at a time.

To do this, we’ll create a named list of vectors, where the name reflects the covariate that is being perturbed, and the vector has all the values to examine.

x <- list(
  WT = c(85, 55), 
  EGFR = c(Severe = 22.6, Moderate = 42.9, Mild = 74.9), 
  ALB = c(5, 3.25), 
  AGE = c(45, 20)
)

For EGFR, we’ve included names for recoding the EGFR as a renal impairment stage (e.g., moderate renal impairment).

Now, we write a function that simulates each covariate at each of the prescribed levels:

ss <- function(values, col) {
  
  COL <- sym(col)
  
  idata <- tibble(!!COL := values, LVL = seq_along(values))
  idata <- crossing(post, idata)
  
  out <-
    mod %>% 
    mrgsim_i(idata, carry_out = c(col, "LVL", "iter")) %>% 
    mutate(name = col, value = !!COL,  !!COL := NULL) %>% 
    arrange(LVL)
  
  if(is_named(values)) {
    out <- mutate(
      out, 
      value := factor(value, labels = names(values), levels=values)
    )
  } else {
    out <- mutate(out, value = fct_inorder(as.character(value)))  
  }
  out
}

This function gets called usiung an imap variant to simulate clearances:

out <- imap_dfr(x, ss)
head(out)
# A tibble: 6 × 7
     ID  time   LVL  iter    CL name  value
  <dbl> <dbl> <dbl> <dbl> <dbl> <chr> <fct>
1     2     0     1   128  3.72 WT    85   
2     4     0     1   104  3.49 WT    85   
3     6     0     1   123  3.60 WT    85   
4     8     0     1    18  3.64 WT    85   
5    10     0     1     1  3.73 WT    85   
6    12     0     1    59  3.70 WT    85

This function:

  • Creates an idata_set with the current covariate name and values
  • Uses tidyr::crossing to expand idata to include all the bootstrap samples we loaded from post
  • Simulates the clearance
  • After the simulation, we log the name of the covariate and the values which were simulated
  • Finally, we check to see if names were passed and use those to recode the covariate values

The result of the function is 200 clearances simulated at multiple levels of multiple covariates.

count(out, name, value)
# A tibble: 9 × 3
  name  value        n
  <chr> <fct>    <int>
1 AGE   45         200
2 AGE   20         200
3 ALB   5          200
4 ALB   3.25       200
5 EGFR  Severe     200
6 EGFR  Moderate   200
7 EGFR  Mild       200
8 WT    85         200
9 WT    55         200

9 Plot

9.1 Get ready to plot

Merge in the unit by name:

out <- left_join(out, unit, by = "name")
out <- mutate(out, cov_level = paste(value, unit))

Merge in the reference clearances by iter and calculate the simulated clearance relative to the reference (relcl):

out <- left_join(out, ref, by = "iter")
out <- mutate(out, relcl = CL/ref)

Set up labels and create a labeller object:

all_labels <- ys_get_short(spec, title_case = TRUE)
all_labels$EGFR <- 'Renal Function'
all_labels$CL <- 'CL (L/hr)'

plot_labels <- as_labeller(unlist(all_labels))

9.2 Summarize the data

Call summarize_data from the pmforest package to generate summaries. We’re asking for the 2.5th and 97.5th percentiles of the clearance at each covariate level. summarize_data also gives us the median for plotting.

sum_data <- summarize_data(
  data = out , 
  value = "relcl",
  group = "name",
  group_level = "cov_level",
  probs = c(0.025, 0.975),
  statistic = "median"
)

head(sum_data)
# A tibble: 6 × 5
  group group_level   mid    lo    hi
  <chr> <chr>       <dbl> <dbl> <dbl>
1 AGE   "20 years"  1.03  0.957 1.10 
2 AGE   "45 years"  0.988 0.959 1.02 
3 ALB   "3.25 g/dL" 0.873 0.827 0.908
4 ALB   "5 g/dL"    1.05  1.03  1.06 
5 EGFR  "Mild "     0.915 0.900 0.927
6 EGFR  "Moderate " 0.698 0.653 0.738

9.3 Create the plot

Please see the ?plot_forest documentation for details around each argument.

clp <- plot_forest(
  data = sum_data,
  summary_label = plot_labels,
  text_size = 3.5,
  vline_intercept = 1,
  x_lab = "Fraction and 95% CI \nRelative to Reference",
  CI_label = "Median [95% CI]",
  plot_width = 8, 
  x_breaks = c(0.4,0.6, 0.8, 1, 1.2, 1.4,1.6), 
  x_limit = c(0.4,1.45),
  annotate_CI = T,
  nrow = 1
) 
clp

10 Other resources

The following script from the Github repository is discussed on this page. If you’re interested running this code, visit the About the Github Repo page first.