Time-varying covariates

This vignette shows how time-varying covariates can be implemented.

Body weight as a time varying covariate

As a demonstration example, let’s implement allometric scaling on the clearance and volume of a 1-compartment PK model:

model <- model_suite$nonmem$advan2_trans2 %>%
  replace(Equation("CL", "THETA_CL*exp(ETA_CL)*pow(BW/70, 0.75)")) %>%
  replace(Equation("V", "THETA_V*exp(ETA_V)*BW/70"))

Assume our drug is given once a month and BW varies over time. A time-varying covariate can be added to the dataset as follows:

dataset <- Dataset(1) %>%
  add(Bolus(time = 0, amount = 1000)) %>%
  add(Observations(times = seq(0, 30, by = 0.1))) %>%
  add(TimeVaryingCovariate(
    "BW",
    data.frame(TIME = c(0, 7, 14, 21), VALUE = c(80, 75, 70, 65))
  ))

The typical profile can be simulated in the following way:

results <- model %>%
  disable("IIV") %>%
  simulate(dataset = dataset, seed = 1, outvars = "BW")
gridExtra::grid.arrange(
  spaghetti_plot(results, "CONC"),
  spaghetti_plot(results, "BW"),
  ncol = 1
)

Let’s now compare this profile with another typical individual having a constant body weight of 70 kg:

scenarios <- Scenarios() %>%
  add(Scenario("BW as time-varying covarite")) %>%
  add(Scenario("Fixed BW", dataset = ~ .x %>% replace(Covariate("BW", 70))))

results <- model %>%
  disable("IIV") %>%
  simulate(dataset = dataset, seed = 1, outvars = "BW", scenarios = scenarios)
gridExtra::grid.arrange(
  spaghetti_plot(results, "CONC"),
  spaghetti_plot(results, "BW"),
  ncol = 1
)

Finally, time-varying covariates can also be individualized by specifying an ID column:

dataset <- Dataset(2) %>%
  add(Bolus(time = 0, amount = 1000)) %>%
  add(Observations(times = seq(0, 30, by = 0.1))) %>%
  add(TimeVaryingCovariate(
    "BW",
    data.frame(
      ID = c(rep(1, 4), rep(2, 4)),
      TIME = c(0, 7, 14, 21, 0, 7, 14, 21),
      VALUE = c(80, 75, 70, 65, 65, 70, 75, 80)
    )
  ))
results <- model %>%
  disable("IIV") %>%
  simulate(dataset = dataset, seed = 1, outvars = "BW")
gridExtra::grid.arrange(
  spaghetti_plot(results, "CONC", "ID"),
  spaghetti_plot(results, "BW", "ID"),
  ncol = 1
)