A simple, clean workflow for sensitivity analysis with mrgsolve.
library(mrgsim.sa)Models in mrgsolve have “parameters” associated with them.
mod <- modlib("pk1", end = 48, delta = 0.1)
param(mod).
. Model parameters (N=3):
. name value . name value
. CL 1 | V 20
. KA 1 | . .
Parameters are name-value pairs that are usually involved in controlling
how the system advances in time. Parameters could be clearances (CL),
rate constants (k), pharmacodynamic parameters (EC50) or even
covariates (WT … weight). mrgsim.sa does one-at-a-time sensitivity
analysis on parameters in your model.
The nominal (in model) parameter value is divided and multiplied by a
factor, generating minimum and maximum bounds for simulating a sequence
of parameter values. In this example, we vary CL and V, each one at
a time.
out <-
mod %>%
ev(amt = 100) %>%
select_par(CL, V) %>%
parseq_fct(.n = 5) %>%
sens_each()
sens_plot(out, "CP")
In this sensitivity analysis, CL is varied at the value of V in the
model parameter list and V is varied at the value of CL in the model
parameter list. The black dashed line indicates the model prediction
based on CL and V both as they are in the parameter list; this is
the “reference”.
The simulated data is returned in a long format
out. # A tibble: 14,520 × 7
. case time p_name p_value dv_name dv_value ref_value
. * <int> <dbl> <chr> <dbl> <chr> <dbl> <dbl>
. 1 1 0 CL 0.5 EV 0 0
. 2 1 0 CL 0.5 EV 0 100
. 3 1 0 CL 0.5 CENT 0 0
. 4 1 0 CL 0.5 CENT 0 0
. 5 1 0 CL 0.5 CP 0 0
. # ℹ 14,515 more rows
The previous plot focused on relative changes in the PK profile for
“lower” and “higher” values of CL and V according to the parseq_
method. You can plot with a more quantitative color scale and legend
using grid = TRUE.
sens_plot(out, "CP", grid = TRUE)
In another example, we look at latent infected cell pool development over ten years at different “burst” size, or the number of HIV particles released when one cell lyses.
mod <- mread("hiv", "inst/example")
mod %>%
update(end = 365*10) %>%
parseq_range(N = c(900,1500), .n = 10) %>%
sens_each(tscale = 1/365) %>%
sens_plot("L", grid = TRUE)
The model is rifampicin PBPK.
mod <- mread("inst/example/rifampicin.cpp", delta = 0.1). Building rifampicin_cpp ... done.
sims <-
mod %>%
ev(amt = 600) %>%
parseq_manual(
SFKp = seq_fct(.$SFKp, n = 20),
Kp_muscle = seq_even(0.001, 0.1, n = 6)
) %>% sens_each()
sens_plot(sims, "Ccentral")
To this point, we have always used sens_each() so that each value for
each parameter is simulated one at a time. Now, simulate the grid or all
combinations of the sensitivity parameters.
We use parseq_cv() here, which generates lower and upper bounds for
the range using 50% coefficient of variation.
out <-
mod %>%
update(outvars = "Ccentral") %>%
ev(amt = 600) %>%
parseq_cv(fBCLint_all_kg, .n = 5) %>%
parseq_cv(SFKp, Kp_muscle, .n = 3) %>%
sens_grid(recsort = 3)
out. # A tibble: 10,980 × 8
. case fBCLint_all_kg SFKp Kp_muscle time dv_name dv_value ref_value
. * <int> <dbl> <dbl> <dbl> <dbl> <chr> <dbl> <dbl>
. 1 1 0.138 3.65 0.0520 0 Ccentral 0 0
. 2 1 0.138 3.65 0.0520 0 Ccentral 0 0
. 3 1 0.138 3.65 0.0520 0 Ccentral 0 0
. 4 1 0.138 3.65 0.0520 0 Ccentral 0 0
. 5 1 0.138 3.65 0.0520 0.1 Ccentral 3.66 3.14
. # ℹ 10,975 more rows
sens_plot(out, "Ccentral")
The output is more complicated because all the selected parameters have varying “sensitivity” values.
In local sensitivity analysis, we vary each sensitivity parameter a very small amount around the parameter list (model) value and see how much the output changes for a unit change in the parameter. The “sensitivity” is plotted over time.
mod <- modlib("pk2", delta = 0.1, end = 48)
doses <- ev(amt = 100)
out <- lsa(mod, var = "CP", par = "CL,V2,Q,V3", events = doses)
out. # A tibble: 1,928 × 5
. time dv_name dv_value p_name sens
. <dbl> <chr> <dbl> <chr> <dbl>
. 1 0 CP 0 CL 0
. 2 0 CP 0 CL 0
. 3 0.1 CP 0.472 CL -0.00254
. 4 0.2 CP 0.893 CL -0.00514
. 5 0.3 CP 1.27 CL -0.00782
. # ℹ 1,923 more rows
lsa_plot(out)