Individual and Population Simulations
Introduction
The workshop (workshop.ubiquity.tools) provides several examples of how to perform simulations in ubiquity. To make a copy of these scripts and other supporting files in the current working directory run the following:
This should create the following scripts:
analysis_single.rSimulating the response for a single indiviudalanalysis_multiple.rMote Carlo simulations using IIVanalysis_multiple_file.rMonte Carlo simulations reading subject information from a file
These rely on a PK model of mAbs in humans (Davda etal. mAbs, 6(4),
1094-1102). The contents of the system file for this model can be
seen at the bottom (use ?system_new to see a list of the
available system file examples). The first step in any analysis
(simulation, estimation, etc) is building the system file creating the
ubiquity model object (cfg).
After building any system you can then create templates. To create a
template script for running simulations use
system_fetch_template and specify "Simulation"
as the template argument:
This will create the file analysis_simulate.R in the
working directory. This template should have common options and dosing
information commented out. You simply need to uncomment them and run the
simulation.
Simulating an Individual Response
(analysis_single.r)
We’ll begin by demonstrating how to simulate an indiviudal response to dosing. The system parameters for the default parameter set can be pulled out of this object:
To alter system parameters at the scripting level, you can just
reassign the elements in parameters. For example to change
the celarance to a value of .015 you could simply use:
parameters$CL = 0.15.
Next different simulation options can be set. For example the following will set the duration of the simulation to three months $\left(3\ \mbox{months} \times 4\frac{\mbox{weeks}}{\mbox{month}}\times7\frac{\mbox{days}}{\mbox{week}}\right)$ in days:
The system file is written to allow both IV (Cp) and SC
(At) dosing. So we zero out any default dosing specified in
the system file. The next line specifies the SC dosing we want to
simulate.
cfg = system_zero_inputs(cfg)
cfg = system_set_bolus(cfg, state = "At",
times = c( 0, 14, 28, 42 ), # day
values = c(200, 200, 200, 200 )) # mgNext we run the simulation:
The variable som is a list containing the mapped
simulation output, and the time course is stored in the
simout element. The first column (time)
contains the simulation time in the units of the simulation, days in
this case. Next there is a column for each state (At,
Cc, Cp) and a column for each output
(C_ng_ml, C_DOSE). Each system parameter is
passed through the simulation into the output (F1, …
MW). This model has two covariates specified DOSE and WT.
The initial value of these covariates is passed through as well as the
values at each time point. For the covariate DOSE this is
SIMINT_CVIC_DOSE and DOSE, respectively. Next
secondary parameters are also provided (kel, …
kpc). Lastly each timescale specified in the system file is
also passed through with a “ts.” prefix:
p = ggplot() +
geom_line(data=som$simout, aes(x=ts.days, y=C_ng_ml), color="blue") +
xlab("Time (days)")+
ylab("C (ng/ml) (units)")
p = gg_log10_yaxis(p, ylim_min=1e3, ylim_max=3e5)
p = prepare_figure("print", p)
print(p)
Simulating Population Response From IIV
(analysis_multiple.r)
Next we want to simulate the response of multiple subjects. This system has IIV specified in the following manner:
IIV details
IIV/Parameter set:
Short Name: default
Variance/covariance matrix
ETAka ETACL ETAVc ETAVp ETAQ
ETAka 0.4160 0 0 0 0
ETACL 0 0.0988 0.0786 0.0619 0
ETAVc 0 0.0786 0.1160 0.0377 0
ETAVp 0 0.0619 0.0377 0.0789 0
ETAQ 0 0 0 0 0.6990
On parameters
Vp, ETAVp(LN)
CL, ETACL(LN)
Q, ETAQ(LN)
ka, ETAka(LN)
Vc, ETAVc(LN)Different aspects of the Monte Carlo simulations can be specified.
For example the following states that we want to simulate 20 subjects
and the simulation is run using simulate_subjects:
cfg=system_set_option(cfg, group = "stochastic",
option = "nsub",
value = 20)
som = simulate_subjects(parameters, cfg)The output here, som, has a different structure than the
output from an individual simulation. It is a list with the following
elements
som$subjects$parameters- Matrix with a row for each subject containing that subjects parameterssom$subjects$secondary_parameters- Matrix containing the static secondary parameters (one row for each subject)som$tcsummary- Data frame containing time course summary level information for the simulations there are columns for- Timescales (prefix
ts.) - States (prefix
s.) and Outputs (prefixo.) with the mean (suffix.mean) , median (suffix.median) and upper (suffix.ub_ci) and lower (suffix.lb_ci) bounds on the specified confidence interval (default 95%)
- Timescales (prefix
som$states- List with an element for each state. Each of these is a matrix containing the subject level predictions for that state (one row for each subject)som$output- List with an element for each output. Each of these is a matrix containing the subject level predictions for that output (one row for each subject)som$times- Data frame with a column for the simulation time (time) and a column for each timescale with ats.prefix.
p = ggplot(som$tcsummary, aes(x=ts.days, y=o.C_ng_ml.mean)) +
geom_ribbon(aes(ymin=o.C_ng_ml.lb_ci,
ymax=o.C_ng_ml.ub_ci),
fill="lightblue",
alpha=0.6) +
geom_line(linetype="solid", size=0.7, color="blue") +
geom_line(aes(x=ts.days, y=o.C_ng_ml.ub_ci), linetype="dashed", size=0.2, color="blue") +
geom_line(aes(x=ts.days, y=o.C_ng_ml.lb_ci), linetype="dashed", size=0.2, color="blue") +
xlab("Time (days)")+
ylab("C (ng/ml) (units)")+
guides(fill="none")
p = gg_log10_yaxis(p , ylim_min=1e3, ylim_max=3e5)
p = prepare_figure("print", p )
print(p)
Simulating Population Response From File
(analysis_multiple_file.r)
Subject information can be pulled from a data file. First we need to
load the dataset using system_load_data, here the dataset
is named SUBS.
cfg = system_load_data(cfg,
dsname = "SUBS",
data_file = system.file("ubinc", "csv", "mab_pk_subjects.csv",
package = "ubiquity"))The format of the dataset is shown below. There needs to be an column
for the subject ID (SIMINT_ID) and the simulation time
(SIMINT_TIME). Next the subject level parameters can be
specified where the column headers correspond to the parameter names. If
a parameter is not specified, the default value will be taken from the
parameters input. In this case MW was not
specified in the dataset, so it will be taken from
parameters.
Optionally, covariates can also be specified by name as well. For
time varying covariates, multiple records can be specified for the same
subject (the parameter values for that subject should remain constant
between records). In this example WT and SEX
are covariates but only WT has been defined in the system
file, so SEX will be ignored. The covariate
DOSE is not defined so the default from the system file
will be used.
With the dataset loaded, we need to link that subject file to the
stochastic simulations using the dataset name (SUBS) and
then we can tell the scripts how to handle sampling from the
dataset:
cfg=system_set_option(cfg, group = "stochastic",
option = "sub_file",
value = "SUBS")
cfg=system_set_option(cfg, group = "stochastic",
option = "sub_file_sample",
value = "with replacement")Then we just use simulate_subjects to run the simulation
as before:
Parallelization
If you are using simulate_subjects to perform population
simulations and have multiple cores on your computer you can utilize
those cores by setting the following options in the
"simulation" group:
Contents of system.txt
# Implementation of the two compartment model from Davda 2014
#
# Davda, J. P., Dodds, M. G., Gibbs, M. A., Wisdom, W., & Gibbs, J. (2014). A
# model-based meta-analysis of monoclonal antibody pharmacokinetics to guide
# optimal first-in-human study design. mAbs, 6(4), 1094-1102.
# http://doi.org/10.4161/mabs.29095
#
# System Units:
# mass [=] nmoles
# volume [=] L
# concentration [=] nM
# time [=] day
#
# #-------------#
# | Parameters |
# #-------------#
# System parameters
#name value lower upper units editable grouping
# bound bound
<P> F1 0.744 eps inf --- yes System
<P> ka 0.282 eps inf 1/day yes System
<P> CL 0.200 eps inf L/day yes System
<P> Vc 3.61 eps inf L yes System
<P> Vp 2.75 eps inf L yes System
<P> Q 0.747 eps inf L/day yes System
<P> MW 140 eps inf kD yes System
<PSET:default> mAb in Humans
# Interindividual Variability
# Taken from Table 3
<IIV:ETAka> 0.416
<IIV:ETAka:LN> ka
<IIV:ETACL> 0.09875
<IIV:ETACL:LN> CL
<IIV:ETAVc> 0.116
<IIV:ETAVc:LN> Vc
<IIV:ETAVp> 0.0789
<IIV:ETAVp:LN> Vp
<IIV:ETAQ> 0.699
<IIV:ETAQ:LN> Q
<IIVCOR:ETACL:ETAVc> 0.0786
<IIVCOR:ETACL:ETAVp> 0.0619
<IIVCOR:ETAVp:ETAVc> 0.0377
# Covariates
<CV:DOSE> ; times; [ 0 ]; day
<CV:DOSE> ; values; [400]; mg
<CVINTERP:DOSE> step
<CV:WT> ; times; [ 0 ]; day
<CV:WT> ; values; [ 60]; kg
<CVINTERP:WT> step
# static secondary parameters
<As> kel = CL/Vc
<As> kcp = Q/Vc
<As> kpc = Q/Vp
# #-------------------#
# |Input Information |
# #-------------------#
#
# 1e6 ng 1 nmole 1
# X mg x ------ x ----------------- x --- => X*1e3/MW/Vc
# 1 mg MW (KDA) * 1000 V(L)
#
# Bolus Events
# times/events state values scale units
<B:times>; [ 0.0, 7, 14 ]; 1; days
<B:events>; At; [400.0, 0, 0 ]; 1e3/MW; mg
<B:events>; Cc; [ 0.0, 0, 0 ]; 1e3/MW/Vc; mg
<R:Dinf>; times; [0, 30]; 1/60/24; min
<R:Dinf>; levels; [0, 0]; 60*24*1e3/MW; mg/min
# ODEs
<ODE:At> -ka*At
<ODE:Cc> ka*At*F1/Vc -kel*Cc - kcp*Cc + kpc*Cp*Vp/Vc + Dinf/Vc
<ODE:Cp> kcp*Cc*Vc/Vp - kpc*Cp
# #---------#
# | Outputs |
# #---------#
# Outputs that begin with QC will not be displayed in the GUI
# Convert nM to ng/ml
#
# X nM ===> X*MW(KDA)
#
# Convert nM to ug/ml/mg(dose)
#
# X nM ===> X*MW(KDA)/1000/dose
#
<O> C_ng_ml = Cc*MW
<O> C_DOSE = Cc*MW/DOSE/1000
<VP> prop_err 0.1 eps inf -- yes Variance
<VP> add_err 0.1 eps inf ng/ml yes Variance
<EST:LT> Vp; Vc; CL; Q; ka
<EST:P> Vp; Vc; CL; Q; ka; add_err; prop_err
<OE:C_ng_ml> add=add_err; prop=prop_err
<AMTIFY> Cp; Ap; Vp
# #---------#
# | Options #
# #---------#
# General Options:
# specify different time scales
<TS:min> 24.0*60.0
<TS:days> 1.0
<TS:hours> 24.0
<TS:weeks> 1.0/7.0
<TS:months> 1.0/7.0/4.0