sbioelementaryeffects
Perform global sensitivity analysis (GSA) by computing elementary effects (requires Statistics and Machine Learning Toolbox)
Since R2021b
Syntax
Description
performs a global sensitivity analysis of a SimBiology model elementaryEffectsResults
= sbioelementaryeffects(modelObj
,params
,observables
)modelObj
by computing elementary effects of observables
with respect to
individual model quantities or parameters specified in params
.
uses additional options specified by one or more name-value arguments.elementaryEffectsResults
= sbioelementaryeffects(modelObj
,params
,observables
,Name=Value
)
Examples
Perform GSA by Computing Elementary Effects
Load the tumor growth model.
sbioloadproject tumor_growth_vpop_sa.sbproj
Get a variant with estimated parameters and the dose to apply to the model.
v = getvariant(m1);
d = getdose(m1,'interval_dose');
Get the active configset and set the tumor weight as the response.
cs = getconfigset(m1);
cs.RuntimeOptions.StatesToLog = 'tumor_weight';
Simulate the model and plot the tumor growth profile.
sbioplot(sbiosimulate(m1,cs,v,d));
Perform global sensitivity analysis (GSA) on the model to find the model parameters that the tumor growth is sensitive to.
First, define model parameters of interest, which are involved in the pharmacodynamics of the tumor growth. Define the model response as the tumor weight.
modelParamNames = {'L0','L1','w0','k1'}; outputName = 'tumor_weight';
Then perform GSA by computing the elementary effects using sbioelementaryeffects
. Use 100
as the number of samples and set ShowWaitBar
to true
to show the simulation progress.
rng('default');
eeResults = sbioelementaryeffects(m1,modelParamNames,outputName,Variants=v,Doses=d,NumberSamples=100,ShowWaitbar=true);
Show the median model response, the simulation results, and a shaded region covering 90% of the simulation results.
plotData(eeResults,ShowMedian=true,ShowMean=false);
You can adjust the quantile region to a different percentage by specifying Alphas
for the lower and upper quantiles of all model responses. For instance, an alpha
value of 0.1 plots a shaded region between the 100*alpha
and 100*(1-alpha)
quantiles of all simulated model responses.
plotData(eeResults,Alphas=0.1,ShowMedian=true,ShowMean=false);
Plot the time course of the means and standard deviations of the elementary effects.
h = plot(eeResults);
% Resize the figure.
h.Position(:) = [100 100 1280 800];
The mean of effects explains whether variations in input parameter values have any effect on the tumor weight response. The standard deviation of effects explains whether the sensitivity change is dependent on the location in the parameter domain.
From the mean of effects plots, parameters L1
and w0
seem to be the most sensitive parameters to the tumor weight before the dose is applied at t = 7. But, after the dose is applied, k1
and L0
become more sensitive parameters and contribute most to the after-dosing stage of the tumor weight. The plots of standard deviation of effects show more deviations for the larger parameter values in the later stage (t > 35) than for the before-dose stage of the tumor growth.
You can also display the magnitudes of the sensitivities in a bar plot. Each color shading represents a histogram representing values at different times. Darker colors mean that those values occur more often over the whole time course.
bar(eeResults);
You can also plot the parameter grids and samples used to compute the elementary effects.
plotGrid(eeResults)
You can specify more samples to increase the accuracy of the elementary effects, but the simulation can take longer to finish. Use addsamples
to add more samples.
eeResults2 = addsamples(eeResults,200);
The SimulationInfo
property of the result object contains various information for computing the elementary effects. For instance, the model simulation data (SimData) for each simulation using a set of parameter samples is stored in the SimData
field of the property. This field is an array of SimData
objects.
eeResults2.SimulationInfo.SimData
SimBiology SimData Array : 1500-by-1 Index: Name: ModelName: DataCount: 1 - Tumor Growth Model 1 2 - Tumor Growth Model 1 3 - Tumor Growth Model 1 ... 1500 - Tumor Growth Model 1
You can find out if any model simulation failed during the computation by checking the ValidSample
field of SimulationInfo
. In this example, the field shows no failed simulation runs.
all(eeResults2.SimulationInfo.ValidSample)
ans = logical
1
You can add custom expressions as observables and compute the elementary effects of the added observables. For example, you can compute the effects for the maximum tumor weight by defining a custom expression as follows.
% Suppress an information warning that is issued. warnSettings = warning('off', 'SimBiology:sbservices:SB_DIMANALYSISNOTDONE_MATLABFCN_UCON'); % Add the observable expression. eeObs = addobservable(eeResults2,'Maximum tumor_weight','max(tumor_weight)','Units','gram');
Plot the computed simulation results showing the 90% quantile region.
h2 = plotData(eeObs,ShowMedian=true,ShowMean=false); h2.Position(:) = [100 100 1500 800];
You can also remove the observable by specifying its name.
eeNoObs = removeobservable(eeObs,'Maximum tumor_weight');
Restore the warning settings.
warning(warnSettings);
Input Arguments
modelObj
— SimBiology model
SimBiology model object
SimBiology model, specified as a SimBiology model object
.
params
— Names of model parameters, species, or compartments
character vector | string | string vector | cell array of character vectors
Names of model parameters, species, or compartments, specified as a character vector, string, string vector, or cell array of character vectors.
Example: ["k1","k2"]
Data Types: char
| string
| cell
observables
— Model responses
character vector | string | string vector | cell array of character vectors
Model responses, specified as a character vector, string, string vector, or cell
array of character vectors. Specify the names of species, parameters, compartments, or
observables
.
Example: "tumor_growth"
Data Types: char
| string
| cell
Name-Value Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.
Example: eeResults =
sbioelementaryeffects(modelObj,params,observables,StopTime=10)
specifies to use
a stop time of 10.
Bounds
— Parameter bounds
numeric matrix
Parameter bounds, specified as a numeric matrix with two columns. The first column contains
the lower bounds and the second column contains the upper
bounds. The number of rows must be equal to the number of
parameters in params
.
If a parameter has a nonzero value, the default bounds are ±10% of the value. If the
parameter value is zero, the default bounds are [0 1]
.
Example: [0.5 5]
Data Types: double
Doses
— Doses to use during simulations
ScheduleDose
object | RepeatDose
object | vector of dose objects
Doses to use during model simulations, specified as a ScheduleDose
or
RepeatDose
object or a vector of
dose objects.
Variants
— Variants to apply before simulations
variant object | vector of variant objects
Variants to apply before model simulations, specified as a variant object or vector of variant objects.
When you specify multiple variants with duplicate specifications for a property's value, the last occurrence for the property value in the array of variants is used during simulation.
NumberSamples
— Number of samples to compute elementary effects
1000
(default) | positive integer
Number of samples to compute elementary effects, specified as a positive integer.
The function requires (number of input
model simulations to compute the elementary effects.params
+ 1) *
NumberSamples
Data Types: double
PointSelection
— Method to select sample points to compute elementary effects
"chain"
(default) | "radial"
Method to select sample points to compute elementary effects, specified as
"chain"
or "radial"
. The
"chain"
point selection uses the Morris method [1]. The
"radial"
point selection uses the Sohier method [2]. For details, see
Elementary Effects for Global Sensitivity Analysis.
Data Types: char
| string
GridLevel
— Discretization level of parameter domain
10
(default) | positive even integer
Discretization level of the parameter domain, specified as a positive even integer. This
parameter defines a grid of equidistant points in the parameter domain, where each dimension
is discretized using
points. The
following figure shows an example of a grid for parameters p1 and
p2 within given parameter bounds.Gridlevel
+1
For details, see Elementary Effects for Global Sensitivity Analysis.
Data Types: double
GridDelta
— Step size to compute elementary effects
GridLevel/2
(default) | positive integer
Step size for computing elementary effects, specified as a positive integer between 1 and
GridLevel
. The step size is measured in terms of grid points
between neighboring points. The following figure shows examples of different grid delta
values.
For details, see Elementary Effects for Global Sensitivity Analysis.
Data Types: double
AbsoluteEffects
— Flag to use absolute values of elementary effects
true
(default) | false
Flag to use the absolute values of elementary effects, specified as true
or
false
. By default, the function uses the absolute values of
elementary effects. Using nonabsolute values can average out when calculating the mean. For
details, see Elementary Effects for Global Sensitivity Analysis.
Data Types: logical
SamplingMethod
— Method to generate parameter samples
"lhs"
(default) | "random"
Method to generate parameter samples, specified as one of the following:
"lhs"
— Use low-discrepancy Latin hypercube samples."random"
— Use uniformly distributed random samples.
The function selects generated parameter samples by sampling the grid points.
StopTime
— Simulation stop time
nonnegative scalar
Simulation stop time, specified as a nonnegative scalar. If you specify neither
StopTime
nor OutputTimes
, the function uses
the stop time from the active configuration set of the model. You cannot specify both
StopTime
and OutputTimes
.
Data Types: double
OutputTimes
— Simulation output times
numeric vector
Simulation output times, specified as a numeric vector. The function computes the
elementary effects at these output time points. You cannot specify both
StopTime
and OutputTimes
. By default, the
function uses the reported time points of the first model simulation.
Example: [0 1 2 3.5 4 5 5.5]
Data Types: double
UseParallel
— Flag to run model simulations in parallel
false
(default) | true
Flag to run model simulations in parallel, specified as true
or
false
. When the value is true
and Parallel Computing Toolbox™ is available, the function runs simulations in parallel.
Data Types: logical
Accelerate
— Flag to turn on model acceleration
true
(default) | false
Flag to turn on model acceleration, specified as true
or
false
.
Data Types: logical
InterpolationMethod
— Method for interpolation of model simulations
"interp1q"
(default) | character vector | string
Method for interpolation of model responses to a common set of output times, specified as a character vector or string. The valid options follow.
Data Types: char
| string
ShowWaitbar
— Flag to show progress of model simulations
false
(default) | true
Flag to show the progress of model simulations by displaying a wait bar, specified
as true
or false
. By default, no wait bar is
displayed.
Data Types: logical
Output Arguments
elementaryEffectsResults
— Results containing means and standard deviations of elementary effects
SimBiology.gsa.ElementaryEffects
object
Results containing means and standard deviations of elementary effects, returned as
a SimBiology.gsa.ElementaryEffects
object. The object includes information
such as the mean and standard deviation of elementary effects as well as parameter
samples and model simulations used to compute the elementary effects.
More About
Elementary Effects for Global Sensitivity Analysis
sbioelementaryeffects
lets you assess global
sensitivity of a model response with respect to variations in model parameters.
Consider a simple case with one sensitivity input parameter P. The elementary effect EE of P with respect to a model response R is defined as follows.
Here, EEP(x) is the elementary effect of
P. R(x) and R(x+delta) are model
responses at a specific time or the values of observables, evaluated for parameter values
x
and
x+delta
.
In the general case of k sensitivity input parameters,
x is a vector of different parameter values,
x =
[v1,v2,v3,…,vk]
.
The elementary effect of the ith parameter is computed as follows.
Here, ei is the ith
canonical unit vector. Thus, calculating the elementary effects of all parameters
P1,P2,P3,…,Pk
requires k+1
model simulations.
The function provides two methods ('PointSelection'
) to select a set of k+1
points required to compute these elementary effects.
To get the mean and standard deviation of elementary effects, the function computes
N ('NumberSamples'
) elementary effects per parameter, which requires
N*(k+1)
simulations. By
default, the function reports the mean and standard deviation of
absolute elementary effects of each parameter
P1,P2,P3,…,Pk
.
The mean of elementary effects explains whether variations in parameter P have any effect on response R on average.
The standard deviation explains whether the sensitivity change is dependent on the location in the parameter domain.
The function uses the absolute elementary effects by default
because the elementary effects can average out when calculating the mean otherwise.
Optionally, you can set the 'AbsoluteEffects'
name-value argument to false
to get the
means and standard deviations of nonabsolute elementary effects.
The function reports the points used to compute elementary effects in the
ParameterSamples
property of the returned results object. Each block
of k+1
rows in the table of
ParameterSamples
corresponds to the k+1 radial or chained points used
to compute the elementary effects. The SimulationInfo.SimData
property
of the results object contains the corresponding model simulations. The function samples the
points from the parameter grid defined by 'GridLevel'
and
'GridDelta'
.
The following figure illustrates a simple case with two sensitivity inputs
(y1 and y2) with 'NumberSamples'
= 2 using the chain
'PointSelection'
method.
References
[1] Morris, Max D. “Factorial Sampling Plans for Preliminary Computational Experiments.” Technometrics 33, no. 2 (May 1991): 161–74.
[2] Sohier, Henri, Jean-Loup Farges, and Helene Piet-Lahanier. “Improvement of the Representativity of the Morris Method for Air-Launch-to-Orbit Separation.” IFAC Proceedings Volumes 47, no. 3 (2014): 7954–59.
Version History
Introduced in R2021b
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