ParameterConfidenceInterval
Object containing confidence interval results for estimated parameters
Description
The ParameterConfidenceInterval
object contains confidence
interval results for the estimated parameters.
Creation
Create a parameter confidence interval object using sbioparameterci
.
Properties
Type
— Confidence interval type
'gaussian'
| 'profileLikelihood'
| 'bootstrap'
This property is read-only.
Confidence interval type, specified as 'gaussian'
,
'profileLikelihood'
, or
'bootstrap'
.
Example: 'bootstrap'
Alpha
— Confidence level
positive scalar
This property is read-only.
Confidence level, (1-Alpha) * 100%
, specified as a
positive scalar between 0 and 1.
Example: 0.01
GroupNames
— Original group names from data used for fitting
cell array of character vectors
This property is read-only.
Original group names from the data used for fitting the model, specified as a cell array of character vectors. Each cell contains the name of a group.
Example: {'1'}{'2'}{'3'}
Results
— Confidence interval results
table
This property is read-only.
Confidence interval results, specified as a table. The table contains the following columns.
Column Name | Description |
---|---|
Name | Name of the estimated parameter |
Estimate | Estimated parameter value |
Bounds | Lower and upper parameter bounds (if defined in the original fit) |
Group | Group name (if available) |
CategoryVariableName | Name of category (if defined in the original fit) |
CategoryValue | Value of the category variable specified by CategoryVariableName |
ConfidenceInterval | Confidence interval values |
Status | Confidence interval estimation status, specified as
one of the following categorical values:
success ,
constrained ,
estimable , not
estimable (for details, see Parameter Confidence Interval Estimation Status) |
ExitFlags
— Exit flags returned during calculation of bootstrap
confidence intervals
vector
This property is read-only.
Exit flags returned during the calculation of bootstrap
confidence intervals only, specified as a vector of integers. Each integer
is an exit flag returned by the estimation function (except
nlinfit
) used to fit parameters during
bootstrapping. The same estimation function used in the original fit is used
for bootstrapping.
Each flag indicates the success or failure status of the fitting performed to create a bootstrap sample. Refer to the reference page of the corresponding estimation function for the meaning of the exit flag.
If the estimation function does not return an exit flag,
ExitFlags
is set to []
. For the
gaussian
and profileLikelihood
confidence intervals, ExitFlags
is not supported and is
always set to []
.
Object Functions
Examples
Compute Confidence Intervals for Estimated PK Parameters and Model Predictions
Load Data
Load the sample data to fit. The data is stored as a table with variables ID , Time , CentralConc , and PeripheralConc. This synthetic data represents the time course of plasma concentrations measured at eight different time points for both central and peripheral compartments after an infusion dose for three individuals.
load data10_32R.mat gData = groupedData(data); gData.Properties.VariableUnits = {'','hour','milligram/liter','milligram/liter'}; sbiotrellis(gData,'ID','Time',{'CentralConc','PeripheralConc'},'Marker','+',... 'LineStyle','none');
Create Model
Create a two-compartment model.
pkmd = PKModelDesign; pkc1 = addCompartment(pkmd,'Central'); pkc1.DosingType = 'Infusion'; pkc1.EliminationType = 'linear-clearance'; pkc1.HasResponseVariable = true; pkc2 = addCompartment(pkmd,'Peripheral'); model = construct(pkmd); configset = getconfigset(model); configset.CompileOptions.UnitConversion = true;
Define Dosing
Define the infusion dose.
dose = sbiodose('dose','TargetName','Drug_Central'); dose.StartTime = 0; dose.Amount = 100; dose.Rate = 50; dose.AmountUnits = 'milligram'; dose.TimeUnits = 'hour'; dose.RateUnits = 'milligram/hour';
Define Parameters
Define the parameters to estimate. Set the parameter bounds for each parameter. In addition to these explicit bounds, the parameter transformations (such as log, logit, or probit) impose implicit bounds.
responseMap = {'Drug_Central = CentralConc','Drug_Peripheral = PeripheralConc'}; paramsToEstimate = {'log(Central)','log(Peripheral)','Q12','Cl_Central'}; estimatedParam = estimatedInfo(paramsToEstimate,... 'InitialValue',[1 1 1 1],... 'Bounds',[0.1 3;0.1 10;0 10;0.1 2]);
Fit Model
Perform an unpooled fit, that is, one set of estimated parameters for each patient.
unpooledFit = sbiofit(model,gData,responseMap,estimatedParam,dose,'Pooled',false);
Perform a pooled fit, that is, one set of estimated parameters for all patients.
pooledFit = sbiofit(model,gData,responseMap,estimatedParam,dose,'Pooled',true);
Compute Confidence Intervals for Estimated Parameters
Compute 95% confidence intervals for each estimated parameter in the unpooled fit.
ciParamUnpooled = sbioparameterci(unpooledFit);
Display Results
Display the confidence intervals in a table format. For details about the meaning of each estimation status, see Parameter Confidence Interval Estimation Status.
ci2table(ciParamUnpooled)
ans = 12x7 table Group Name Estimate ConfidenceInterval Type Alpha Status _____ ______________ ________ __________________ ________ _____ ___________ 1 {'Central' } 1.422 1.1533 1.6906 Gaussian 0.05 estimable 1 {'Peripheral'} 1.5629 0.83143 2.3551 Gaussian 0.05 constrained 1 {'Q12' } 0.47159 0.20093 0.80247 Gaussian 0.05 constrained 1 {'Cl_Central'} 0.52898 0.44842 0.60955 Gaussian 0.05 estimable 2 {'Central' } 1.8322 1.7893 1.8751 Gaussian 0.05 success 2 {'Peripheral'} 5.3368 3.9133 6.7602 Gaussian 0.05 success 2 {'Q12' } 0.27641 0.2093 0.34351 Gaussian 0.05 success 2 {'Cl_Central'} 0.86034 0.80313 0.91755 Gaussian 0.05 success 3 {'Central' } 1.6657 1.5818 1.7497 Gaussian 0.05 success 3 {'Peripheral'} 5.5632 4.7557 6.3708 Gaussian 0.05 success 3 {'Q12' } 0.78361 0.65581 0.91142 Gaussian 0.05 success 3 {'Cl_Central'} 1.0233 0.96375 1.0828 Gaussian 0.05 success
Plot the confidence intervals. If the estimation status of a confidence interval is success
, it is plotted in blue (the first default color). Otherwise, it is plotted in red (the second default color), which indicates that further investigation into the fitted parameters may be required. If the confidence interval is not estimable
, then the function plots a red line with a centered cross. If there are any transformed parameters with estimated values 0 (for the log transform) and 1 or 0 (for the probit or logit transform), then no confidence intervals are plotted for those parameter estimates. To see the color order, type get(groot,'defaultAxesColorOrder')
.
Groups are displayed from left to right in the same order that they appear in the GroupNames
property of the object, which is used to label the x-axis. The y-labels are the transformed parameter names.
plot(ciParamUnpooled)
Compute the confidence intervals for the pooled fit.
ciParamPooled = sbioparameterci(pooledFit);
Display the confidence intervals.
ci2table(ciParamPooled)
ans = 4x7 table Group Name Estimate ConfidenceInterval Type Alpha Status ______ ______________ ________ __________________ ________ _____ ___________ pooled {'Central' } 1.6626 1.3287 1.9965 Gaussian 0.05 estimable pooled {'Peripheral'} 2.687 0.89848 4.8323 Gaussian 0.05 constrained pooled {'Q12' } 0.44956 0.11445 0.85152 Gaussian 0.05 constrained pooled {'Cl_Central'} 0.78493 0.59222 0.97764 Gaussian 0.05 estimable
Plot the confidence intervals. The group name is labeled as "pooled" to indicate such fit.
plot(ciParamPooled)
Plot all the confidence interval results together. By default, the confidence interval for each parameter estimate is plotted on a separate axes. Vertical lines group confidence intervals of parameter estimates that were computed in a common fit.
ciAll = [ciParamUnpooled;ciParamPooled]; plot(ciAll)
You can also plot all confidence intervals in one axes grouped by parameter estimates using the 'Grouped' layout.
plot(ciAll,'Layout','Grouped')
In this layout, you can point to the center marker of each confidence interval to see the group name. Each estimated parameter is separated by a vertical black line. Vertical dotted lines group confidence intervals of parameter estimates that were computed in a common fit. Parameter bounds defined in the original fit are marked by square brackets. Note the different scales on the y-axis due to parameter transformations. For instance, the y-axis of Q12
is in the linear scale, but that of Central
is in the log scale due to its log transform.
Compute Confidence Intervals for Model Predictions
Calculate 95% confidence intervals for the model predictions, that is, simulation results using the estimated parameters.
% For the pooled fit ciPredPooled = sbiopredictionci(pooledFit); % For the unpooled fit ciPredUnpooled = sbiopredictionci(unpooledFit);
Plot Confidence Intervals for Model Predictions
The confidence interval for each group is plotted in a separate column, and each response is plotted in a separate row. Confidence intervals limited by the bounds are plotted in red. Confidence intervals not limited by the bounds are plotted in blue.
plot(ciPredPooled)
plot(ciPredUnpooled)
More About
Parameter Confidence Interval Estimation Status
The following are the definitions of confidence interval estimation statuses for different types of confidence intervals.
not estimable
– The confidence interval is unbounded.constrained
– The confidence interval is constrained by a parameter bound defined in the original fit. Parameter transformations (such aslog
,probit
, orlogit
) impose implicit bounds on the estimated parameters, for example, positivity constraints. Such bounds can lead to the overestimation of the confidence, that is, the confidence interval can be smaller than expected.success
– All confidence intervals for all parameters are computed successfully.estimable
– The confidence interval is computed successfully, but other parameters have an estimation status ofnot estimable
orconstrained
.
For more details about the algorithm, see Gaussian Confidence Interval Calculation.
not estimable
– The computation of the confidence interval is unsuccessful. This can happen when the profile likelihood curve is not strictly monotonically decreasing, or due to computation failures in the profile likelihood.constrained
– The profile likelihood curve is bounded by the bounds on the estimated parameters defined in the original fit. Parameter transformations, such aslog
,logit
,probit
, impose implicit bounds on the estimated parameters, for example, positivity constraints.success
– If there is no parameter estimate with the confidence interval estimation statusconstrained
ornot estimable
, then the function sets all estimation statuses tosuccess
.estimable
– The confidence interval is computed successfully, but other parameters have an estimation status ofnot estimable
orconstrained
.
For more details about the algorithm, see Profile Likelihood Confidence Interval Calculation.
constrained
– The confidence interval is closer thanTolerance
to the parameter bounds defined in the original fit.success
– All confidence intervals were further away from the parameter bounds thanTolerance
.estimable
– The confidence interval is computed successfully, but other parameters have an estimation status ofconstrained
.
For more details about the algorithm, see Bootstrap Confidence Interval Calculation.
Version History
Introduced in R2017b
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