predict

Simulate and evaluate fitted SimBiology model

Syntax

[ynew,parameterEstimates] = predict(resultsObj)

[ynew,parameterEstimates] = predict(resultsObj,data,dosing)

[ynew,parameterEstimates] = predict(___,Name,Value)

Description

[ynew,parameterEstimates] = predict(resultsObj) returns simulation results ynew from evaluating the fitted SimBiology^® model. The estimated parameter values parameterEstimates used to compute ynew are from the original fit by sbiofitmixed.

[ynew,parameterEstimates] = predict(resultsObj,data,dosing) returns simulation results ynew from evaluating the fitted SimBiology model by using the specified data and dosing information.

[ynew,parameterEstimates] = predict(___,Name,Value) uses additional options specified by one or more name-value arguments.

Tip

Use this method to get model responses at specific time points or to predict model responses using different covariate data and dosing information.

Examples

Perform Nonlinear Mixed-Effects Estimation

Estimate nonlinear mixed-effects parameters using clinical pharmacokinetic data collected from 59 infants. Evaluate the fitted model given new data or dosing information.

Load Data

This example uses data collected on 59 preterm infants given phenobarbital during the first 16 days after birth [1]. ds is a table containing the concentration-time profile data and covariate information for each infant (or group).

load pheno.mat ds

Convert to groupedData

Convert the data to the groupedData format for parameter estimation.

data = groupedData(ds);

Display the first few rows of data.

data(1:5,:)

ans =

  5x6 groupedData

    ID    TIME    DOSE    WEIGHT    APGAR    CONC
    __    ____    ____    ______    _____    ____

    1        0     25      1.4        7       NaN
    1        2    NaN      1.4        7      17.3
    1     12.5    3.5      1.4        7       NaN
    1     24.5    3.5      1.4        7       NaN
    1       37    3.5      1.4        7       NaN

Visualize Data

Display the data in a trellis plot.

t = sbiotrellis(data, 'ID', 'TIME', 'CONC', 'marker', 'o',...
       'markerfacecolor', [.7 .7 .7], 'markeredgecolor', 'r', ...
       'linestyle', 'none');
t.plottitle = 'Concentration versus Time';

Create a One-Compartment PK Model

Create a simple one-compartment PK model, with bolus dose administration and linear clearance elimination, to fit the data.

pkmd = PKModelDesign;
addCompartment(pkmd,'Central','DosingType','Bolus',...
                    'EliminationType','linear-clearance',...
                    'HasResponseVariable',true,'HasLag',false);
onecomp = pkmd.construct;

Map model species to response data.

responseMap = 'Drug_Central = CONC';

Define Estimated Parameters

The parameters to estimate in this model are the volume of the central compartment (Central) and the clearance rate (Cl_Central). sbiofitmixed calculates fixed and random effects for each parameter. The underlying algorithm computes normally distributed random effects, which might violate constraints for biological parameters that are always positive, such as volume and clearance. Therefore, specify a transform for the estimated parameters so that the transformed parameters follow a normal distribution. The resulting model is

$$log(V_i)=log({\varphi }_{V,i})={\theta }_V+{\eta }_{V,i}$$

and

$$log(C{l}_i)=log({\varphi }_{Cl,i})={\theta }_{Cl}+{\eta }_{Cl,i},$$

where $$\theta$$, $$eta$$, and $$\varphi$$ are the fixed effects, random effects, and estimated parameter values respectively, calculated for each infant (group) $$i$$. Some arbitrary initial estimates for V (volume of central compartment) and Cl (clearance rate) are used here in the absence of better empirical data.

estimatedParams = estimatedInfo({'log(Central)','log(Cl_Central)'},'InitialValue',[1 1]);

Define Dosing

All infants were given the drug, represented by the Drug_Central species, where the dosing schedule varies among infants. The amount of drug is listed in the data variable DOSE. You can automatically generate dose objects from the data and use them during fitting. In this example, Drug_Central is the target species that receives the dose.

sampleDose = sbiodose('sample','TargetName','Drug_Central');
doses = createDoses(data,'DOSE','',sampleDose);

Fit the Model

Use sbiofitmixed to fit the one-compartment model to the data.

nlmeResults = sbiofitmixed(onecomp,data,responseMap,estimatedParams,doses,'nlmefit');

Visualize Results

Visualize the fitted results using individual-specific parameter estimates.

plot(nlmeResults,'ParameterType','individual');

Use New Dosing Data to Simulate the Fitted Model

Suppose you want to predict how infants 1 and 2 would have responded under different dosing amounts. You can predict their responses as follows.

Create new dose objects with new dose amounts.

dose1 = doses(1);
dose1.Amount = dose1.Amount*2;
dose2 = doses(2);
dose2.Amount = dose2.Amount*1.5;

Use the predict function to evaluate the fitted model using the new dosing data. If you want response predictions at particular times, provide the new output time vector. Use the 'ParameterType' option to specify individual or population parameters to use. By default, predict uses the population parameters when you specify output times.

timeVec = [0:25:400];
newResults = predict(nlmeResults,timeVec,[dose1;dose2],'ParameterType','population');

Visualize the predicted responses while overlapping the experimental data for infants 1 and 2.

figure;
subplot(2,1,1)
plot(data.TIME(data.ID == 1),data.CONC(data.ID == 1),'bo')
hold on
plot(newResults(1).Time,newResults(1).Data,'b')
hold off
ylabel('Concentration')
legend('Observation(CONC)','Prediction')
subplot(2,1,2)
plot(data.TIME(data.ID == 2),data.CONC(data.ID == 2),'rx')
hold on
plot(newResults(2).Time,newResults(2).Data,'r')
hold off
legend('Observation(CONC)','Prediction')
ylabel('Concentration')
xlabel('Time')

Create a Covariate Model for the Covariate Dependencies

Suppose there is a correlation between volume and weight, and possibly volume and APGAR score. Consider the effect of weight by modeling two of these covariate dependencies: the volume of central (Central) and the clearance rate (Cl_Central) vary with weight. The model becomes

$$log(V_i)=log({\varphi }_{V,i})={\theta }_V+{\theta }_{V/weight}*weigh{t}_i+{\eta }_{V,i}$$

and

$$log(C{l}_i)=log({\varphi }_{Cl,i})={\theta }_{Cl}+{\theta }_{Cl/weight}*weigh{t}_i+{\eta }_{Cl,i}$$

Use the CovariateModel object to define the covariate dependencies. For details, see Specify a Covariate Model.

covModel = CovariateModel;
covModel.Expression = ({'Central = exp(theta1 + theta2*WEIGHT + eta1)',...
                        'Cl_Central = exp(theta3 + theta4*WEIGHT + eta2)'});

Use constructDefaultInitialEstimate to create an initialEstimates struct.

initialEstimates = covModel.constructDefaultFixedEffectValues;

Use the FixedEffectNames property to display the thetas (fixed effects) defined in the model.

covModel.FixedEffectNames

ans = 4x1 cell
    {'theta1'}
    {'theta3'}
    {'theta2'}
    {'theta4'}

Use the FixedEffectDescription property to show the descriptions of corresponding fixed effects (thetas) used in the covariate expression. For example, theta2 is the fixed effect for the weight covariate that correlates with the volume (Central), denoted as 'Central/WEIGHT'.

disp('Fixed Effects Description:');

Fixed Effects Description:

disp(covModel.FixedEffectDescription);

    {'Central'          }
    {'Cl_Central'       }
    {'Central/WEIGHT'   }
    {'Cl_Central/WEIGHT'}

Set the initial guesses for the fixed-effect parameter values for Central and Cl_Central using the values estimated from fitting the base model.

initialEstimates.theta1 = nlmeResults.FixedEffects.Estimate(1);
initialEstimates.theta3 = nlmeResults.FixedEffects.Estimate(2);
covModel.FixedEffectValues = initialEstimates;

Fit the Model

nlmeResults_cov = sbiofitmixed(onecomp,data,responseMap,covModel,doses,'nlmefit');

Display Fitted Parameters and Covariances

disp('Estimated Fixed Effects:');

Estimated Fixed Effects:

disp(nlmeResults_cov.FixedEffects);

       Name            Description         Estimate    StandardError
    __________    _____________________    ________    _____________

    {'theta1'}    {'Central'          }    -0.45664      0.078933   
    {'theta3'}    {'Cl_Central'       }     -5.9519        0.1177   
    {'theta2'}    {'Central/WEIGHT'   }     0.52948      0.047342   
    {'theta4'}    {'Cl_Central/WEIGHT'}     0.61954      0.071386   

disp('Estimated Covariance Matrix:');

Estimated Covariance Matrix:

disp(nlmeResults_cov.RandomEffectCovarianceMatrix);

              eta1        eta2  
            ________    ________

    eta1    0.046503           0
    eta2           0    0.041609

Visualize Results

Visualize the fitted results using individual-specific parameter estimates.

plot(nlmeResults_cov,'ParameterType','individual');

Use New Covariate Data to Evaluate the Fitted Model

Suppose you want to explore the responses of infants 1 and 2 using different covariate data, namely WEIGHT. You can do this by specifying the new WEIGHT data. The ID variable of the data corresponds to individual infants.

newData = data(data.ID == 1 | data.ID == 2,:);
newData.WEIGHT(newData.ID == 1) = 1.3;
newData.WEIGHT(newData.ID == 2) = 1.4;

Simulate the responses of infants 1 and 2 using the new covariate data.

[newResults_cov, newEstimates] = predict(nlmeResults_cov,newData,[dose1;dose2]);

newEstimates contains the updated parameter estimates for each individual (infants 1 and 2) after the model is reevaluated using the new covariate data.

newEstimates

newEstimates=4×3 table
    Group         Name         Estimate 
    _____    ______________    _________

      1      {'Central'   }       2.5596
      1      {'Cl_Central'}    0.0065965
      2      {'Central'   }       1.7123
      2      {'Cl_Central'}    0.0064806

Compare to the estimated values from the original fit using the old covariate data.

nlmeResults_cov.IndividualParameterEstimates( ...
            nlmeResults_cov.IndividualParameterEstimates.Group == '1' | ...
            nlmeResults_cov.IndividualParameterEstimates.Group == '2',:)

ans=4×3 table
    Group         Name         Estimate 
    _____    ______________    _________

      1      {'Central'   }       2.6988
      1      {'Cl_Central'}    0.0070181
      2      {'Central'   }       1.8054
      2      {'Cl_Central'}    0.0068948

Visualize the new simulation results together with the experimental data for infant 1 and 2.

figure;
subplot(2,1,1);
plot(data.TIME(data.ID == 1),data.CONC(data.ID == 1),'bo')
hold on
plot(newResults_cov(1).Time,newResults_cov(1).Data,'b')
hold off
ylabel('Concentration')
legend('Observation(CONC)','Prediction','Location','NorthEastOutside')
subplot(2,1,2)
plot(data.TIME(data.ID == 2),data.CONC(data.ID == 2),'rx')
hold on
plot(newResults_cov(2).Time,newResults_cov(2).Data,'r')
hold off
legend('Observation(CONC)','Prediction','Location','NorthEastOutside')
ylabel('Concentration')
xlabel('Time')

References

[1] Grasela, T. H. Jr., and S. M. Donn. "Neonatal population pharmacokinetics of phenobarbital derived from routine clinical data." Dev Pharmacol Ther 1985:8(6). 374-83.

Input Arguments

resultsObj — Estimation results

scalar NLMEResults object

Estimation results, specified as a scalar NLMEResults object, which contains nonlinear mixed-effects estimation results returned by sbiofitmixed.

data — Grouped data or output times

groupedData object | vector | cell array of vectors

Grouped data or output times, specified as a groupedData object, vector, or cell array of vectors of output times.

If data is a groupedData object, it must have both group labels and output times specified. The group labels can refer to new groups or existing groups from the original fit. If the mixed-effects model from the original fit (returned by sbiofitmixed) uses covariates, the groupedData object must also contain the covariate data with the same labels for the covariates (CovariateLabels property) specified in the original CovariateModel object.

By default, individual parameter estimates are used for simulating groups from the original fit, while population parameters are used for new groups, if any. See the value argument description for details.

The total number of simulation results in the output ynew depends on the number of groups or output time vectors in data and the number of rows in the dosing matrix. For details, see the table in the ynew argument description.

dosing — Dosing information

[] | {} | 2-D matrix of dose objects | cell vector of dose objects

Dosing information, specified as empty [] or {}, 2-D matrix or cell vector of SimBiology dose objects (ScheduleDose object or RepeatDose object).

If dosing is empty, no doses are applied during simulation, even if the model has active doses.

For a matrix of dose objects, it must have a single row or one row per group in the input data. If it has a single row, the same doses are applied to all groups during simulation. If it has multiple rows, each row is applied to a separate group, in the same order as the groups appear in the input data. Multiple columns are allowed so that you can apply multiple dose objects to each group.

For a cell vector of doses, it must have one element or one element per group in the input data. Each element must be [] or a vector of doses. Each element of the cell is applied to a separate group, in the same order as the groups appear in the input data.

In addition to manually constructing dose objects using sbiodose, if the input groupedData object has dosing information, you can use the createDoses method to construct doses.

Dose objects of the dosing input must be consistent with the original dosing data used with sbiofitmixed. The objects must have the same values for dose properties (such as TargetName) or must be parameterized in the same way as the original dosing data. For instance, suppose that the original dosing matrix has two columns of doses, where the doses in the first column target species x and those in the second column target species y. Then dosing must have doses in the first column targeting species x and those in the second column targeting species y. A parameterized dose example is as follows. Suppose that the Amount property of a dose used in the original sbiofitmixed call is parameterized to a model-scoped parameter 'A'. All doses for the corresponding group (column) in the dosing matrix input must have the Amount property parameterized to 'A'.

The number of rows in the dosing matrix or number of elements in the dosing cell vector and the number of groups or output time vectors in data determine the total number of simulation results in the output ynew. For details, see the table in the ynew argument description.

Note

If UnitConversion is turned on for the underlying SimBiology model that was used for fitting, dosing must specify valid amount and time units.

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.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: 'ParameterType','population' specifies to use population parameter estimates.

ParameterType — Parameter type

'individual' (default) | 'population'

Parameter type, specified as 'individual' (default) or 'population'. If value is 'population', the predict method returns the simulation results using the population parameter estimates, that is, parameter values that are estimated using fixed effects (θs) only. The estimated parameter values used in simulation are identical to those in the resultsObj.PopulationParameterEstimates property, unless you specify a new groupedData object data with new covariate data. In this case, the method reevaluates the covariate model and the parameter estimates based on the new groupedData and covariate data.

If value is 'individual', the method returns the simulation results using the corresponding parameter values of the group in the resultsObj.IndividualParameterEstimates property. These values include both fixed- and random-effects estimates, that is, parameter values estimated using both fixed effects (θs) and random effects (ηs). If data contains new groups, only fixed effects (population parameter estimates of the results object) are used for these groups.

By default, predict uses the individual parameter estimates of the results object when data is a groupedData object. If data is a vector of output times or cell array of vectors, predict uses the population parameter estimates of the results object instead.

Data Types: char | string

Variants — Variants to apply

[] | {} | 2-D matrix of variants | cell vector of variants

Variants to apply, specified as an empty array ([], {}), 2-D matrix or cell vector of variant objects.

If you do not specify this argument, the function has the following behavior depending on whether the second input argument (data) is specified also or not.

• If data is not specified, the function applies the group-specific variants from the original call to sbiofitmixed.

• If data is a vector or cell array of output times, the function does not apply the group-specific variants.

• If data is a groupedData object, the function applies variants only to groups whose group identifier matches a group identifier in the original training data that was used in the call to sbiofitmixed.

Note

• The baseline variants that were specified by the variants positional input argument in the original call to sbiofitmixed are always applied to the model, and they are applied before any group-specific variants.

• If there are no baseline variants, that is, you did not specify the variants input when calling sbiofitmixed, the function still applies the model active variants if there are any.

If the argument value is [] or {}, the function applies no group-specific variants.

If it is a matrix of variants, it must have either one row or one row per group. Each row is applied to a separate group, in the same order as the groups appear in data or dosing. If it has a single row, the same variants are applied to all groups during simulation. If there are multiple columns, the variants are applied in order from the first column to the last.

If it is a cell vector of variant objects, the number of cells must be one or must match the number of groups in the input data. Each element must be [] or a vector of variants. If there is a single cell containing a vector of variants, they are applied to all simulations. If there are multiple cells, the variants in the ith cell are applied to the simulation of the ith group.

The function defines the number of groups by examining the data, and dosing input arguments.

• data can have 1 or N groups.

• If data and dosing arguments are not specified, then the default data and dosing are determined as follows:

  • For unpooled fits, they are the data and dosing for the single group associated with that fit results.

  • For all other fits, they are the entire set of data and dosing associated with the call to sbiofitmixed.

Output Arguments

ynew — Simulation results

vector of SimData objects

Simulation results, returned as a vector of SimData objects. The states reported in ynew are the states included in the responseMap input argument of sbiofitmixed and any other states listed in the StatesToLog property of the runtime options (RuntimeOptions) of the SimBiology model.

The total number of simulation results in ynew depends on the number of groups or output time vectors in data and the number of rows in the dosing matrix.

Number of groups or output time vectors in data	Number of rows in the dosing matrix	Simulation results
1	0, that is, dosing is empty []	The total number of SimData objects in ynew is 1. No doses are applied during simulation.
1	1	The total number of SimData objects in ynew is 1. The given row of doses is applied during the simulation.
1	N	The total number of SimData objects in ynew is N. Each row of dosing is applied to each simulation.
N	0, that is, dosing is empty []	The total number of SimData objects in ynew is N. No doses are applied during simulation.
N	1	The total number of SimData objects in ynew is N. The same row of doses is applied to each simulation.
N	N	The total number of SimData objects in ynew is N. Each row of dosing is applied to a separate group, in the same order that groups appear in data.
M	N	The function throws an error when M ≠ N.

parameterEstimates — Estimated parameter values

table

Estimated parameter values used for the predicted simulation results, returned as a table.

If 'ParameterType' is 'individual', the reported parameter values are identical to the values in the resultsObj.IndividualParameterEstimates property. However, if data contains new groups, then only population parameter estimates (fixed effects) are used for these groups. The corresponding reported values in parameterEstimates for these groups are identical to the values in resultsObj.PopulationParameterEstimates.

If 'ParameterType' is 'population', the reported parameter values are identical to the values in the resultsObj.PopulationParameterEstimates property unless you specify new covariate information in data. See the value argument description for details.

If data is a vector or a cell array of vectors of output times, the reported parameter values are identical to the values in resultsObj.PopulationParameterEstimates. Also, the groups reported represent the enumeration of simulations performed and are unrelated to group names in the original fit.

Version History

Introduced in R2014a