Main Content

constructDefaultFixedEffectValues

Create structure containing initial estimates fixed effects needed for fit

collapse all in page

Syntax

FEInitEstimates = constructDefaultFixedEffectValues(CovModel)

Description

FEInitEstimates = constructDefaultFixedEffectValues(CovModel) returns FEInitEstimates, a structure containing the initial estimates for the fixed effects in CovModel, a CovariateModel object. By default, the values of initial estimates are set to zero.

example

Examples

collapse all

Open Live Script

Create an empty CovariateModel object.

covModel = CovariateModel;

Set its Expression property to define the relationships between parameters (Cl, V, and k) and covariate (w). You must use theta as a prefix for all fixed effects and eta for random effects.

covModel.Expression = ["Cl = theta1 + theta2*w + eta1","V = theta3 + eta2","k = theta4 + eta3"];

Display the names of fixed effects.

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

The FixedEffectDescription property displays which fixed effects correspond to which parameter. For instance, theta1 is the fixed effect for the Cl parameter, and theta2 is the fixed effect for the weight covariate that has a correlation with Cl parameter, denoted as Cl/w.

covModel.FixedEffectDescription
ans = 4x1 cell
    {'Cl'  }
    {'V'   }
    {'k'   }
    {'Cl/w'}

Specify initial estimates for the fixed effects. Create a default structure containing initial estimates using the constructDefaultFixedEffectValues function.

initialEstimates = constructDefaultFixedEffectValues(covModel)
initialEstimates = struct with fields:
    theta1: 0
    theta3: 0
    theta4: 0
    theta2: 0

Update the initial estimate value of each fixed effects.

initialEstimates.theta1 = 1.20;
initialEstimates.theta2 = 0.30;
initialEstimates.theta3 = 0.90;
initialEstimates.theta4 = 0.10;

Update the FixedEffectValues property to use the updated initial estimates.

covModel.FixedEffectValues = initialEstimates;

Check the covariate model for errors.

verify(covModel)
Open Live Script

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';

Figure contains 64 axes objects. Axes object 1 with title ID 1 contains a line object which displays its values using only markers. Axes object 2 with title ID 2 contains a line object which displays its values using only markers. Axes object 3 with title ID 3 contains a line object which displays its values using only markers. Axes object 4 with title ID 4 contains a line object which displays its values using only markers. Axes object 5 with title ID 5 contains a line object which displays its values using only markers. Axes object 6 with title ID 6 contains a line object which displays its values using only markers. Axes object 7 with title ID 7 contains a line object which displays its values using only markers. Axes object 8 with title ID 8 contains a line object which displays its values using only markers. Axes object 9 with title ID 9 contains a line object which displays its values using only markers. Axes object 10 with title ID 10 contains a line object which displays its values using only markers. Axes object 11 with title ID 11 contains a line object which displays its values using only markers. Axes object 12 with title ID 12 contains a line object which displays its values using only markers. Axes object 13 with title ID 13 contains a line object which displays its values using only markers. Axes object 14 with title ID 14 contains a line object which displays its values using only markers. Axes object 15 with title ID 15 contains a line object which displays its values using only markers. Axes object 16 with title ID 16 contains a line object which displays its values using only markers. Axes object 17 with title ID 17 contains a line object which displays its values using only markers. Axes object 18 with title ID 18 contains a line object which displays its values using only markers. Axes object 19 with title ID 19 contains a line object which displays its values using only markers. Axes object 20 with title ID 20 contains a line object which displays its values using only markers. Axes object 21 with title ID 21 contains a line object which displays its values using only markers. Axes object 22 with title ID 22 contains a line object which displays its values using only markers. Axes object 23 with title ID 23 contains a line object which displays its values using only markers. Axes object 24 with title ID 24 contains a line object which displays its values using only markers. Axes object 25 with title ID 25 contains a line object which displays its values using only markers. Axes object 26 with title ID 26 contains a line object which displays its values using only markers. Axes object 27 with title ID 27 contains a line object which displays its values using only markers. Axes object 28 with title ID 28 contains a line object which displays its values using only markers. Axes object 29 with title ID 29 contains a line object which displays its values using only markers. Axes object 30 with title ID 30 contains a line object which displays its values using only markers. Axes object 31 with title ID 31 contains a line object which displays its values using only markers. Axes object 32 with title ID 32 contains a line object which displays its values using only markers. Axes object 33 with title ID 33 contains a line object which displays its values using only markers. Axes object 34 with title ID 34 contains a line object which displays its values using only markers. Axes object 35 with title ID 35 contains a line object which displays its values using only markers. Axes object 36 with title ID 36 contains a line object which displays its values using only markers. Axes object 37 with title ID 37 contains a line object which displays its values using only markers. Axes object 38 with title ID 38 contains a line object which displays its values using only markers. Axes object 39 with title ID 39 contains a line object which displays its values using only markers. Axes object 40 with title ID 40 contains a line object which displays its values using only markers. Axes object 41 with title ID 41 contains a line object which displays its values using only markers. Axes object 42 with title ID 42 contains a line object which displays its values using only markers. Axes object 43 with title ID 43 contains a line object which displays its values using only markers. Axes object 44 with title ID 44 contains a line object which displays its values using only markers. Axes object 45 with title ID 45 contains a line object which displays its values using only markers. Axes object 46 with title ID 46 contains a line object which displays its values using only markers. Axes object 47 with title ID 47 contains a line object which displays its values using only markers. Axes object 48 with title ID 48 contains a line object which displays its values using only markers. Axes object 49 with title ID 49 contains a line object which displays its values using only markers. Axes object 50 with title ID 50 contains a line object which displays its values using only markers. Axes object 51 with title ID 51 contains a line object which displays its values using only markers. Axes object 52 with title ID 52 contains a line object which displays its values using only markers. Axes object 53 with title ID 53 contains a line object which displays its values using only markers. Axes object 54 with title ID 54 contains a line object which displays its values using only markers. Axes object 55 with title ID 55 contains a line object which displays its values using only markers. Axes object 56 with title ID 56 contains a line object which displays its values using only markers. Axes object 57 with title ID 57 contains a line object which displays its values using only markers. Axes object 58 with title ID 58 contains a line object which displays its values using only markers. Axes object 59 with title ID 59 contains a line object which displays its values using only markers. This object represents CONC. Axes object 60 is empty. Axes object 61 is empty. Axes object 62 is empty. Axes object 63 is empty. Axes object 64 is empty.

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(Vi)=log(ϕV,i)=θV+ηV,i

and

log(Cli)=log(ϕCl,i)=θCl+ηCl,i,

where θ, eta, and ϕ 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');

Figure contains 65 axes objects. Axes object 1 is empty. Axes object 2 is empty. Axes object 3 is empty. Axes object 4 is empty. Axes object 5 is empty. Axes object 6 with title 59 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 7 with title 58 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 8 with title 57 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 9 with title 56 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 10 with title 55 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 11 with title 54 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 12 with title 53 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 13 with title 52 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 14 with title 51 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 15 with title 50 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 16 with title 49 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 17 with title 48 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 18 with title 47 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 19 with title 46 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 20 with title 45 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 21 with title 44 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 22 with title 43 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 23 with title 42 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 24 with title 41 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 25 with title 40 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 26 with title 39 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 27 with title 38 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 28 with title 37 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 29 with title 36 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 30 with title 35 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 31 with title 34 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 32 with title 33 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 33 with title 32 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 34 with title 31 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 35 with title 30 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 36 with title 29 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 37 with title 28 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 38 with title 27 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 39 with title 26 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 40 with title 25 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 41 with title 24 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 42 with title 23 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 43 with title 22 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 44 with title 21 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 45 with title 20 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 46 with title 19 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 47 with title 18 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 48 with title 17 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 49 with title 16 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 50 with title 15 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 51 with title 14 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 52 with title 13 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 53 with title 12 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 54 with title 11 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 55 with title 10 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 56 with title 9 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 57 with title 8 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 58 with title 7 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 59 with title 6 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 60 with title 5 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 61 with title 4 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 62 with title 3 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 63 with title 2 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 64 with title 1 contains 2 objects of type line. One or more of the lines displays its values using only markers Hidden axes object 65 contains 2 objects of type line. One or more of the lines displays its values using only markers These objects represent Predicted - individual (Predicted - individual.Central.Drug_Central), Observed (Observed.CONC).

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')

Figure contains 2 axes objects. Axes object 1 with ylabel Concentration contains 2 objects of type line. One or more of the lines displays its values using only markers These objects represent Observation(CONC), Prediction. Axes object 2 with xlabel Time, ylabel Concentration contains 2 objects of type line. One or more of the lines displays its values using only markers These objects represent Observation(CONC), Prediction.

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(Vi)=log(ϕV,i)=θV+θV/weight*weighti+ηV,i

and

log(Cli)=log(ϕCl,i)=θCl+θCl/weight*weighti+ηCl,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');

Figure contains 65 axes objects. Axes object 1 is empty. Axes object 2 is empty. Axes object 3 is empty. Axes object 4 is empty. Axes object 5 is empty. Axes object 6 with title 59 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 7 with title 58 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 8 with title 57 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 9 with title 56 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 10 with title 55 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 11 with title 54 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 12 with title 53 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 13 with title 52 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 14 with title 51 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 15 with title 50 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 16 with title 49 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 17 with title 48 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 18 with title 47 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 19 with title 46 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 20 with title 45 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 21 with title 44 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 22 with title 43 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 23 with title 42 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 24 with title 41 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 25 with title 40 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 26 with title 39 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 27 with title 38 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 28 with title 37 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 29 with title 36 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 30 with title 35 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 31 with title 34 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 32 with title 33 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 33 with title 32 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 34 with title 31 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 35 with title 30 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 36 with title 29 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 37 with title 28 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 38 with title 27 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 39 with title 26 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 40 with title 25 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 41 with title 24 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 42 with title 23 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 43 with title 22 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 44 with title 21 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 45 with title 20 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 46 with title 19 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 47 with title 18 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 48 with title 17 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 49 with title 16 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 50 with title 15 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 51 with title 14 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 52 with title 13 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 53 with title 12 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 54 with title 11 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 55 with title 10 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 56 with title 9 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 57 with title 8 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 58 with title 7 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 59 with title 6 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 60 with title 5 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 61 with title 4 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 62 with title 3 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 63 with title 2 contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 64 with title 1 contains 2 objects of type line. One or more of the lines displays its values using only markers Hidden axes object 65 contains 2 objects of type line. One or more of the lines displays its values using only markers These objects represent Predicted - individual (Predicted - individual.Central.Drug_Central), Observed (Observed.CONC).

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')

Figure contains 2 axes objects. Axes object 1 with ylabel Concentration contains 2 objects of type line. One or more of the lines displays its values using only markers These objects represent Observation(CONC), Prediction. Axes object 2 with xlabel Time, ylabel Concentration contains 2 objects of type line. One or more of the lines displays its values using only markers These objects represent Observation(CONC), Prediction.

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

collapse all

Covariate model, specified as a CovariateModel object.

Output Arguments

collapse all

Initial estimates for fixed effects, returned as a structure. Each field of the structure represents a fixed effect and its value. By default, the values of initial estimates are set to zero, but you can edit these estimates as needed. If you do, make sure that the number and names of the fields in the FEInitEstimates structure matches the number and names of fixed effects (theta values) in the Expression property of CovModel.

Version History

Introduced in R2011b

See Also

Topics