Structure tab

The Structure tab is used to set up the Phoenix model. When selections are made in this tab, the PML that defines the model changes. The changes to the PML can be viewed in the Model Text tab.

SetuptabdefaultPopPKmodel.png 

Structure model options tab set up for a PK intravenous population model

•PK: See “PK model options” for PK model options.

•Emax: See “Emax model options” for Emax model options.

•PK/Emax: The options for the PK/Emax model are the same as those listed under “PK model options” and “Emax model options”.

•PK/Indirect: See “PK/Indirect model options” for Indirect model options. The options for the PK portion of the model are the same as those listed under “PK model options”

•Linear: See “Linear model options” for Linear model options.

•PK/Linear: The options for the PK/Linear model are the same as those listed under “PK model options” and “Linear model options”.

Caution:Changing the structural model after random effects have been set up can result in reordering of the random effects. Caution is advised in double-checking the random effects entries after a model is changed.

Structure tab options change depending on the type of model selected.

PK model options

•Micro: Model is expressed as differential equations having mass transfer rate constants associated with a compartmental model. Adds the mass transfer rate parameters, such as Ke, the rate of elimination, and writes the derivatives in terms of compartmental masses.

•Clearance: Model is expressed as differential equations having clearances associated with a compartmental model. Adds the inter-compartmental clearance parameters, such as Cl, the clearance rate. If Clearance is selected, the Saturating checkbox becomes available. Check the Saturating checkbox to convert the model to a saturable elimination model. A saturable model uses two parameters:
Km: Concentration to achieve half of maximal metabolic rate.
Vmax: The maximum metabolic rate.

•Macro: Model is expressed as a closed-form sum of exponentials. This option directly models concentration in the central compartment. Volume is not in the model but can be derived as a secondary parameter. This is the same parameterization as the WNL5 Classic model. Pri­mary parameters are the sum of exponential terms that model concentration in the central compartment. The user can enter the dose (A1) as well as a stripping dose (A1Strip). If no stripping dose is mapped on the Main or Dosing panels, the stripping dose is assume to be equal to the dose.

•Macro1: Model is expressed as a closed-form sum of exponentials. This option models the amount in the central compartment (A) and Volume is a primary parameter. Primary parame­ters are the sum of exponential terms plus the parameter Volume. The amount in the central compartment is modeled as a sum of exponentials and then the Volume parameter is used to convert that amount to a concentration. Note that, because both macro options are closed-form models, the Closed form? option is removed.

Note:Adding an elimination compartment to a Clearance model removes the Closed form? option and adds the Fe.? option for toggling the inclusion of the fraction excreted parameter.

•There can only be one observed variable, such as central compartment amount or concentra­tion.

•The differential system being converted must be linear (no nonlinear kinetics).

•Any covariates used in the model must be constant for the duration of the observations. For example, no change in subject's weight as samples are collected.

•Intravenous: The drug is introduced directly into the blood.

•Extravascular: The drug is introduced indirectly into the blood.

Selecting the Extravascular option adds an extra parameter, Ka, which is the rate of absorption and adds an extra checkbox that allows users to set the rate of absorption equal to the rate of elimination.

Number of compartments or terms

Parameterization

Micro

Clearance

Macro

Macro1

1

V, Ke

V, Cl

A, Alpha

V, Alpha

2

K12, K21

V2, Cl2

B, Beta

B, Beta

3

K13, K31

V3, Cl3

C, Gamma

C, Gamma

•If Add+Mult is selected, type a name for the parameter in the Mult Stdev field or accept the default name.

•If Mix Ratio is selected, type a name for the mixed ratio parameter in the mix Ratio field or accept the default name.

•If Power is selected, type a value for the exponent in the Power field.

•If Custom is selected, type a custom error model definition in the Defn field.

For PK models, Multiplicative followed by Power are the preferred error models over Additive. This is because PK model types usually have concentrations spanning several orders of magni­tude and, on a log scale, Additive has large errors at low concentrations.

For PD model types, with effect ranges usually less than an order of magnitude, Additive is the first choice.

Note:Phoenix models with censored data (BQL? option) use the log of the probabilities between 0 and the censored number in the log likelihoods. If the censoring numbers are very small, the loglikeli­hood might overflow, resulting in a Fortran error. This seems to be more often the case when using multiplicative error models. If the error occurs, try increasing the BQL value if possible or change error types.

•In the first unlabeled menu, select one of the 19 PK models, or one of the four Michaelis-Menten models, or one of the 19 PK/PD simultaneous link models. The PK/PD simultaneous link models are labeled 401 to 419 and link PK models 1 through 19 with PD model 105 (e.g., PK/PD model 407 is a linked model of PK model 7 with PD model 105). For more on PK/PD simultaneous link models, see “Differential equations in NLME”.

•If the model specified in the first unlabeled menu is not a macro-parameterization model, the CL/V checkbox is made available. Check this box to add clearance and volume parameters to the model.

Set_WNL_model_Cl_V.png 

WNL model setup with additional parameters option

•If a linked model is specified in the first unlabeled menu, a second unlabeled menu is made available. Select one of eight PD models, or one of four Indirect Response models to link.

Set_WNL_model_2menus.png 

WNL linked model setup

•Each WNL model has a set of secondary parameters that available for loading when that model is selected. Use the radio buttons to indicate what should be done with secondary parameters that are already defined in the interface when the model is loaded. Choose to Replace currently defined parameters with those and load the ones from the model, Keep currently defined parameters and ignore those from the selected model, or Combine them by keeping the existing parameters and adding those from the selected model to the list.

•Click Apply to apply the selected model or models or click Cancel to exit the model selection menus without applying any changes.

Additional details on error models 

The Log-additive option corresponds to a form like C*exp(epsilon). If the Log-additive error model is specified, and if there is only one error model, such as one observe statement, then the predictions and observations are log-transformed and are fit in that space. This is because the error model becomes additive in log-space, which allows for higher performance and accuracy. This affects all the plots results and residuals, because they are in log-space. The simulation tables are transformed back so they are not in log-space.

Because the logs of zero or negative numbers are not allowed, they are truncated to a value which is ¼ (0.25) of the smallest positive observation value. If the model is Log-additive, but the conditions have not been met for log-transforming to take place, the model behaves the same as Multiplicative.

The residual model that is displayed in the model text is:

 

observe(CObs=C*exp(CEps))
or
observe(CObs=exp(log(C)+CEps))

(1)

The engines implement the model by log-transforming both sides and see if the derivative of the right-hand side with respect to CEps is 1. If so, and if there is only one observe statement, then it does log-transformation.

observe(log(CObs)=log(C)+CEps)

(2)

This check is accomplished by examining the text of the model, so it can be applied to models other than built-in models.

The main advantages of Log-additive are that the engines, particularly the Lindstrom-Bates FOCE engine, can run faster when a simple additive error model is used, and the FOCE approximation can be more accurate.

Since the modeling engines in NLME can only handle a single error variable (or epsilon), and some error models are best specified as having an additive component and a multiplicative component, some complexities are needed. The Mix Ratio uses the following formula:

C+eps*(1+C*mixRatio)

(3)

where mixRatio is a fixed effect and is understood to be the multiplicative sigma divided by addi­tive sigma.

Another way to specify a mixed error model having a fixed effect, but with the fixed effect signifying the multiplicative sigma, rather than the ratio of multiplicative to additive sigma is Add+Multi. It makes use of a built-in function called “sigma()” that can only be used in this context, and its value is the cur­rent estimate of the standard deviation of eps. The formula is:

C+eps*sqrt(1+(C*multStdev/sigma())^2)

(4)

where multStdev is the multiplicative sigma.

So when this error model is used, the additive sigma is called stdev, and the multiplicative sigma is called multStdev. Since multStdev is a fixed effect, its name can be changed as desire.

To justify the above formula, look at the variance. Suppose the additive standard deviation is called sigma1, the multiplicative standard deviation is called sigma2, and suppose the corresponding epsi­lons eps1 and eps2 are drawn from a unit normal distribution. Then the formula would be:

C+eps1*sigma1+C*eps2*sigma2

(5)

The variance of this is the sum of the variances from each term, or:

sigma1^2+(C*sigma2)^2

(6)

Now let r be the ratio: r=sigma2/sigma1, then the variance is:

sigma1^2+(C*r*sigma1)^2
or
sigma1^2 *(1+(C*r)^2)

(7)

which is the variance of:

C+eps*sqrt(1+(C*r)^2)

(8)

Then replace r with sigma2/sigma1 to obtain:

C+eps*sqrt(1+(C*sigma2/sigma1)^2)

(9)

where sigma1 is represented by the sigma() function, and sigma2 is represented by multStdev.

So, by choosing the option Add+Mult, this formula will be used to estimate both stdev (the additive standard deviation) and multStdev (the multiplicative standard deviation).

Emax model options

•E in the residual error model represents the effect observation.

•Changes made in the Residual Error field are shown in the observe statement.

Note:Phoenix models with censored data (BQL? option) use the log of the probabilities between 0 and the censored number in the log likelihoods. If the censoring numbers are very small, the loglikeli­hood might overflow, resulting in a Fortran error. This seems to be more often the case when using multiplicative error models. If the error occurs, try increasing the BQL value if possible or change error types.

To include a hysteresis plot, on the Run Options tab, add a Table with Times and Variables C, E, CObs, EObs, Ce for built-in models (or use the specified Variable names from graphical or textual models), and then create the desired plot from the Table output.”

PK/Indirect model options

The following options are for the Indirect portion of the PK/Indirect model. Options for the PK portion of the model are the same as those listed under “PK model options”.

•Stim. Limited (limited stimulation of input)

•Stim. Infinite (infinite stimulation of input)

•Inhib. Limited (limited inhibition of input)

•Inhib. Inverse (inverse inhibition of input)

•Stim. Linear (linear stimulation of input)

•Stim. Log Linear (logarithmic and linear stimulation of input)

Use the Indirect menu options to select a model in which the response formation (build-up) or degradation (loss) is stimulated or inhibited by increased concentrations. The default response setting is the build-up of the response, or the production of the response.

Linear model options

•E = Alpha, a constant model, where y(x)=constant.

•E = Alpha + Beta * C, a linear model, where y(x)=intercept+slope*x.

•E = Alpha + Beta * C + Gamma * C^2, a quadratic model, where y(x)=A0+A1*x+A2*x^2.

In the above equations, y is the dependent variable and x is the independent variable.

Last modified date:9/10/19
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