Faculty of Medical and Health Sciences
Department of Pharmacology & Clinical Pharmacology, University of Auckland
Faculty of Medical and Health Sciences
Department of Pharmacology & Clinical Pharmacology, University of Auckland

Time course of drug effect

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Objective and introduction

Objectives

The objectives are to:

  1. Define common models for the time course of drug effect.
  2. Learn how to perform a simultaneous fit of concentration and effect data.
  3. Use simulation to understand the properties of the turnover model for delayed drug effect.

Introduction


The time course of drug effect can be described by linking separate models for concentration and effect.

  1. Immediate: Drug effects are determined by the concentration in a compartment of the pharmacokinetic model.
  2. Delayed:
    1. Effect Compartment: Drug effects are determined by the concentration in a hypothetical effect compartment whose input is from a compartment of the pharmacokinetic model.
    2. Physiological mediator: Drug effects are determined by the concentration of a physiological mediator. The concentration of the mediator is influenced by the drug concentration in one of 4 basic ways:
      1. Decreased synthesis of mediator
      2. Increased synthesis of mediator
      3. Decreased elimination of mediator
      4. Increased elimination of mediator

 

"It had long been believed that there is no relationship between the drug concentration in plasma and time course of action for many drugs..." (1)

We prescribe and administer drugs to produce effects. Clinical preoccupation with merely what dose to give misses the point, and assumes an easy equivalence between dose and effect. What effect are we hoping to achieve, what concentration is this effect associated with, and what dose will give this concentration? This kind of thinking involves cognisance of the many variables known and unknown which can influence each of these steps.

Dosing results in drug concentration. So achieving an appropriate drug concentration is the first goal of drug administration. However plasma concentration monitoring is only readily available for a small number of drugs with low therapeutic index including digoxin, theophylline, and a handful of antibiotics, immunosuppressants, and anticonvulsants. In clinical practice adjusting drug dosing to concentration can be fraught with difficulty due to misconceptions about pharmacokinetics and lack of appreciation of factors causing individual variation.

Drug doses are more commonly adjusted according to clinical effect rather than concentration. This titration is more rapidly accomplished in settings of more intensive clinical monitoring, such as intensive care and anaesthesia. Titration to effect is most satisfying to the clinician for drugs with faster apparent onset and offset of effect, potentially resulting in instant gratification for the drug administrator, and hopefully more effective targeting of drug response for the patient.

Pharmacokinetics gives us drug concentration versus time, while pharmacodynamics gives us drug effect versus concentration. Concentration is the link between drug dosing and effect. Linking pharmacokinetics and pharmacodynamics gives us drug effect versus time. This is called the time course of effect.

Both the timing of onset and offset of drug effect may be important. When will the effect start to be observed, when will the effect peak, when will the effect be at steady state (where applicable), and when will the effect decrease and then cease to be observable? The Emax model is the most fundamental description of the relationship between drug concentration and effect. This model is named after the parameter Emax, which describes the maximum effect of a drug. Since this implies effect at infinite drug concentration, Emax can never be measured, but can only ever be estimated from the shape of the response curve, approaching its asymptote.

Drugs work by having action on physiological systems. The drug action produces a response in the physiological systems and associated control mechanisms. These changes lead to an observed drug effect. The unbound portion of the drug is responsible for its action, however plasma concentration measures total concentration (both bound and unbound).

Which effects are important? For ease of data collection faster onset effects that are easy to measure are most often reported scientifically and used for clinical titration of dose. However more meaningful effects are often delayed and sometimes cumulative. For example antihypertensives are used for cardiovascular disease risk reduction where the goal effect is not just reduction in blood pressure but reduction in myocardial ischaemia and stroke rates. The goal effects of many drugs relate not to easily measurable short term physiological change, but longterm reduction in morbidity and mortality. There are many examples in intensive care medicine where a focus on short term physiological change observed as drug effect does not equate to long term beneficial outcome. For example early studies on inotropic drugs in heart failure ( eg dobutamine) reported improved haemodynamic parameters, which may be clinically insignificant, while subsequent outcome studies demonstrated an increase or no effect on mortality.

The timing of drug effects may be classified as immediate, delayed, or cumulative. Very few drugs have immediate effects, heparin being a rare example. Most drugs have a delayed effect. This delay may be due to many different pharmacokinetic and pharmacodynamic factors eg absorption after administration more peripherally; distribution and transport to effect side eg (target organ, cell membrane, organelle), receptor binding interactions, protein binding interactions, effects on enzymes and other physiological mediators.

Three main causes of delay in time course of effect will be explored: absorption, effect compartments, and indirect or physiological substance mediated effects.

Absorption: Any drug that is not administered directly into a central compartment usually has to be absorbed. Typically this is described for the following routes of administration: oral, rectal, subcutaneous, intramuscular, but may also include the systemic and local effects of topical application such as transcutaneous, transmucosal, conjunctival. Inhalational drugs are typically described in terms of uptake rather than absorption, but the basic concept is similar.

Absorption is complex process: it may involve diffusion down concentration gradients, or osmotic gradient, or specific transport factors. An absorption constant may be estimated to explain delays in drug concentration and effect due to absorption.

Effect compartments: Theoretical effect compartments were introduced to help explain the time delay between plasma concentration and observed effect for some drugs. This delay may occur because the effect site is not the central compartment, and hence time is required for drug delivery to effect site, by perfusion, diffusion or transport. At steady state plasma concentrations, then there will be a constant rate of input into the effect compartment, so the time to steady state effect site concentration will be determined by the rate of equilibration half-life. Equilibration half-life is determined by volume of distribution (organ size, tissue binding), and clearance (blood flow, diffusion).

Physiological substance mediated effects: Drug effects may be defined as immediate or delayed. In reality almost no drugs have a truly immediate effect due to complex physiological control systems and interactions that exist at baseline and after drug administration. Drugs act typically at receptors, but the observed effect is only seen later. Delayed effects may be due to drug effect on a physiological mediator, often an enzyme system. A mediator is something which affects a transition between one stage and another. It can be thought of as a go between or intermediatory, occupying an intermediate position, forming a connecting link between one thing and another.

Physiological mediators may be defined as physiological substances that can be affected by a administered drug or physiological process to produce an effect on another physiological process. A mediator may be an enzyme, or other biologically active molecule, for example nitric oxide.

Drugs that have an effect via a physiological mediator can be modelled using delay due to the turnover of the mediator, hence these models are known as turnover models. Time course of effect models link pharmacokinetic and pharmacodynamic models to describe changes in effect over time. Differential equations can be used to describe delays in observed drug effect due to absorption, effect compartment disposition and drug action via physiological mediators. Changes in concentration over time are described by changes in rate in and changes in rate out. In the case of drugs that work via physiological mediators, the change in concentration of the mediator over time is used as a monitor of drug effect.

Introduction by Anita Sumpter (2008).

Reference

  1. Shoenwald RD. Pharmacokinetics in Drug Discovery and Development. CRC Press, Boca Raton 2002. p. 34

Workshop hints

Note: All files should be loaded from and saved to your Pharmacometrics Data\Time Course of Effect folder for this assignment.

Excel

Find the file Pharmacometrics Data\Time Course of Effect\pkpd.xls

  1. Open pkpd.xls with Excel.
  2. Look at the ka1+emaxc worksheet.
  3. Identify
    1. The model code
    2. The model parameters
    3. The independent variables
  4. Export the simulated ka1emaxc data from pkpd.xls to a format that can be used by other programs
  5. Create a new Excel workbook and add the following headings in the top row. It is important to put the # before ID so that the same file can be used for NONMEM.
    #ID TIME DV DVID
  6. Fill the ID column with the value 1 down to row 23. 
  7. Rows 2 to 12 will be populated with concentration observation records. Copy the Time values from pkpd.xls into the TIME column and copy the Conc values to the DV column in rows 2 to 12. Fill the DVID column with the value 1 for rows 2 to 11. The DVID value is used to identify the type of observation (1=conc, 2=effect).
  8. Rows 13 to 23 will be populated with effect observation records. The ID remains as 1, because the data is from the same single subject. Copy the Time values from pkpd.xls into the TIME column and copy the Effect values to the DV column in rows 13 to 23. Fill the DVID column with the value 2 for these rows.

    Your worksheet should look similar to Table 1, but your DV values will be slightly different.

        A B C D
    1 #ID TIME DV DVID
    2
    1
    0
    -0.1
    1
    3
    1
    0.25
    1.7
    1
    4
    1
    0.5
    2.5
    1
    5
    1
    0.75
    3.5
    1
    6
    1
    1
    4.1
    1
    7
    1
    1.5
    5.1
    1
    8
    1
    2
    5.4
    1
    9
    1
    3
    5.1
    1
    10
    1
    4
    4.4
    1
    11
    1
    6
    2.6
    1
    12
    1
    8
    1.5
    1
    13
    1
    0
    -0.1
    2
    14
    1
    0.25
    33.7
    2
    15
    1
    0.5
    47.3
    2
    16
    1
    0.75
    54.5
    2
    17
    1
    1
    58.7
    2
    18
    1
    1.5
    62.5
    2
    19
    1
    2
    63.8
    2
    20
    1
    3
    62.2
    2
    21
    1
    4
    58.5
    2
    22
    1
    6
    46.9
    2
    23
    1
    8
    33.7
    2
    Table 1. Data file for ka1emaxc.
  9. Now save the data file in "My Pharmacometrics Data\Time Course of Effect" using 'Save As' and choose CSV (Comma delimited, *.csv) format. Name the file ka1emaxc.csv.
  10. The Phoenix program requires this kind of data in a less flexible format. The concentration and effect observations need to be in separate columns. You should move the effect observations and put them in column D. Rename column C to 'CONC' and column D to 'EFFECT'. Then delete rows 13 to 23. The worksheet should look like this:
        A B C D
    1 #ID TIME CONC EFFECT
    2
    1
    0
    -0.1
    -0.1
    3
    1
    0.25
    1.7
    33.7
    4
    1
    0.5
    2.5
    47.3
    5
    1
    0.75
    3.5
    54.5
    6
    1
    1
    4.1
    58.7
    7
    1
    1.5
    5.1
    62.5
    8
    1
    2
    5.4
    63.8
    9
    1
    3
    5.1
    62.2
    10
    1
    4
    4.4
    58.5
    11
    1
    6
    2.6
    46.9
    12
    1
    8
    1.5
    33.7
    Table 2. Phoenix data file for ka1emaxc.
  11. Save the file as ka1emaxc_CE.csv in the "My Pharmacometrics Data\Time Course of Effect" folder.

Berkeley Madonna

Emax model

  1. Open Berkeley Madonna using the shortcut in the Pharmacometrics Programs folder.
  2. Add code to the Equations window defining the STARTTIME and STOPTIME, the output interval (DTOUT), the model parameters and the model equation (Figure 1).
  3. Click on Run to run the model .
  4. Save your model in your Time Course of Effect folder with the name Ka1EmaxC.mmd.
  5. Click on the Graph window and use the Graph>Choose Variables option to show Conc and Effect.
  6. View a table of times, concentrations and effects by clicking on the Table icon in the Run 1 graph window.
METHOD RK4
STARTTIME = 0
STOPTIME=10
DT = 0.02
DTOUT=1
Dose=100
CL=3
V=10
Tabs=1
KA=logn(2)/Tabs
Emax=100
C50=3
E0=0

Conc=Dose*Ka/V/(Ka-CL/V)*(EXP(-CL/V*Time)-EXP(-Ka*Time))
Effect=E0+Emax*Conc/(C50+Conc)

Figure 1. Code for Ka1EmaxC.mmd



Effect compartment model

  1. Save the Ka1EmaxC Model in your Time Course of Effect folder with the new name:

    Ka1EmaxCe.mmd
  2. Add an effect compartment for delayed concentrations (Ce) (Figure 2).
  3. Click on Run to run the model.
  4. Save your model. Click on the Graph window and use the Graph>Choose Variables option to show Conc, Ce and Efffect.
  5. View a table of times, concentrations and effects by clicking on the Table icon in the Run 1 graph window.
METHOD RK4
STARTTIME = 0
STOPTIME=10
DT = 0.02
DTOUT=1
Dose=100
CL=3
V=10
Tabs=1
Ka=logn(2)/Tabs

Emax=100
C50=3
E0=0
Teq=3
Keq=logn(2)/Teq

init(Gut)=Dose
init(Conc)=0
init(Ce)=0

d/dt(Gut)= - Gut*Ka
d/dt(Conc)=(Gut*Ka - CL*Conc)/V
d/dt(Ce) = Keq*(Conc - Ce)

Effect=E0+Emax*Ce/(C50+Ce)
 Figure 2. Code for Ka1EmaxCe.mmd

Monolix

  1. Open the MONOLIX shortcut in folder "Pharmacometrics Programs".
  2. Click on the
     
    New Project icon (top left of MONOLIX GUI).
  3. In MONOLIX, click 'The data', locate your ka1emaxc.csv file and click open. The data information window will appear.
  4. MONOLIX should identify that your input file has a header row and your data should appear under the headings: ID TIME Y YTYPE. If necessary, place a check in the 'Use header' box so that MONOLIX can identify the data by your header row. Click accept.
  5. Instead of using the model library, we will use MLXTRAN to write out the ka1emaxc model. Start by opening a text editor (e.g. Editplus) and enter the code shown in Figure 3. Note that the variable name "effect" cannot be used in MLXTRAN so use "eff".
    ;One compartment first order input and elimination, immediate Emax effect

    INPUT:
    parameter={cl,v,tabs,emax,c50}

    EQUATION:
    dose=100 ; nominal dose
    k=cl/v
    ka=log(2)/tabs
    conc=dose/v*ka/(ka-k)*(exp(-k*t)-exp(-ka*t))
    eff=emax*conc/(c50+conc)

    OUTPUT:
    output= {conc,eff}
     Figure 3. Code for ka1emaxc_mlxt.txt

    IMPORTANT: MLXTRAN is case sensitive. Take care to be consistent with upper and lower case letters in names.

  1. Create a "Time Course of Drug Effect\Monolix" folder and save the model as ka1emaxc_mlxt.txt in the "Time Course of Effect\Monolix" folder. You can create the Monolix folder using Windows Explorer or from the Monolix Save project dialog box.
  2. Return to the Monolix window, click 'The structural model' and the model library will appear. Click 'Other list' and navigate to your "Time Course of Effect\Monolix" folder and click 'OK'. Select ka1emaxc_mlxt.txt and click 'Compile', then 'Accept'.

    If you get a compile error. Double check that your code is identical to that shown in the Figure and be sure to press ENTER after the last line of code - this is required to 'end' the last statement.

  3. Change the initial parameter estimates under Fixed effects to reasonable starting values based on the Excel parameters used for simulation. Holding the mouse over each box will tell you, which parameter the value is for.
  4. Set the 'Stand. dev. of the random effects' to 0 for each parameter by setting all the elements of 'The covariance model' to 0 by clicking on any elements containing 1.

    Because these are data from a single individual, there is no between subject variability (random effects). The SD of random effects is therefore 0.

  5. Set the residual error model to 'const' for both models.
  6. Set the 'Residual error parameters' to 1 (SD of residual error) for both types of observation (concentration, effect).
  7. Click 'Check initial fixed effects'. A plot of predictions based on the model and initial parameter estimates will display along with the observed values. Close the 'Check initial fixed effects' window.
  8. When you have more than one output you will need to select the 'y_1' or y_2' output variable for each graph.

    You can visualise the effect of changing your parameter estimates by adjusting the values in the bottom left of the window. When you have chosen initial estimates that form a prediction that is similar to the observations, click 'Set as initial values' to apply these values and close the window.

  9. IMPORTANT: Save the project as ka1_emaxc_project.mat in your Time Course of Effect\Monolix folder.
  10. Set the calculation options by ticking the 'Estimate the population parameters', 'Estimate the Fisher Information Matrix' and 'Estimate the log-likelihood' boxes which are next to the 'Run' icon at the top of the Monolix window). Make sure the other boxes are not checked especially 'Estimate the individual parameters'.
  11. Estimate the parameters by clicking on Run. This will take a while depending on the complexity of the model. During the estimation process you can see how the parameter estimates are being changed and settle down towards the final value.
  12. When the estimation finishes click on 'List' button below 'Graphics' at the bottom of the Monolix window. Click to check both boxes (for Y1 conc and Y2 effect outputs) for 'Individual Fits' and 'VPC' as Outputs. Uncheck all the other types of plot. 
  13. Click on OK to close the 'Graphics' list window.
  14. Then click on 'Display the Graphics' at the top of the Monolix window. 
  15. Look at the Individual fits for Conc and Effect.You can select the graphic plots by clicking on the tab at the bottom of the 'Figures' window.
  16. Save a pdf copy of each plot in your Time Course of Drug Effect\Monolix project folder.
  17. Look at the VPC plots for Conc and Effect.
  18. Click on Settings, use the default settings and add 'Individual Data'. Then click on 'Bins and CI' at the bottom of the list of options. Click on 'Equal width' and then click on 'Display'. Save a pdf copy of each VPC plot in your Time Course of Drug Effect\Monolix project folder.
  19. View the parameter estimates by clicking   'Last Results'. A text file containing these results is saved in a 'pop_parameters.txt' in the project folder.

Phoenix

  1. Open the Phoenix shortcut in the folder "Pharmacometrics Programs"
  2. Click on 'File New Project' in the menu line
  3. Change the Project name to 'Time Course of Drug Effect'
  4. Right click on 'Data' in the Time Course of Drug Effect list and click on 'Import'
  5. Navigate to the "Pharmacometrics Data\Time Course of Drug Effect" folder and open the 'ka1emaxc_CE.csv' file you created previously
  6. Click on 'Finish'

    This adds the ka1emaxc_CE data set to the project. If you make changes to ka1emaxc_CE.csv you will need to delete the ka1emaxc_CE data set and import the changed ka1emaxc_CE.csv file again.


  7. Right click on 'WorkFlow' then 'New', 'Phoenix Modeling', 'Phoenix Model'
  8. Change the Workflow Phoenix Model name to 'ka1emaxc'
  9. Drag the Data ka1emaxc object to the Main (ka1emaxc) window. You will return later to this window to map the input data columns to variables used by Phoenix.
  10. Click on the Structure tab and make sure the 'Population?' box is checked.
  11. Click on 'Edit as Textual'. This allows you to write the model without relying on the Built In library of models.
  12. Click on the Setup Model icon to open a window containing the test() model function
  13. Replace the contents of the 'Model' window with the code shown below then click on 'Main (ka1emaxc)'. 
  14. Check that you can see the "No warnings" message (top of the lower part of the workflow bo1 window). If there are warnings then click on this tabe and correct the code. 
  15. ka1emaxc(){
    covariate(Time)
    fixef(grpKa = c(, 0.7, ))
    fixef(grpV = c(, 10, ))
    fixef(grpCL = c(, 3, ))
    fixef(grpC50 = c(, 3, ))
    fixef(grpEmax = c(, 100, ))

    stparm(Ka = grpKa)
    stparm(V = grpV)
    stparm(CL = grpCL)
    stparm(C50 = grpC50)
    stparm(Emax = grpEmax)

    dose=100 # nominal dose
    K=CL/V
    Conc=dose/V*Ka/(Ka-K)*(exp(-K*Time)-exp(-Ka*Time))
    Effect=Emax*Conc/(C50+Conc)

    error(CEps = 1)
    observe(CObs(Time) = Conc + CEps)

    error(EEps = 1)
    observe(EObs(Time) = Effect + EEps)
    }

     Figure 4. Code for ka1emaxc text model
  16. Return to the Workflow ka1emaxc object and click on the 'Setup Main (ka1emaxc)' icon.
  17. If the source is not defined then drag the Data ka1emaxc object to the Mappings window.
  18. Click on the radio buttons to associate TIME with Time, CONC with CObs, EFFECT with Eobs.
  19. Click on the Initial Estimates tab and set appropriate initial parameter values. Change the plot variables to 'Conc v Time' (drop down box under the parameter values) and 'Effect v Time' to see the observations and predictions. Confirm that the initial estimates give a reasonable fit to the data.
  20. Click on the 'Structure' tab and UN-check the 'Population?' box (upper left) to perform an individual subject analysis..
  21. Click on the Plots tab, then Disable All, then select Ind DV, IPRED vs IVAR (individual plot).
  22. Save the project with the name Time Course of Effect.phxproj in a Time_Course_of_Effect\Phoenix folder.
  23. Select the ka1emaxc icon in the Workflow (Object Browser window). Click on the Execute ka1emaxc icon at the top of the Phoenix window. This will start the parameter estimation process.
  24. Click on Output Data Theta icon to see the parameter estimates.
  25. Create a new Excel workbook in the Time Course of Effect\Phoenix folder called "Time Course of Effect Results.xlsx". 
  26. Select the Theta table values (including columns and rows) then copy and paste the parameter estimates to the Excel workbook.
  27. Create a new Word document in the Time Course of Effect\Phoenix folder called "Time Course of Effect Results.docx". 
  28. Copy the Excel parameter table and paste it into the Word document.
  29. Look at the Ind DV, IPRED vs IVAR plot then right click on it and copy a bitmap to clipboard. Paste the clipboard contents to the Word document.
  30. Click on the ka1emaxc workflow object the press Ctrl-C to copy it.
  31. Click on the Workflow object then press Ctrl-V to paste the ka1emaxc workflow object.
  32. Rename the 'Copy of ka1emaxc' object to 'VPC ka1emaxc' and click on it to see its contents.
  33. Click on the 'Structure' tab and check the 'Population?' box (upper left) to peform a population analysis. This willl allow a VPC plot to be generated.
  34. Set up a visual predictive check by clicking on the Sim./Pred Check button then click on Main and set # Replicates to 100, click on Binning and check the None option, click on Quantiles and use the values (5, 50, 95) for a 90% prediction interval, then click on Quantile % and set the values to 2.5, 50 , 97.5 for a 95% confidence interval
  35. Click on the Plots tab and select Pop PredCheck SimQCI (visual predictive check).
  36. Select the bo1 icon in the Workflow (Object Browser window). Click on the Execute ka1emaxc icon at the top of the Phoenix window. This will create the VPC (visual predictive check)..
  37. Look at the Plot PopPredCheckQI plot then right click on it and copy a bitmap to clipboard. Paste the clipboard contents to the Word document.
  38. Save the project as 'Time Course of Effect' in the "Time Course of Effect\Phoenix' folder.

NONMEM

  1. Open the NONMEM shortcut in the folder "Pharmacometrics Programs".
  2. Change directory to the Time Course of Drug Effect folder by typing this command in the NONMEM window then press <ENTER>.
    cd Time*

    All commands shown in the green boxes should end by pressing <Enter>.


  3. Make a NONMEM directory by typing this command in the NONMEM window.
    md NONMEM

    You only have to make the directory once.


  4. Change to the NONMEM directory from the Time Course of Effect directory.
    cd NONMEM
  5. Use EditPlus from Windows Explorer to create the following code in a file named bo1.ctl.
  6. Enter the code for ka1emaxc.ctl shown in Figure 2.

    $PROB one compartment first-order input and elimination plus emax effect
    $INPUT ID TIME DV DVID
    $DATA ..\..\ka1emaxc.csv
    $ESTIM METHOD=CONDITIONAL
    $COV
    $THETA
    (0,3,) ; POP_CL
    (0,10,) ; POP_V
    (0,1,) ; POP_TABS
    (0,100,) ; POP_EMAX
    (0,3,) ; POP_c50
    $OMEGA
    0 FIX ; ETA_CL
    0 FIX ; ETA_V
    0 FIX ; ETA_TABS
    0 FIX ; ETA_EMAX
    0 FIX ; ETA_C50
    $SIGMA 1 ; ERR_CONC
    $SIGMA 25 ; ERR_EFFECT
    $PRED
    DOSE=100
    CL=THETA(1)*EXP(ETA(1))
    V=THETA(2)*EXP(ETA(2))
    TABS=THETA(3)*EXP(ETA(3))
    EMAX=THETA(4)*EXP(ETA(4))
    C50=THETA(5)*EXP(ETA(5))
    K=CL/V
    KA=LOG(2)/TABS
    CONC=DOSE/V*KA/(KA-K)*(EXP(-K*TIME)-EXP(-KA*TIME))
    EFFECT=EMAX*CONC/(C50+CONC)
    IF (DVID.EQ.1) THEN
    Y=CONC + ERR(1)
    ELSE
    Y=EFFECT + ERR(2)
    ENDIF
    $TABLE ID TIME CL V TABS EMAX C50 DVID Y
    NOPRINT ONEHEADER FILE=ka1emaxc.fit

    Figure 2. NM-TRAN code for ka1emaxc.ctl (NONMEM)

    The $OMEGA parameters are FIXed to 0. This is because there is only one individual being modelled. These random effects parameters are used to describe between subject variability when there is more than one individual.


  7. Save the file. Check using Windows Explorer that you can find the file "ka1emaxc.ctl" in the User Defined Models\NONMEM folder.
  8. The data file name must match in the $DATA record of the ka1emaxc.ctl file.

    In order for NONMEM to find the data file the $DATA record has to include a path relative to the folder where NONMEM is executed. This is why the '..\..\' is put before the name of the data file which is located in the Time Course of Effect folder.


  9. Execute NONMEM with this command in the NONMEM window:
    nmgo ka1emaxc

    When you get errors from NONMEM with the nmgo command then please read the error message carefully and try to understand what it is telling you. The usual errors that occur with these example problems will give you some clues to what you might need to change in your ctl file.

    Commands can be recalled by using the Up arrow on your keyboard. You can easily repeat the command without more typing or edit it to save the amount of typing you do.

  10. Use Excel to open the ka1emaxc.fit file in the ka1emaxc.reg results folder.   
  11. Select column A then click on the "Data" menu item then click on "Text to Columns". Click on "Finish". This will separate the values into separate columns.
  12. Select all cells in the worksheet (e.g. press ctrl-A) then right click on a cell and click on "Format cells". Click on the "General" option.. This will make the numeric values easier to read.
  13. Delete row 1 which contains the value "TABLE 1".
  14. Click on cell A1 then click on the "Data" menu item then click on "Data Filter". This will let you choose rows with specific values of DVID by clickiing on the arrow in the corner of the column with the heading "DVID".
  15. Use the Data Filter to select rows with DVID=1 (concentrations). Create a graph of TIME  versus Y and DV. 
  16. Use the Data Filter to select rows with DVID=2 (effects). Create a graph of TIME  versus Y and DV. 
  17. Save the Excel file with the graphs as ka1emaxc.xlsx in the Time Course of Effect\NONMEM folder.
  18. Use EditPlus to look at the saved results in the '.smr' file in the ka1emaxc.reg folder. The results are saved in a folder with the same name as the ctl file but with the extension '.reg' e.g. use the following command or open the file using the Windows Explorer.

    notepad ka1emaxc.reg\ka1emaxc.smr

Assignment

Physiological mediator model

Turnover models are used to describe delayed responses due to the turnover of a physiological mediator. The physiological mediator (M) without drug is formed at a rate proportional to its initial concentration (M0) and its elimination rate constant (kout). There are 4 basic ways that drugs can affect a turnover model. These give rise to characteristic time courses of response.

  1. Use Berkeley Madonna to open Pharmacometrics Data\Time Course of Effect\turnover.mmd
  2. Look at the model equations
  3. Run the model and make a graph of Time vs Conc (left axis) and Time vs M1, M2, M3, M4 (right axis)
  4. Use the Parameters Batch Runs option to vary Dose from 10 to 1000 in 5 steps
  5. Explain the pattern of times of peak effect shown for each of the response curves (M1, M2, M3, M4)

Parameter Estimation

  1. Write up the results of parameter estimation using MONOLIX, Phoenix and NONMEM.
  2. Describe the differences between the parameters used for simulation and the parameter estimates obtained from MONOLIX, Phoenix and NONMEM. 
  3. Discuss how you might change the experimental design in order to get better agreement between the simulation parameters and the parameter estimates.