Example 3: PK Model, ODE model

Example 3 is quite different from the two previous examples. First, it is an ODE model, using ADVAN13. Second, different models in the search space required different data sets. Therefore, there is a token in the $DATA record. Next, urine PK is included in the model. Finally, this example involves Michaelis-Menten, whereas the previous examples were linear. The token groups/set are quite complex.

While the search space is small (324 models), we’ll perform an exhaustive search. Because of the complexity of the model and the ODE solution, model run times are long. For faster search, the FO method is used.

The Template file

$PROBLEM ORAL BOLUS WITH PLASMA AND URINE OBSERVATIONS
     ;
     ; NUMBER OF COMPARTMENTS        : 1 OR 2 OR 3
     ;
     ; ABSORPTION                    : ZERO-ORDER OR FIRST-ORDER OR ZERO-ORDER FOLLOWED BY FIRST-ORDER
     ;
     ; ELIMINATION                   : FIRST-ORDER OR MICHAELIS-MENTEN
     ;
     ; BIOAVAILABLITY                : EITHER 1 OR BETWEEN 0 AND 1 (ASSOCIATED IIV IS ALSO SEARCHED)
     ;
     ; RESIDUAL ERROR FOR PLASMA OBS : PROPORTIONAL OR COMBINED
     ; RESIDUAL ERROR FOR URINE OBS  : ADDITIVE OR PROPORTIONAL OR COMBINED


; ====================================================================================================
; DATA
; ====================================================================================================

$INPUT       ID TIME AMT CMT {ODE[1]} DV DVID EVID MDV
$DATA      {data_dir}/{ODE[2]} IGNORE=@


; ====================================================================================================
; SUBROUTINE
; ====================================================================================================
$SUBROUTINE ADVAN13 TOL = 6

$MODEL
NCOMP = {ODE[3]}
COMP = (URINE)


; ===================================================================================================
; STRUCTURAL PARAMETERS
; ===================================================================================================
$PK

{ODE[4]}

{BIOAVAIL[1]}

; ====================================================================================================
; INITIAL VALUES FOR FIXED EFFECTS
; ====================================================================================================
$THETA

{ODE[5]}
{BIOAVAIL[2]}


; ====================================================================================================
; INITIAL VALUES FOR OMEGA
; ====================================================================================================
$OMEGA

{ODE[6]}
{BIOAVAIL[3]}


; ====================================================================================================
; ODE MODEL
; ====================================================================================================
$DES

{ODE[7]}


; ===================================================================================================
; RESIDUAL ERROR MODEL
; ===================================================================================================
$ERROR

; IPRED
{ODE[8]}

; RESIDUAL ERROR MODEL
IF (DVID == 1) Y = IPREDC {RESERRC[1]}
IF (DVID == 2) Y = IPREDU {RESERRU[1]}


$SIGMA

{RESERRC[2]}
{RESERRU[2]}


; ==================================================================================================
; ESTIMATION METHOD AND SE
; ==================================================================================================

$EST METHOD = 0 NOABORT MAX = 9999 SIGL = 6 NSIG = 2 PRINT = 5

$COV UNCOND PRINT = E

Example 3 template file: text

The Tokens file

The tokens file is quite complex:

{
   "ODE": [
      ["RATE",
         "OralBolus_PlasmaUrine_ResetCpt2.csv",
         " 2 \n COMP = (CENTRAL)",
         "R1 = THETA(ODER1F) * EXP(ETA(ODER1R)) \n \n VC = THETA(ODEVCF) * EXP(ETA(ODEVCR)) \n \n {ELIM[1]}",
         "(0, 50) \t ; THETA(ODER1F) TVR1 \n (0, 5) \t ; THETA(ODEVCF) TVVC \n {ELIM[2]}",
         "1 \t ; ETA(ODER1R) ETA ON R1 \n 1 \t ; ETA(ODEVCR) ETA ON VC \n {ELIM[3]}",
         "C = A(1)/VC \n \n DADT(1) = - {ELIM[4]} \n DADT(2) = {ELIM[4]}",
         "IPREDC = A(1)/VC \n IPREDU = A(2)"
      ],
      ["DROP",
         "OralBolus_PlasmaUrine_ResetCpt3.csv",
         " 3 \n COMP = (DEPOT) \n COMP = (CENTRAL)",
         "KA = THETA(ODEKAF) * EXP(ETA(ODEKAR)) \n \n VC = THETA(ODEVCF) * EXP(ETA(ODEVCR)) \n \n {ELIM[1]}",
         "(0, 1) \t ; THETA(ODEKAF) TVKA \n (0, 5) \t ; THETA(ODEVCF) TVVC \n {ELIM[2]}",
         "1 \t ; ETA(ODEKAR) ETA ON KA \n 1 \t ; ETA(ODEVCR) ETA ON VC \n {ELIM[3]}",
         "C = A(2)/VC \n \n DADT(1) = - KA * A(1) \n DADT(2) = KA * A(1) - {ELIM[4]} \n DADT(3) = {ELIM[4]}",
         "IPREDC = A(2)/VC \n IPREDU = A(3)"
      ],
      ["RATE",
         "OralBolus_PlasmaUrine_ResetCpt3.csv",
         " 3 \n COMP = (DEPOT) \n COMP = (CENTRAL)",
         "R1 = THETA(ODER1F) * EXP(ETA(ODER1R)) \n \n KA = THETA(ODEKAF) * EXP(ETA(ODEKAR)) \n \n VC = THETA(ODEVCF) * EXP(ETA(ODEVCR)) \n \n {ELIM[1]}",
         "(0, 5000) \t ; THETA(ODER1F) TVR1 \n (0, 1) \t ; THETA(ODEKAF) TVKA \n (0, 5) \t ; THETA(ODEVCF) TVVC \n {ELIM[2]}",
         "1 \t ; ETA(ODER1R) ETA ON R1 \n 1 \t ; ETA(ODEKAR) ETA ON KA \n 1 \t ; ETA(ODEVCR) ETA ON VC \n {ELIM[3]}",
         "C = A(2)/VC \n \n DADT(1) = - KA * A(1) \n DADT(2) = KA * A(1) - {ELIM[4]} \n DADT(3) = {ELIM[4]}",
         "IPREDC = A(2)/VC \n IPREDU = A(3)"
      ],
      ["RATE",
         "OralBolus_PlasmaUrine_ResetCpt3.csv",
         " 3 \n COMP = (CENTRAL) \n COMP = (PERIPH)",
         "R1 = THETA(ODER1F) * EXP(ETA(ODER1R)) \n \n VC = THETA(ODEVCF) * EXP(ETA(ODEVCR)) \n \n VP = THETA(ODEVPF) * EXP(ETA(ODEVPR)) \n \n CLQ = THETA(ODECLQF) * EXP(ETA(ODECLQR)) \n \n {ELIM[1]}",
         "(0, 50) \t ; THETA(ODER1F) TVR1 \n (0, 5) \t ; THETA(ODEVCF) TVVC \n (0, 5) \t ; THETA(ODEVPF) TVVP \n (0, 1) \t ; THETA(ODECLQF) TVCLQ \n {ELIM[2]}",
         "1 \t ; ETA(ODER1R) ETA ON R1 \n 1 \t ; ETA(ODEVCR) ETA ON VC \n 1 \t ; ETA(ODEVPR) ETA ON VP \n 1 \t ; ETA(ODECLQR) ETA ON CLQ \n {ELIM[3]}",
         "C = A(1)/VC \n \n DADT(1) = - {ELIM[4]} - CLQ * (A(1)/VC - A(2)/VP) \n DADT(2) = CLQ * (A(1)/VC - A(2)/VP) \n DADT(3) = {ELIM[4]}",
         "IPREDC = A(1)/VC \n IPREDU = A(3)"
      ],
      ["DROP",
         "OralBolus_PlasmaUrine_ResetCpt4.csv",
         " 4 \n COMP = (DEPOT) \n COMP = (CENTRAL) \n COMP = (PERIPH)",
         "KA = THETA(ODEKAF) * EXP(ETA(ODEKAR)) \n \n VC = THETA(ODEVCF) * EXP(ETA(ODEVCR)) \n \n VP = THETA(ODEVPF) * EXP(ETA(ODEVPR)) \n \n CLQ = THETA(ODECLQF) * EXP(ETA(ODECLQR)) \n \n {ELIM[1]}",
         "(0, 1) \t ; THETA(ODEKAF) TVKA \n (0, 5) \t ; THETA(ODEVCF) TVVC \n (0, 5) \t ; THETA(ODEVPF) TVVP \n (0, 1) \t ; THETA(ODECLQF) TVCLQ \n {ELIM[2]}",
         "1 \t ; ETA(ODEKAR) ETA ON KA \n 1 \t ; ETA(ODEVCR) ETA ON VC \n 1 \t ; ETA(ODEVPR) ETA ON VP \n 1 \t ; ETA(ODECLQR) ETA ON CLQ \n {ELIM[3]}",
         "C = A(2)/VC \n \n DADT(1) = - KA * A(1) \n DADT(2) = KA * A(1) - {ELIM[4]} - CLQ * (A(2)/VC - A(3)/VP) \n DADT(3) = CLQ * (A(2)/VC - A(3)/VP) \n DADT(4) = {ELIM[4]}",
         "IPREDC = A(2)/VC \n IPREDU = A(4)"
      ],
      ["RATE",
         "OralBolus_PlasmaUrine_ResetCpt4.csv",
         " 4 \n COMP = (DEPOT) \n COMP = (CENTRAL) \n COMP = (PERIPH)",
         "R1 = THETA(ODER1F) * EXP(ETA(ODER1R)) \n \n KA = THETA(ODEKAF) * EXP(ETA(ODEKAR)) \n \n VC = THETA(ODEVCF) * EXP(ETA(ODEVCR)) \n \n VP = THETA(ODEVPF) * EXP(ETA(ODEVPR)) \n \n CLQ = THETA(ODECLQF) * EXP(ETA(ODECLQR)) \n \n {ELIM[1]}",
         "(0, 5000) \t ; THETA(ODER1F) TVR1 \n (0, 1) \t ; THETA(ODEKAF) TVKA \n (0, 5) \t ; THETA(ODEVCF) TVVC \n (0, 5) \t ; THETA(ODEVPF) TVVP \n (0, 1) \t ; THETA(ODECLQF) TVCLQ \n {ELIM[2]}",
         "1 \t ; ETA(ODER1R) ETA ON R1 \n 1 \t ; ETA(ODEKAR) ETA ON KA \n 1 \t ; ETA(ODEVCR) ETA ON VC \n 1 \t ; ETA(ODEVPR) ETA ON VP \n 1 \t ; ETA(ODECLQR) ETA ON CLQ \n {ELIM[3]}",
         "C = A(2)/VC \n \n DADT(1) = - KA * A(1) \n DADT(2) = KA * A(1) - {ELIM[4]} - CLQ * (A(2)/VC - A(3)/VP) \n DADT(3) = CLQ * (A(2)/VC - A(3)/VP) \n DADT(4) = {ELIM[4]}",
         "IPREDC = A(2)/VC \n IPREDU = A(4)"
      ],
      ["RATE",
         "OralBolus_PlasmaUrine_ResetCpt4.csv",
         " 4 \n COMP = (CENTRAL) \n COMP = (PERIPH) \n COMP = (PERIPH2)",
         "R1 = THETA(ODER1F) * EXP(ETA(ODER1R)) \n \n VC = THETA(ODEVCF) * EXP(ETA(ODEVCR)) \n \n VP = THETA(ODEVPF) * EXP(ETA(ODEVPR)) \n \n CLQ = THETA(ODECLQF) * EXP(ETA(ODECLQR)) \n \n VP2 = THETA(ODEVP2F) * EXP(ETA(ODEVP2R)) \n \n CLQ2 = THETA(ODECLQ2F) * EXP(ETA(ODECLQ2R)) \n \n {ELIM[1]}",
         "(0, 50) \t ; THETA(ODER1F) TVR1 \n (0, 5) \t ; THETA(ODEVCF) TVVC  \n (0, 5) \t ; THETA(ODEVPF) TVVP \n (0, 1) \t ; THETA(ODECLQF) TVCLQ \n (0, 0.1) \t ; THETA(ODEVP2F) TVVP2  \n (0, 1) \t ; THETA(ODECLQ2F) TVCLQ2 \n {ELIM[2]}",
         "1 \t ; ETA(ODER1R) ETA ON R1 \n 1 \t ; ETA(ODEVCR) ETA ON VC  \n 1 \t ; ETA(ODEVPR) ETA ON VP \n 1 \t ; ETA(ODECLQR) ETA ON CLQ  \n 1 \t ; ETA(ODEVP2R) ETA ON VP2 \n 1 \t ; ETA(ODECLQ2R) ETA ON CLQ2 \n {ELIM[3]}",
         "C = A(1)/VC \n \n DADT(1) = - {ELIM[4]} - CLQ * (A(1)/VC - A(2)/VP) - CLQ2 * (A(1)/VC - A(3)/VP2) \n DADT(2) = CLQ * (A(1)/VC - A(2)/VP) \n DADT(3) = CLQ2 * (A(1)/VC - A(3)/VP2) \n DADT(4) = {ELIM[4]}",
         "IPREDC = A(1)/VC \n IPREDU = A(4)"
      ],
      ["DROP",
         "OralBolus_PlasmaUrine_ResetCpt5.csv",
         " 5 \n COMP = (DEPOT) \n COMP = (CENTRAL) \n COMP = (PERIPH) \n COMP = (PERIPH2)",
         "KA = THETA(ODEKAF) * EXP(ETA(ODEKAR)) \n \n VC = THETA(ODEVCF) * EXP(ETA(ODEVCR)) \n \n VP = THETA(ODEVPF) * EXP(ETA(ODEVPR)) \n \n CLQ = THETA(ODECLQF) * EXP(ETA(ODECLQR))\n \n VP2 = THETA(ODEVP2F) * EXP(ETA(ODEVP2R)) \n \n CLQ2 = THETA(ODECLQ2F) * EXP(ETA(ODECLQ2R)) \n \n {ELIM[1]}",
         "(0, 1) \t ; THETA(ODEKAF) TVKA \n (0, 5) \t ; THETA(ODEVCF) TVVC  \n (0, 5) \t ; THETA(ODEVPF) TVVP \n (0, 1) \t ; THETA(ODECLQF) TVCLQ \n (0, 0.1) \t ; THETA(ODEVP2F) TVVP2 \n (0, 1) \t ; THETA(ODECLQ2F) TVCLQ2 \n {ELIM[2]}",
         "1 \t ; ETA(ODEKAR) ETA ON KA \n 1 \t ; ETA(ODEVCR) ETA ON VC  \n 1 \t ; ETA(ODEVPR) ETA ON VP \n 1 \t ; ETA(ODECLQR) ETA ON CLQ \n 1 \t ; ETA(ODEVP2R) ETA ON VP2 \n 1 \t ; ETA(ODECLQ2R) ETA ON CLQ2 \n {ELIM[3]}",
         "C = A(2)/VC \n \n DADT(1) = - KA * A(1) \n DADT(2) = KA * A(1) - {ELIM[4]} - CLQ * (A(2)/VC - A(3)/VP) - CLQ2 * (A(2)/VC - A(4)/VP2) \n DADT(3) = CLQ * (A(2)/VC - A(3)/VP) \n DADT(4) = CLQ2 * (A(2)/VC - A(4)/VP2) \n DADT(5) = {ELIM[4]}",
         "IPREDC = A(2)/VC \n IPREDU = A(5)"
      ],
      ["RATE",
         "OralBolus_PlasmaUrine_ResetCpt5.csv",
         " 5 \n COMP = (DEPOT) \n COMP = (CENTRAL) \n COMP = (PERIPH) \n COMP = (PERIPH2)",
         "R1 = THETA(ODER1F) * EXP(ETA(ODER1R)) \n \n KA = THETA(ODEKAF) * EXP(ETA(ODEKAR)) \n \n VC = THETA(ODEVCF) * EXP(ETA(ODEVCR)) \n \n VP = THETA(ODEVPF) * EXP(ETA(ODEVPR)) \n \n CLQ = THETA(ODECLQF) * EXP(ETA(ODECLQR)) \n \n VP2 = THETA(ODEVP2F) * EXP(ETA(ODEVP2R)) \n \n CLQ2 = THETA(ODECLQ2F) * EXP(ETA(ODECLQ2R)) \n \n {ELIM[1]}",
         "(0, 5000) \t ; THETA(ODER1F) TVR1 \n (0, 1) \t ; THETA(ODEKAF) TVKA \n (0, 5) \t ; THETA(ODEVCF) TVVC \n (0, 5) \t ; THETA(ODEVPF) TVVP \n (0, 1) \t ; THETA(ODECLQF) TVCLQ \n (0, 0.1) \t ; THETA(ODEVP2F) TVVP2 \n (0, 1) \t ; THETA(ODECLQ2F) TVCLQ2 \n {ELIM[2]}",
         "1 \t ; ETA(ODER1R) ETA ON R1 \n 1 \t ; ETA(ODEKAR) ETA ON KA \n 1 \t ; ETA(ODEVCR) ETA ON VC \n 1 \t ; ETA(ODEVPR) ETA ON VP \n 1 \t ; ETA(ODECLQR) ETA ON CLQ \n 1 \t ; ETA(ODEVP2R) ETA ON VP2 \n 1 \t ; ETA(ODECLQ2R) ETA ON CLQ2 \n {ELIM[3]}",
         "C = A(2)/VC \n \n DADT(1) = - KA * A(1) \n DADT(2) = KA * A(1) -{ELIM[4]} - CLQ * (A(2)/VC - A(3)/VP) - CLQ2 * (A(2)/VC - A(4)/VP2) \n DADT(3) = CLQ * (A(2)/VC - A(3)/VP) \n DADT(4) = CLQ2 * (A(2)/VC - A(4)/VP2) \n DADT(5) = {ELIM[4]}",
         "IPREDC = A(2)/VC \n IPREDU = A(5)"
      ]
   ],

   "ELIM":[
      ["CLC = THETA(ODECLCF) * EXP(ETA(ODECLCR))",
         "(0, 2) \t ; THETA(ODECLCF) TVCLC",
         "1 \t ; ETA(ODECLCR) ETA ON CLC",
         "CLC * C"
      ],
      ["VM = THETA(ODEVMF) * EXP(ETA(ODEVMR)) \n \n KM = THETA(ODEKMF) * EXP(ETA(ODEKMR))",
         "(0, 20) \t ; THETA(ODEVMF) TVVM \n (0, 10) \t ; THETA(ODEKMF) TVKM",
         "1 \t ; ETA(ODEVMR) ETA ON VM \n 1 \t ; ETA(ODEKMR) ETA ON KM",
         "VM * C/(KM + C)"
      ]
   ],


   "BIOAVAIL": [
      ["",
         "",
         ""
      ],
      ["F1 = THETA(BIOAVAIL)",
         "(0, 0.9, 1) \t ; THETA(BIOAVAIL) TVF",
         ""
      ],
      ["TEMP = EXP(THETA(BIOAVAILF) + ETA(BIOAVAILR)) \n F1 = TEMP/(1 + TEMP)",
         "3 \t ; THETA(BIOAVAILF) TVLOGITF",
         "1 \t ; ETA(BIOAVAILR) ETA ON LOGITF"
      ]
   ],

   "RESERRC":[
      ["* (1 + EPS(RESERRCP))",
         "0.01 \t ; EPS(RESERRCP) VARIANCE OF PROPORTIONAL ERROR FOR PLASMA OBSERVATION"
      ],
      ["* (1 + EPS(RESERRCP)) + EPS(RESERRCA)",
         "0.01 \t ; EPS(RESERRCP)) VARIANCE OF PROPORTIONAL ERROR FOR PLASMA OBSERVATIONS \n 0.1 \t ; EPS(RESERRCA) VARIANCE OF ADDITIVE ERROR FOR PLASMA OBSERVATIONS"
      ]
   ],

   "RESERRU":[
      ["+ EPS(RESERRUA)",
         "0.1 \t ; EPS(RESERRUA) VARIANCE OF ADDITIVE ERROR FOR URINE OBSERVATIONS"
      ],
      ["* (1 + EPS(RESERRUP))",
         "0.01 \t ; EPS(RESERRUP) VARIANCE OF PROPORTIONAL ERROR FOR URINE OBSERVATIONS"
      ],
      ["* (1 + EPS(RESERRUP)) + EPS(RESERRUA)",
         "0.01 \t ; EPS(RESERRUP)) VARIANCE OF PROPORTIONAL ERROR FOR URINE OBSERVATIONS \n 0.1 \t ; EPS(RESERRUA) VARIANCE OF ADDITIVE ERROR FOR URINE OBSERVATIONS"
      ]
   ]

   }

Note again, the use of THETA(parameter identifier), e.g.,

(-4,.7,4) \t; THETA(CL~WT)

for ALL initial estimate token text (THETA, OMEGA, and SIGMA).

Example 3 tokens file: json

The Options file

The options file is traditional, exhaustive search. Note that the NONMEM timeout is long (9600 seconds), as the run time for the ODE solution is long.

The user should provide an appropriate path for “nmfe_path”. NONMEM version 7.4 and 7.5 are supported.

Note that, to run in the environment used for this example, the directories are set to:

"working_dir": "u:/pyDarwin/example3/working",
"temp_dir": "u:/pyDarwin/example3/rundir",
"output_dir": "u:/pyDarwin/example3/output",

It is recommended that the user set the directories to something appropriate for their environment. If directories are not set, the default is:

{user_dir}\pydarwin\{project_name}

In either case, the folder names are given in the initial and final output to facilitate finding the files and debugging.

{
 "author": "Certara",

 "algorithm": "EX",
 "exhaustive_batch_size": 100,

 "working_dir": "u:/pyDarwin/example3/working",
 "temp_dir": "u:/pyDarwin/example3/rundir",
 "output_dir": "u:/pyDarwin/example3/output",
 "num_parallel": 4,

 "crash_value": 99999999999,

 "penalty": {
     "theta": 2,
     "omega": 2,
     "sigma": 2,
     "convergence": 100,
     "covariance": 100,
     "correlation": 100,
     "condition_number": 100,
     "non_influential_tokens": 0.00001
 },

 "remove_run_dir": false,

 "nmfe_path": "c:/nm744/util/nmfe74.bat",
 "model_run_timeout": 9600
}

Example 3 options file: json

Execute Search

Usage details for starting a search in pyDarwin can be found here.

See “Examples” for additional details about accessing example files.

Initialization output should look like:

[12:30:54] Options file found at ..\examples\user\Example3\options.json
[12:30:54] Preparing project working folder...
[12:30:54] Preparing project output folder...
[12:30:54] Preparing project temp folder...
[12:30:54] Model run priority is below_normal
[12:30:54] Using darwin.MemoryModelCache
[12:30:54] Project dir: c:\fda\pyDarwin\examples\user\Example3
[12:30:54] Data dir: c:\fda\pyDarwin\examples\user\Example3
[12:30:54] Project working dir: u:/pyDarwin/example3/working
[12:30:54] Project temp dir: u:/pyDarwin/example3/rundir
[12:30:54] Project output dir: u:/pyDarwin/example3/output
[12:30:54] Writing intermediate output to u:/pyDarwin/example3/output\results.csv
[12:30:54] Models will be saved in u:/pyDarwin/example3/working\models.json
[12:30:54] Template file found at ..\examples\user\Example3\template.txt
[12:30:54] Tokens file found at ..\examples\user\Example3\tokens.json
[12:30:54] Search start time = Sun Jul 31 12:30:54 2022
[12:30:54] Total of 324 to be run in exhaustive search
[12:30:54] NMFE found: c:/nm744/util/nmfe74.bat
[12:30:54] Not using Post Run R code
[12:30:54] Not using Post Run Python code
[12:30:54] Checking files in u:\pyDarwin\example3\rundir\0\001
[12:30:54] Data set # 1 was found: c:\fda\pyDarwin\examples\user\Example3/OralBolus_PlasmaUrine_ResetCpt2.csv