Interpolate covariates

Interpolate missing covariates

In this example ("examples/infnexa2"), the data set contains missing values for WT item and the model performs interpolation within the $INFN block. The main model control stream is shown below.

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$PROB  THEOPHYLLINE   POPULATION DATA
$INPUT      ID DOSE=AMT TIME CP=DV WT
$DATA       THEOPP
$SUBROUTINES  ADVAN2

$ABBR REPLACE INTVBL=WT     ;# to be interpolated
$ABBR REPLACE NULLVAL=0.0   ;# null
$ABBR DECLARE U(MAXIDS,NO)  ;# U(IS,I)=time of the non-null value of subj.
$ABBR DECLARE V(MAXIDS,NO)  ;# Ith non-null value of subj.
$ABBR DECLARE INTEGER IS    ;# SUBJECT number
$ABBR DECLARE IVAL(NO)      ;# IVAL(IS)= # of non-null values for subj. IS
$ABBR DECLARE INTEGER I, INTEGER J, INTEGER L
$INFN
 INCLUDE 'infnabbr'

$PK
;# THETA(1)=MEAN ABSORPTION RATE CONSTANT (1/HR)
;# THETA(2)=MEAN ELIMINATION RATE CONSTANT (1/HR)
;# THETA(3)=SLOPE OF CLEARANCE VS WEIGHT RELATIONSHIP (LITERS/HR/KG)
;# SCALING PARAMETER=VOLUME/WT SINCE DOSE IS WEIGHT-ADJUSTED
   KA=THETA(1)+ETA(1)
   K=THETA(2)+ETA(2)
   CL=THETA(3)*WT+ETA(3)
   SC=CL/K/WT

$THETA  (.1,3,5) (.008,.08,.5) (.004,.04,.9)
$OMEGA BLOCK(3)  6 .005 .0002 .3 .006 .4

$ERROR
   Y=F+EPS(1)

$SIGMA  .4
$TABLE ID DOSE TIME DV WT NOAPPEND FILE=THEOPPexa2

Here we use $ABBR REPLACE to assign aliases to WT and zero, and $ABBR DECLARE to declare helper variables. They are used in the included "infnabbr" file:

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    ;! $INFN FOR INTERPOLATING INDEPENDENT VARIABLE INTVBL
    IS=0
    IF (ICALL.EQ.1) THEN
       ;! FIRST PASS.  SAVE VALUES OF TIME & INDEP VAR. WHEN IT IS NON-NULL
       DO WHILE (DATA)
          IF (NEWIND < 2) THEN  ;! INITIALIZE NEW INDIVIDUAL
             IS=IS+1
             IVAL(IS)=0
          ENDIF
          IF (INTVBL /= NULLVAL) THEN     ;! SAVE NON-NULL VALUE
             IVAL(IS)=IVAL(IS)+1
             I=IVAL(IS)
             U(IS,I)=TIME
             V(IS,I)=INTVBL
          ENDIF
       ENDDO
       ;! SECOND PASS
       IS=0
       DO WHILE (DATA)
          IF (NEWIND < 2) THEN  ;! INITIALIZE NEW INDIVIDUAL
             IS=IS+1
             I=0
          ENDIF
          ;! IF INDEP VAR IS MISSING AND WAS ONLY NON-NULL ONCE, COPY IT
          IF (INTVBL == NULLVAL .AND. IVAL(IS) == 1) THEN
             INTVBL=V(IS,1)
          ELSE
             IF (INTVBL /= NULLVAL) THEN        ;! COUNT ANOTHER NON-NULL VALUE
                I=I+1
             ELSE                               ;! CURRENT RECORD HAS NULL VALUE
                IF (I==0) THEN ;! EXTRAPOLATE FROM FIRST 2 VALUES
                   J=1
                   L=2
                ELSEIF (I>0 .AND. I<IVAL(IS)) THEN ;! INTERPOLATE FROM VALUES BEFORE AND AFTER
                   J=I
                   L=I+1
                ELSEIF (I==IVAL(IS)) THEN  ;! EXTRAPOLATE FROM LAST 2 VALUES
                   J=I-1
                   L=I
                ENDIF
                SLOPE=(V(IS,J)-V(IS,L))/(U(IS,J)-U(IS,L))
                INTVBL=V(IS,J)+SLOPE*(TIME-U(IS,J))
             ENDIF
          ENDIF
       ENDDO
    ENDIF

The ICALL clause indicates that the interpolation is only done at the beginning of the problem.

Interpolate ODEs parameters

Another interpolation scenario is when the RHS of a differential equation system has time-varying covariates. For example, assume the RHS contains D_WT, the time-dependent variable counterpart of the weight data item WT. We will need calculate D_WT by interpolation before using it in $DES. This can be achieved with the following snippet.

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  $PK
  ;# initialize OLDTIME and OLDWT
  IF (NEWIND.LE.1) THEN
    OLDTIME=TIME
    OLDWT=WT
  ENDIF

  ;# calculate the slope for $DES
  DELTA_TIME=TIME-OLDTIME
  DELTA_WT=WT-OLDWT

  IF (DELTA_TIME>0) THEN
     SLOPE=DELTA_WT/DELTA_TIME
  ELSE
     SLOPE=0.
  ENDIF

  ;# save wt and time for next $PK record
  OLDTIME=TIME
  OLDWT=WT

  $DES
     D_WT=OLDWT+SLOPE*(T-OLDTIME) ;# D_WT is the value of WT at time T
     DADT(1)=D_WT                 ;# compute AUC of D_WT as a test

Here we simply compute a 1-D ODE for the AUC of weight. $DES uses linearly interpolated D_WT between every data record.