Bioequivalence and Bioavailability Forum

Hi Relaxation.

❝ But people said, an ANCOVA was used, as recommended by the "Guideline on adjustment for baseline covariates in clinical trials", so this approach should suffice as a baseline correction.

I also think they took wrong cookbook.
You know EMA 1401 (page 9):

For endogenous substances, the sampling schedule should allow characterisation of the endogenous baseline profile for each subject in each period. Often, a baseline is determined from 2-3 samples taken before the drug products are administered. In other cases, sampling at regular intervals throughout 1-2 day(s) prior to administration may be necessary in order to account for fluctuations in the endogenous baseline due to circadian rhythms (see section 4.1.5).

They done it Ok. but according to EMA 1401 section 4.1.5: Endogenous substances

If the substance being studied is endogenous, the calculation of pharmacokinetic parameters should be performed using baseline correction so that the calculated pharmacokinetic parameters refer to the additional concentrations provided by the treatment. ...

the baseline correction must be done before PK analysis (subtraction of AUC, i.e. whole profile, each sample time has own baseline from predose conc. e.g. day before, or subtraction of mean of several predose concentrations).

Remember, you can restart reading at any time, just saying .

In the study you described there wasn't planned to do baseline correction before PK analysis. But then, theoretically in situation with the circadian rhythms, the maximum concentration from raw uncorrected data and the maximum concentration from baseline corrected data (i.e. after subtraction of predose profile) can be in different time - so different concentration would enter into the calculation.
(Not happened in the study ... results were completly the same when calculation without/with baseline correction.)

❝ Hint: these are not real data.

I have such data too. x)
For simplicity my data are little bit parallel (and as in parallel design but it could be made more complicated ...).
Artificial data example:

Subject Treatment C_max Baseline
      1         1   100     10.0
      2         1    90      9.0
      3         1   110     11.0
      4         1    80      8.0
      5         1   120     12.0
      6         1   100     10.0
      7         2    55      5.0
      8         2    50      4.5
      9         2    60      5.5
     10         2    45      4.0
     11         2    65      6.0
     12         2    55      5.0
C_max of 2(R) = C_max of 1(T) / 2 + 5
Baseline of 1(T) = C_max of 1(T) / 10
Baseline of 2(R) = Baseline of 1(T) / 2 ... (don't look for anything behind it)

This example is perfectly linear and slopes of both treatment in Regression Analysis are the same (although in real study I would not expect the linearity much).

For R users the data are:
n=12
data=matrix(data=0,nrow=n,ncol=4,byrow=TRUE)
colnames(data)=c("Subject","Treatment","C_max","Baseline")
for (i in 1:n){
 data[i,"Subject"]=i # Subject.
}
for (i in seq(1,n/2,1)){
 data[i,"Treatment"]=1 # Treatment T.
}
for (i in seq(n/2+1,n,1)){
 data[i,"Treatment"]=2 # Treatment R.
}
data[,"C_max"]=c(100,90,110,80,120,100,50,45,55,40,60,50)
data[,"Baseline"]=data[,"C_max"]/10
for (i in seq(n/2+1,n,1)){ # shift of data for treatment R only.
 data[i,"C_max"]=data[i,"C_max"]+5
}

data[,"C_max"]=log(data[,"C_max"])
data[,"Baseline"]=log(data[,"Baseline"])

plot(data[,"Baseline"], data[,"C_max"], title=title("ANOVA versus ANCOVA - Artificial Example"), type="p", col="black", lwd=1, xlab=expression(ln~(Baseline)), ylab=expression(ln~(C[max])), las=1)
points(data[data[,"Treatment"]==1,"Baseline"], data[data[,"Treatment"]==1,"C_max"], type="p", col="green", lwd=2, xlab="Baseline", ylab=expression(C[max]), las=1)
points(data[data[,"Treatment"]==2,"Baseline"], data[data[,"Treatment"]==2,"C_max"], type="p", col="blue", lwd=2, xlab="Baseline", ylab=expression(C[max]), las=1)
abline(v=mean(data[,"Baseline"]), lty=3)

There is always one direction (slope) of "mean correction" in ANCOVA (something between slopes of linear regression of T and R - in this example slopes are the same). So means are "corrected" in the direction to the mean baseline (dashed line) as ilustrated in figures if it is keep simple (not complicated e.g. with missings - not balanced sequences). Left side raw data, right side ln-data (of course the same because both axes were ln transformed - that's why I didn't used your data with baseline=0 for R).

Of course, it is not expected to have different baseline for T and R in randomized BE study, so... it's only artificial example (as well as your data).

Anyway the differences of means of T and R:
Raw values: mean of R = 55, 20% of 55 is 11 (so difference from -11 to 11 could be "Ok." - without confidence x) )
difference T-R from ANOVA:                 45
difference T-R from ANCOVA:                -5

From the graphical interpretation of simple example of ANCOVA, if mean(Baseline_conc)ofT = mean(Baseline_conc)ofR = mean(Baseline_conc) then no correction is applied (means are the same) and PE from ANCOVA = PE from ANOVA.
But with more and more difference which is depending on the luck/misfortune of the randomization of subjects we can get more "corrected" means. It seems that we could conclude then something as "Treatments are equivalent ...; evident differences observed by simple comparison of mean of T versus mean of R are caused by different baseline values"?
So ANCOVA does not look as the correct baseline correction in this artificial example.

Moreover some burning points which are not to be answered:
How the sample size was calculated for the BE with ANCOVA evaluation.
Ignoring additional assumptions for ANCOVA.
PE is called in the guideline as GMR (for ANOVA it can be "tolerated" but for ANCOVA, GMR could be far away)
Acceptance BE limits still 0.8-1.25 (90% CI for PE from ANCOVA is different than 90% CI for PE from ANOVA with these limits set in guidelines).
(I would bet that 90% CI from ANCOVA would be always(?) wider ... so then this method would not be the best choise for sponsors.)

Forget it.