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Back to the forum  Query: 2018-04-20 22:31 CEST (UTC+2h)
 
Relaxation
Junior

Germany,
2018-02-13 15:37

Posting: # 18414
Views: 1,433
 

 So you made a baseline correction and now the team discusses ANCOVA [General Sta­tis­tics]

Hello everybody.

Because I was A) not able to find any post that even remotely dealed with this issue and B) had some discussion lately that might also betide anybody else and C) have some spare time and D) was bewildered that this issue caused so much discussion, I would like to show a simple example why in BE/BA the fancy stuff is not necessarily the correct approach.
May be boring for the experienced biometrician/statistician, but was enlightening for a lot of my colleagues.
Remember, you can stop reading at any time, just saying :-D.

We got involved in discussing the evaluation of an endogenous substance (including a pre-dose profile for baseline correction), where we criticized that no baseline correction was implemented at all and, therefore, their conclusion on the compared products was not valid :no:.
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.

From our point of view, this is not correct; as as a matter of fact, the use of a covariate should be considered if there actually is some impact of the starting value on the outcome. Likely fine for clinical endpoints and some PD parameters, but what should be the mechanistical concept in case of an AUC?
:ponder:

So, we did not agree and were able to enforce a "proper" baseline correction by subtraction. This was finally implemented and ... resulted in the exact same results :confused:. By closer examination it was revealed that the same model was applied, i.e. the ANCOVA was conducted considering the values after baseline-correction. Nice try...

As a little illustration to be used when such a discussion comes up consider these values:
Subject Treat Base Measure
   1      T    10    100
   1      R     0     50
   2      T    12    110
   2      R     0     45
   3      T     8     90
   3      R     0     55
   4      T    14    105
   4      R     0     60
   5      T     6     95
   5      R     0     40


Easy to see, we have a pure difference of 50 for T-R and 40 if baseline is considered. Hint: these are not real data.

Now, whatever software you use, the evaluation should resemble something like this:
(if SAS: PROC GLM DATA=XXX;)
CLASS Treatment Subject;
MODEL Result=Treatment Subject Baseline

where "Baseline" is used in case of inclusion of the covariate.
So what results do we get in which evalution (point estimates and 95%CI):
Raw values:                50 ( 36- 64)
ANCOVA:                    45 (-22-112)
Baseline corrected values: 40 ( 26- 54)
ANCOVA:                    45 (-22-112)

As you can see, use of the ANCOVA approach gives us results differing from what we get from the "expected" calculation. And as is to be expected due to the concept of an ANOVA it does not matter, whether you use the change from baseline or the end value. So, in particular in those cases, where officially the baseline-correction in accordance with the guidelines was implemented, but an ANCOVA was conducted...).
And good luck finding a medical writer who will recognize this in the SAS code or Phoenix output or...

Why is this important? Well, in the case that started our discussion, the improper ANOVA shifted the point estimate and allowed to conclude on a statistically significant difference. That is, it allowed to avoid crossing the 100% threshold. Could have been 125% as well.
In the presented case above on the other hand, the improper ANCOVA markedly increased the variance (the baseline values are admittedly a little bit one-sided), so hiding a difference might be possible.

As always, please do not hesitate to correct, add and challenge, if there is something wrong.

Best regards,

Relaxation.


Edit: Tabulators changed to spaces and BBcoded; see also this post #6. [Helmut]
martin
Senior

Austria,
2018-02-15 17:14

@ Relaxation
Posting: # 18424
Views: 1,111
 

 So you made a baseline correction and now the team discusses ANCOVA

Dear Everbody,

Dealing with endogenous compounds is tricky and here are some more thoughts you may find helpful

This could be considered as change from baseline problem and you may have a look at Stephen Senns work on this topic relating to ANCOVA (e.g. Statist. Med. 2006; 25:4334–4344. https://doi.org/10.1002/sim.2682 )

You may find also this article of interest addressing adjustment of endogenous levels in PK modeling: Bauer, A. & Wolfsegger, M.J. Eur J Clin Pharmacol (2014) 70: 1465. https://doi.org/10.1007/s00228-014-1759-x

Best regards & hope this helps

Martin
ElMaestro
Hero

Denmark,
2018-02-15 21:30

@ Relaxation
Posting: # 18425
Views: 1,009
 

 So you made a baseline correction and now the team discusses ANCOVA

Hi Relaxation,

I read your post so many times now and I am somewhat confused.
What were you actually trying to prove or disprove?

Inclusion of a covariate one way or another makes an implicit assumption of a relationship that can be said to be linear between the covariate and the response (in the presence of the factors).

If the variance goes full Tasmanian devil on you when you include the covariate then perhaps this assumption is...well... of a nature that has the potential to cause some degree of debate. And then that is where the problem truly is.

In contrast to classical anovas where an additional factor will always decrease the unexplianed variance (or leave it unchanged, academically), the inclusion of a covariate is not necessarily having this effect.

Help me, please, I really wish to understand what this is all about.

I could be wrong, but…


Best regards,
ElMaestro

- Bootstrapping for dissolution data is a relatively new hobby of mine.
Relaxation
Junior

Germany,
2018-02-16 10:19

@ ElMaestro
Posting: # 18426
Views: 975
 

 So you made a baseline correction and now the team discusses ANCOVA

Hi ElMaestro

» I read your post so many times now and I am somewhat confused.

And I read it over so many times exactly to avoid being too confusing. Sorry for failing.

» What were you actually trying to prove or disprove?

Uh, nothing, really, I only wanted to share my experience with this discussion in a BA-setting as I found it difficult to find anything that was just a simple statement or experience shared. And in favour of our position (Baselines are not(!) a good covariate in PK and will potentially result in a misleading result).

» Inclusion of a covariate one way or another makes an implicit assumption of a relationship that can be said to be linear between the covariate and the response (in the presence of the factors).
»
» If the variance goes full Tasmanian devil on you when you include the covariate then perhaps this assumption is...well... of a nature that has the potential to cause some degree of debate. And then that is where the problem truly is.

Nothing to add here. Back at university, I essentially learned that covariates magically scientifically corrects for an influence, can be implemented by people who know how to do it and is always good. But because I am only a pharmacist I would not need anything more than a t-test anyway.
Remembering the qualities of the two teachers we enjoyed I will just say that statistics is not the most important issue for some university degrees.

» In contrast to classical anovas where an additional factor will always decrease the unexplianed variance (or leave it unchanged, academically), the inclusion of a covariate is not necessarily having this effect.
»
» Help me, please, I really wish to understand what this is all about.

Again, I am sorry. I thought it might be helpful for others who happen to come across the discussion whether or not to implement a baseline as a covariate in a PK evaluation to show in a simple made-up example how this has an impact and that it is not an appropriate idea.

Best regards,
Relaxation
zizou
Junior

Plzeň, Czech Republic,
2018-02-25 00:54

@ Relaxation
Posting: # 18459
Views: 631
 

 So you made a baseline correction and now the team discusses ANCOVA

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 :-D.

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)

[image]
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.
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