Freedom for replicate bears [🇷 for BE/BA]

posted by d_labes  – Berlin, Germany, 2009-04-17 14:06 (5511 d 02:14 ago) – Posting: # 3554
Views: 72,213

Replicate berlin buddy bears

Dear all, especially the Ruses among you,

(ok, the category could also has been Regulatives/guidelines)
continuing my deeper look into R exemplified by the source code of bear I noticed the following:

The key statement in bear for evaluating replicate BE studies (astonishing enough claimed as only 2-sequence designs allowed?) is
  model <- lme(y~seq+prd+drug, random=~1|subj, data=blabla, method="REML")
with y the PK parameter under evaluation (raw or log-transformed).

This is the equivalent of SAS Proc MIXED code:
  Proc MIXED data=BlaBla ;
    class subj drug prd seq;
    model y=drug prd seq /ddfm=BETWITHIN;
    random subj;
    estimate 'T-R' tmt -1 1 /cl alpha=0.1;

The used model assumes equal within/between variabilities for Test and Reference and also no subject-by-treatment-interaction, if I'm right.
This is very stringent and consequent, if we talk about ABE.

But in real world there are regulators out there! :-P
And some of them do not like consequent scientific assumptions / models.
Thus it happens that the FDA model for evaluating ABE within replicate designs (discussed occasionally here in the forum, SEARCH!!!) must have different within/between variabilities for Test and Reference and also subject-by-treatment-interaction included in the model.

After reading again tons of Websites (seems nobody evaluates x-over studies with R) I came up with the following attempt in R:
  model2 <- lme(y~ drug + prd + seq,
# this random statement fits a symmetric positive definite covariance matrix,
# identical to UN in SAS???
                random= ~ tmt-1|subj,
                #different within variabilities                 
                weights=varIdent(form = ~ 1 | drug),
                data=BlaBla, method="REML")

This code gives for the bear built in dataset the same covariance parameters as the SAS code from the FDA statistical guidance except the fact that SAS Proc MIXED uses variances and the lme() code uses standard deviations.
--- snip ----
                             The Mixed Procedure
                              Estimated G Matrix

            Row    Effect    tmt    subject        Col1        Col2
              1    tmt       R       1          0.02220    0.002729
              2    tmt       T       1         0.002729     0.01492

                         Covariance Parameter Estimates

                                              Standard         Z
 Cov Parm     Subject    Group    Estimate       Error     Value        Pr Z
  UN(1,1)      subject              0.02220    0.009077      2.45      0.0072
  UN(2,1)      subject             0.002729    0.005318      0.51      0.6079
  UN(2,2)      subject              0.01492    0.006095      2.45      0.0072

  Residual     subject    tmt R    0.000058    0.000023      2.50      0.0061
  Residual     subject    tmt T    0.000011    4.762E-6      2.37      0.0090

R (have changed drug to tmt, prd to period, subj to subject)
cat("G matrixn")
G matrix
Random effects variance covariance matrix
          tmtR      tmtT
tmtR 0.0222050 0.0027286
tmtT 0.0027286 0.0149240
  Standard Deviations: 0.14901 0.12216
Linear mixed-effects model fit by REML
  Data: PKparms
  Log-restricted-likelihood: 98.1282
  Fixed: y ~ tmt + period + sequence
 (Intercept)         tmtT      period2      period3      period4 sequenceTRRT
  7.35627371   0.06373952  -0.06170010  -0.05964129   0.00348174   0.00266416

Random effects:
 Formula: ~tmt - 1 | subject
 Structure: General positive-definite, Log-Cholesky parametrization
         StdDev     Corr
tmtR     0.14901302 tmtR
tmtT     0.12216340 0.15
any body out there who knows how to get more decimals here? Residual 0.00335726     

Variance function:
 Structure: Different standard deviations per stratum
 Formula: ~1 | tmt
 Parameter estimates:
      T       R
1.00000 2.27674
Number of Observations: 56
Number of Groups: 14

--- end snip ---
I was soooo happy: An old SAS dog, nothing learned else, has become a Ruser! :-D

But then it came to the freedom to some degree:
--- snip ---
SAS: now with the DDFM=SATTERTHWAITE (DDFM = denominator degree of freedom method)
          Type 3 Tests of Fixed Effects

               Num     Den
 Effect         DF      DF    F Value    Pr > F

 Drug            1      12       1.79    0.2053
 prd             3    14.3       2.59    0.0930
 seq             1      12       0.00    0.9623

         numDF denDF  F-value p-value
tmt          1    38 1.793900  0.1884
period       3    38 2.593551  0.0667
sequence     1    12 0.002331  0.9623

--- end snip ---

Ok, I have learned (by reading again tons of websites) that R has no package with Satterthwaite denominator degrees of freedom in mixed models.
But all other available DDFM in Proc MIXED gave not a denDF=38 for the treatment effect. One gets always lower denDF in SAS and as a consequence of that wider 90% confidence intervals!

Thus my choice of software would be lme() and R because with that it is easier to make my sponsors happy :-D.
But the question is: Are regulators evenly happy with that?

Whats going on here? Do I miss anything in the R approach?
Or is the denominator DF question also like type III SumOfSquares? (I have read some Websites indicating that).

BTW: Parallel Bears (crossing at infinity according to the geometric axioms) have also same variance :-(. But this is another story.



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