Bioequivalence and Bioavailability Forum

if you look at my post I think I said it was the AUC paramater I was working with from the 4 period FDA ABAB template using the simulated data set.

I have not looked at the Cmax, but I will.

I have a recent email from Ana over at Pharsight: Please see below and let me know your thoughts. Evidently there has been confusion in the past and I am wondering whether it has been resolve (below).

"Some additional discussion about the questions that you asked about BE has taken place within Pharsight. I just wanted to give you an update.

1. We entered an enhancement on our tracking system “Provide additional output in Pop/Indiv Bioequivalence - sigmaD, sigmaWT (for subject by formulation interaction variance)”. WinNonlin is calculating this but not providing it in the output.
2. For certain designs the documentation has some information that might be useful to you:

For an RTRT/TRTR study, if the default model for replicated crossovers is used, which has a random model using type FA0(2), look at the Parameter and the Group_Level columns on the Parameter Key output workbook to determine which variance parameter is for the reference formulation and which is for the test formulation. In the following equations, it is assumed that the first output parameter is for the test formulation.

The within-subject variance of the test, sig_WT^2, and the within-subject variance of the reference, sig_WR^2, are in the output as:
sig_WT^2 = Var(Period*Formulation*Subject)_21
sig_WR^2 = Var(Period*Formulation*Subject)_22

The intra-subject CV's can be computed as:
IntraCV_T = 100%*sqrt(exp(sig_WT^2)-1)
IntraCV_R = 100%*sqrt(exp(sig_WR^2)-1)

The between-subject variance of test, sig_BT^2, the between-subject variance of reference, sig_BR^2, and the G matrix for the random model, can be computed as follows. This still assumes that the test formulation precedes the reference. The '_11' notation on the lambda parameters (which indicates that they are for the first random model and first group) has been dropped to improve readability:

G(1,1) = sig_BT^2 = lambda(1,1)^2
G(2,2) = sig_BR^2 = lambda(2,1)^2+lambda(2,2)^2
G(1,2) = rho*sig_BT*sig_BR = lambda(1,1)*lambda(2,1) (= between subject covariance for test and reference)

The subject-by-formulation interaction variance in general is sig_D^2 = sig_BT^2 + sig_BR^2 - rho*sig_BT*sig_BR, and can be computed from the above equations as:
sig_D^2=G(1,1)+G(2,2)-2*G(1,2)

The inter-subject CV's can be computed as:
InterCV_T = 100%*sqrt(exp(sig_BT^2)-1)
InterCV_R = 100%*sqrt(exp(sig_BR^2)-1)

If the CSH variance structure is used instead of FA0(2), the following equations change. This still assumes the first output parameter is for test and the second for reference.

G(1,1) = sig_BT^2 = cshSD(1)^2
G(2,2) = sig_BR^2 = cshSD(2)^2
G(1,2) = cshCorr * cshSD(1) * cshSD(2)"

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The parameter name or units is not in the file I have: it is from the FDA template, it is the same file for EMEA.

Here is the output from Phoenix. Now one has to look at Ana's email

Dependent Units Parameter Estimate
Data lambda(1,1)_11 0.85299471
Data lambda(1,2)_11 0.82840678
Data lambda(2,2)_11 8.34E-07
Data Var(Period*Formulation*Subject)_21 0.20211811
Data Var(Period*Formulation*Subject)_22 0.11739421

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Herr is my paramater key and the REFERENCE IS first. My file is RTRT

Dependent Units Parameter Source Type Bands Subject_Term Group_Term Group_Level
Data lambda(1,1)_11 Random No-Diag Factor Analytic 2 Subject
Data lambda(1,2)_11 Random No-Diag Factor Analytic 2 Subject
Data lambda(2,2)_11 Random No-Diag Factor Analytic 2 Subject
Data Var(Period*Formulation*Subject)_21 Repeated Variance Components Subject Formulation Formulation_R
Data Var(Period*Formulation*Subject)_22 Repeated Variance Components Subject Formulation Formulation_T


That is why the parameters are switched from yours.

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Edit: Merged with two later post. Note that you can edit your original post within 24 hours. [Helmut]

Hello friends, I am getting below output using this SAS code. I dont know why I am getting value 0 (I think it is a rounded value) for FA(2,2).
Please guide me.

proc mixed data=sample method=reml ITDETAILS CL=WALD ALPHA=0.1;
class Subject sequence period formulation;
model logDATA=sequence period formulation/ddfm=satterth;
random formulation/type=FA0(2) subject=subject G;
repeated/group=formulation subject=subject;
lsmeans formulation/pdiff cl alpha=0.1;
estimate 'T-R' formulation 1 -1 /CL ALPHA=0.1;
ods output Estimates=BLUEUN CovParms=COVUN AsyCov=ascovun;
run;

Dependent  Parameter                   Estimate
Ln(data)   FA(1,1)                     0.8530
Ln(data)   FA(1,2)                     0.8284
Ln(data)   FA(2,2)                     0
Ln(data)   Res(Formulation R*Subject)  0.2021
Ln(data)   Res(Formulation T*Subject)  0.1174

From above message the output 4 period replicate FDA template is repeated as follows:

Dependent Parameter Estimate
ln Cmax lambda(1,1)_11 is 0.82840679
ln Cmax lambda(1,2)_11 is 0.85299475
ln Cmax lambda(2,2)_11 is 5.63E-07
ln Cmax Var(Period*Formulation*Subject)_21 is 0.11739425
ln Cmax Var(Period*Formulation*Subject)_22 is 0.20211805

From Ana’s message the value for subj. formulation interaction(sig_D^2) is as follows:

(0.82840679)+(5.63E-07)-2*(0.85299475)= -0.87758

Here are my results from the same data set in Phoenix: my input structure is different
Data lambda(1,1)_11 0.85299471
Data lambda(1,2)_11 0.82840678
Data lambda(2,2)_11 8.34E-07
Data Var(Period*Formulation*Subject)_21 0.20211811
Data Var(Period*Formulation*Subject)_22 0.11739421

I used BABA for the input for the first subject. If you look at the Parameter Key and Group Levels on the Parameter Key Output Workbook in Phoenix I have first output parameter as reference not test. That is why there is transposition in the parameter values.

Not really, it's 100% normal result for pharmaceutical quality. Pharmacop. normally requires 95% to 105% content of the respective compound...