Bioequivalence and Bioavailability Forum

Dear Risherd,
I like to quickly respond to your question here.

1. In R, there is no way to calculate Type III MS (still same right now?) when we developed bear, but Type I MS. SAS can calculate both. Only when you have a complete crossover study design (same subj. # for ref. and test), Type I MS will be equal to Type III MS, as you can see from your bear output file. That's what we do with bear.
   
2. We validated ANOVA results obtained from bear with SAS whiles ago. And we got the same results using the dataset of a complete crossover study design.
   
3. I don't know how WNL calculates Type I/III MS. But I would strongly suggest that you probably should use SAS to confirm your validations.
   

❝ As you can see according to bear there is a sequence effect for AUCo-t while in WinNonlin it's not. This same situation happen with AUC0-Inf.

❝ However, the results for NCA, period, drug, seq(subj) effect, Confidence Intervals are exactly the same in both programs. So, why only the sequence effect is different?

Hi Risherd,

I think this issue is related to the denominator of the F-test.

The sequence factor level is unique between subjects (not within) and therefore the sequence effect is often tested with the between-subject-MS in the denominator - this is what the bogus random statement in SAS effectuates. I think WinNonLin doesn't do it this way.

I have a feeling Bear does this as well. It can be rather easily implemented, although at the outset R will not by default do it this way but will spit out a 'normal' table where all fixed factors are tested with the residual MS in the denominator.

Try this:

1. Look at the anova table from WNL and add the sums of squares incl. the residual. If they add up to the null sums of sqaures, then it means that WNL does not test the Seq effect with the between-subject variability in the denominator for the F-test.
   
2. Try to remove the bogus statement from the SAS script and compare directly with WNL.

PS - to yjlee: For type III SS you can use drop1 in R, or you can work around manually by adding and removing factors in the lm specification. For Seq, the latter might be the best option since Subjects are uniquely split out on Seqs. A drop1 with Subj, Seq, Per, Trt as factors will for Seq just give flat zero (plusminus some machine/convergence precision) due to the design.

Dear Risherd!

It is not helpful if you give numerical results without stating the data set you used (+ the version of WinNonlin). SAS’ Type III is not given by WinNonlin – only sequential and partial tests. Sequential = SAS Type I, but (quoting WinNonlin’s User’s Guide):

The partial tests in LinMix are not equivalent to the Type III method in SAS though they coincide in most situations.
The Partial Tests worksheet is created by testing each model term given every other model term. Unlike sequential tests, partial tests are invariant under the order in which model terms are listed in the Fixed Effects tab. Partial tests factor out of each model term the contribution attribut­able to the remaining model terms.
This is computed by modifying the basis created by the QR factorization to yield a basis that more closely resembles that found in balanced data.
For fixed effects models, certain properties can be stated for the two types of ANOVA. For the sequential ANOVA, the sums of squares are statistically independent. Also, the sum of the indi­­vi­­dual sums of squares is equal to the model sum of squares; which means the ANOVA represents a partitioning of the model sum of squares. However, some terms in ANOVA may be conta­mi­nat­ed with undesired effects. The partial ANOVA is designed to eliminate the conta­mi­nation problem, but the sums of squares are correlated and do not add up to the model sums of squares. The mixed effects tests have similar properties.

(my emphasis)

Or Phoenix User’s Guide:

Sequential Tests worksheet
   The Sequential Tests worksheet is created by testing each model term sequentially. The first model term is tested to determine whether or not it should enter the model. Then the second model term is tested to determine whether or not it should enter the model, given that the first term is in the model. Then the third model term is tested to determine whether or not it should enter the model, given that the first two terms are in the model. The model term tests continue until all model terms are exhausted.
The tests are computed using a QR factorization of the XY matrix. The QR factorization is seg­ment­ed to match the number of columns that each model term contributes to the X matrix.
Partial Tests worksheet
   The Partial Tests worksheet is created by testing each model term given every other model term. Unlike sequential tests, partial tests are invariant under the order in which model terms are listed in the Fixed Effects tab. Partial tests factor out of each model term the contribution attri­but­able to the remaining model terms.
This is computed by modifying the basis created by the QR factorization to yield a basis that more closely resembles that found in balanced data.
ANOVA
   For fixed effects models, certain properties can be stated for the two types of ANOVA. For the sequential ANOVA, the sums of squares are statistically independent. Also, the sum of the indi­vi­dual sums of squares is equal to the model sum of squares; which means the ANOVA repre­sents a partitioning of the model sum of squares. However, some terms in ANOVA may be contam­inat­ed with undesired effects. The partial ANOVA is designed to eliminate the contami­na­tion problem, but the sums of squares are correlated and do not add up to the model sums of squares. The mixed effects tests have similar properties.

Hi Risherd,

if you paste the ANOVA tables from Winnonlin and Bear then it will be possible thorugh the MS to immediately determine if the source of this phenomenon is linked to type I/III SS phenomena or to the F-test's denominator.

Thanks.