## ANOVA Model: Factors [General Sta­tis­tics]

Hi Scopy,

❝ […] (although I'm still looking for a much more simplified book).

Maybe Hauschke et al.1

❝ However I noticed they only considered carryover factor, formulation factor and the period factor in the ANOVA model. I don't get to see the sequence factor as stipulated in the WHO guidelines.

❝ Could it be that the Carryover factor is one and same as the Sequence factor?

Exactly. They are synonyms. An equal carryover does not hurt (will not bias the treatment effect). However, an unequal one will.

❝ I'd appreciate is someone could explain this to me as if I were a kindergarten pupil .

I’ll try. Which factors do we have in a 2×2 crossover? Subjects2 (1–n), treatments (T and R), periods (1 and 2), and sequences (RT and TR). Actually we have two groups of subjects, one is treated in the order RT and the other in the order TR. Hence, in the statistical literature (not about BE) sometimes you find ‘group’ instead of ‘sequence’… Let’s explore which effects will influence the treatment effect. Simple example: Untransformed data, true values of the reference 100 and of the test 95, balanced sequences. Therefore, we can work with unadjusted means.
• Period effect: 0%
Sequence (carryover) effects: RT 0%, TR 0%
                       period     sequence   sequence            1      2      means      RT             100     95       97.5      TR              95    100       97.5 period means         97.5   97.5     97.5 treatment means  R  100                  T   95                T/R   95.00%
Unbiased treatment effect in the absence of a period effect.
Unbiased treatment effect in the presence of equal carryover effects.

• Period effect: +20%
Sequence (carryover) effects: RT 0%, TR 0%
                       period     sequence   sequence            1      2      means      RT             100    114      107      TR              95    120      107.5 period means         97.5  117      107.25 treatment means  R  110                  T  104.5                T/R   95.00%
Unbiased treatment effect in the presence of a period effect..
Unbiased treatment effect in the presence of equal carryover effects.

• Period effect: +20%
Sequence (carryover) effects: RT +20%, TR +20%
                       period     sequence   sequence            1      2      means      RT             100    133      116.5      TR              95    140      117.5 period means         97.5  136.5    117 treatment means  R  120                  T  114                T/R   95.00%
Unbiased treatment effect in the presence of a period effect.
Unbiased treatment effect in the presence of equal carryover effects.

• Period effect: 0%
Sequence (carryover) effects: RT +10%, TR +20%
                       period     sequence   sequence            1      2      means      RT             100    104.5    102.25      TR              95    120      107.5 period means         97.5  112.25   104.875 treatment means  R  110                  T   99.75                T/R   90.68%
Biased treatment effect in the presence of unequal carryover effects.
Problems:
• No method exists to correct the bias if there is a true unequal carryover.
• A test for unequal carryover has low sensitivity (you may be hit by false positives).
Likely unequal carryover doesn’t exist in a properly designed study (sufficiently long washout). The test should go to the statistical waste bin and is of historic interest only (EMA GL: “A test for carry-over is not considered relevant and no decisions regarding the analysis (e.g. analysis of the first period only) should be made on the basis of such a test.”).

1. Hauschke D, Steinijans VW, Pigeot I. Bioequivalence Studies in Drug Development: Methods and Applications. New York: Wiley; 2007.
2. Since subjects are uniquely coded, stating ‘subject(sequence)’ in the model is superfluous. Say ‘subject 1’ is in the sequence ‘RT’. There is no ‘subject 1’ in the sequence ‘TR’, right? Using ‘subject(sequence)’ instead of simply ‘subject’ drives El­Maestro’s Silly-O-Meter as far as it will go.
Try the simple model instead. You will get exactly the same PE and residual error and therefore, the CI as in the model stated in the guidelines. The only difference is that you get rid of the many lines in the software’s output stating just “not estimable” (Phoenix/WinNonlin) or “.” (SAS).

Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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