## ANOVA Model: Factors [General Statistics]

Hi Scopy,

Maybe Hauschke

Exactly. They are synonyms. An

I’ll try. Which factors do we have in a 2×2 crossover? Subjects

❝ […] (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? Subjects

^{2}(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.

- 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).

*“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.”*).- Hauschke D, Steinijans VW, Pigeot I.
*Bioequivalence Studies in Drug Development: Methods and Applications.*New York: Wiley; 2007.

- 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).

—

Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮

Science Quotes

*Dif-tor heh smusma*🖖🏼 Довге життя Україна!_{}Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮

Science Quotes

### Complete thread:

- ANOVA Model: Carry Over Factor vs Sequence Factor Obinoscopy 2018-06-25 19:48 [General Statistics]
- ANOVA Model: FactorsHelmut 2018-06-26 12:38
- ANOVA Model: Factors Obinoscopy 2018-07-01 02:20
- ANOVA Model: Factors Helmut 2018-07-01 12:14

- ANOVA Model: Factors Obinoscopy 2018-07-01 02:20

- ANOVA Model: FactorsHelmut 2018-06-26 12:38