Bioequivalence and Bioavailability Forum

Dear yuvrajkatkar

First of all I would like to tell u that if number of periods or sequences are greater than the treatments which are to be compared, this refers to a higher order crossover design, such a design u mentioned in ur query, model for the crossover design and higher order crossover design are different so point estimate obtained from both designs are not similar so there is no way to obtaine the CV for the 2 X 2 crossover design based on the information obtained from higher order crossover design, you should consider the point estimate and 90% CI from 2 X 2 crossover design to obtained the CV for 2X2 crossover design,

best regerds

rasheed.

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Edit: Full quote removed. Please delete anything from the text of the original poster which is not necessary in understanding your answer; see also this post! [Ohlbe]

Dear yuvrajkatkar,

❝ If we have 3 period, 2 treatment crossover study design and we have the information (point estimate, 90% CI and sample size) for this design then how to calculate Intra CV for 2 treatment- 2 sequence crossover study

Do it the same way as here in the forum and in Helmut's lectures described for the classical 2x2 cross-over but take into account the modifications of the CI formulas according to the replicate design.
These can be found f.i. in

Chow, Liu
"Design and analysis of bioavailability and bioequivalence studies"
Third edition 2009
CRC Press, Chapman and Hall
Chapter 9
-- or --
Chow, Liu
On assessment of bioequivalence under a higher-order crossover design
J. Biopharm. Stat. 2(2), 239-256 (1992)

For instance the CI in the log-domain for the 3-period-2-sequence dual design (TRR/RTT) is (Chow/Liu, chapter 9, page 269):

  CIlower,upper=point + t(alpha,2*N-3))*S*sqrt((3/8)*(1/n1+1/n2))

where n₁ and n₂ are the numbers of subjects in the two sequences. If you don't have these, assume n₁=n₂=N/2 in the formula. N is total sample size. The square root in the CI formula then reduces to sqrt(1.5/N).

In case you have only the CI without a point estimator calculate the latter according to:

  point = sqrt(upper*lower)

before taking the logarithm.

With a little school math you get s from that formula for the CI and from s the intra-subject CV according to the well known relationship:

  CV=sqrt(exp(s2)-1)*100   (in %)

For the criticasters : Of course this algorithm relies on the evaluation of replicate studies via the same ANOVA model as for a classical 2x2 crossover. If the CI was obtained via a Mixed model evaluation (but not in Europe!) the algorithm is at least a very good approximation. Moreover I have adjusted the degrees of freedom for the t-quantil to a model without carry-over.

In summary I disagree totally with rasheed's "... there is no way to obtain the CV for the 2 X 2 crossover design based on the information obtained from higher order crossover design ..."
Where there's a will, there's a way.