## No relationship between inter- and intra-subject CV [Power / Sample Size]

Hi arl_stat,

» Mostly in public domain, the inter subject CV of drug is not mentioned.

You fell into trap of wrong terminology. Even if a study was performed in a parallel design, one gets the total (a.k.a. pooled)

Simply: The total variance (which you observe in

» […] can we use this intra-subject CV to estimate sample size for parallel study design?

No.

» Is there any formula to calculate inter-subject CV using 90% confidence interval ranges and number of subjects?

No, since you need the

See also this post and followings.

» First can we calculate the sample size of 2 way crossover study design and then double the subjects and finalize the sample size for parallel study design?

No (see above). For ages rumors are swirling around a factor of two but that’s plain nonsense. Think about a drug with low

Run a – not too small! – pilot study or a TSD.*

» Mostly in public domain, the inter subject CV of drug is not mentioned.

You fell into trap of wrong terminology. Even if a study was performed in a parallel design, one gets the total (a.k.a. pooled)

*CV*– not the inter-subject*CV*.$$CV_{\textrm{total}}=\sqrt{\exp\left(\log_{e}(CV_{\textrm{inter}}^{2}+1)+\log_{e}(CV_{\textrm{intra}}^{2}+1)\right)-1}\tag{1}$$Simply: The total variance (which you observe in

*any*design) is the sum of inter- and intra-subject variances.$$s_{\textrm{total}}^{2}=s_{\textrm{inter}}^{2}+s_{\textrm{intra}}^{2}\tag{2}$$ The inter-subject*CV*is only accessible in a crossover study (see this post).» […] can we use this intra-subject CV to estimate sample size for parallel study design?

No.

» Is there any formula to calculate inter-subject CV using 90% confidence interval ranges and number of subjects?

No, since you need the

*CV*_{total}calculated acc. to \((1)\) from a crossover – or directly observed in a parallel design – and there is no relationship between*CV*_{inter}and*CV*_{intra}. Hence,*CV*_{intra}from a crossover*alone*does not help.See also this post and followings.

» First can we calculate the sample size of 2 way crossover study design and then double the subjects and finalize the sample size for parallel study design?

No (see above). For ages rumors are swirling around a factor of two but that’s plain nonsense. Think about a drug with low

*CV*_{intra}and polymorphic metabolism. Then the factor can easily be >5 and by doubling the sample size of a crossover the parallel study will be grossly underpowered. BTW, in rare cases*CV*_{intra}>*CV*_{inter}.Run a – not too small! – pilot study or a TSD.*

- Fuglsang A.
*Sequential Bioequivalence Approaches for Parallel Designs.*AAPS J. 2014;16(3):373–8.

doi:10.1208/s12248-014-9571-1. Open access.

—

Helmut Schütz

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

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*Dif-tor heh smusma*🖖Helmut Schütz

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

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### Complete thread:

- Parallel design from crossover CV arl_stat 2020-10-14 06:39
- No relationship between inter- and intra-subject CVHelmut 2020-10-14 11:00
- No relationship between inter- and intra-subject CV arl_stat 2020-10-14 15:02

- No relationship between inter- and intra-subject CVHelmut 2020-10-14 11:00