## 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) 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 CVtotal calculated acc. to $$(1)$$ from a crossover – or directly observed in a parallel design – and there is no relationship between CVinter and CVintra. Hence, CVintra from a crossover alone does not help.

» 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 CVintra 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 CVintra > CVinter.

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

Dif-tor heh smusma 🖖
Helmut Schütz

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