arl_stat
★

India,
2020-10-14 04:39
(250 d 15:26 ago)

Posting: # 21996
Views: 1,254

## Parallel design from crossover CV [Power / Sample Size]

Greetings to all !!

Hope all of you are safe in this pandemic situation.

Mostly in public domain, the inter subject CV of drug is not mentioned. Either intra-subject cv or confidence interval ranges are mentioned. So can we use this intra-subject CV to estimate sample size for parallel study design?

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

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?

Stay Safe.

Thank You

Helmut
★★★

Vienna, Austria,
2020-10-14 09:00
(250 d 11:05 ago)

@ arl_stat
Posting: # 21998
Views: 1,040

## No relationship between inter- and intra-subject CV

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

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes
arl_stat
★

India,
2020-10-14 13:02
(250 d 07:03 ago)

@ Helmut
Posting: # 22001
Views: 963

## No relationship between inter- and intra-subject CV

Thank you so much sir for your quick response and guidance.