## N(μ, σ²) [Software]

Hi Yong,

» » » I prefer the following formula ：

» » » intersubject CV = sqrt(Var(Sequence*Subject)) / RefLSM

» » Why?

» Because this is also used for ln_transformed data.

No it isn’t! Back to the basics. The model of a 2×2×2 crossover assumes [

log(

Since

» Like one formula for intrasubject CV for both transformed and none transformed data, I think this formula is generally accepted both for transformed and none transformed data.

I think that for untransformed data dividing

» » » I prefer the following formula ：

» » » intersubject CV = sqrt(Var(Sequence*Subject)) / RefLSM

» » Why?

» Because this is also used for ln_transformed data.

No it isn’t! Back to the basics. The model of a 2×2×2 crossover assumes [

*sic*] IID. For log-transformed data:log(

*μ*∕_{T}*μ*) =_{R}*μ*−_{T}*μ*, which is_{R}*estimated*by the difference of the*LSM*s of log-transformed data*x*−_{T}*x*. Now it gets interesting (_{R}*i.e.*, the assumption!): In the balanced case for simplicity (where*n*_{1}=*n*_{2}and*n*=*n*_{1}+*n*_{2}),*x*−_{T}*x*follows a normal distribution_{R}*N*(log(*μ*∕_{T}*μ*), 2_{R}*σ*^{2}∕*n*)).Since

*σ*^{2}is unknown, it is estimated by the*MSE*from ANOVA. Then we can estimate*CV*= √ℯ^{MSE}− 1. Do you see*x*in this derivation? I don’t. Remember that the normal distribution is described by two parameters,_{R}*μ*and*σ*^{2}, which are independent. If you are interested in the variance component, please leave the mean(s) completely out of it (as it it correctly done in PHX/WNL for log-transformed data).» Like one formula for intrasubject CV for both transformed and none transformed data, I think this formula is generally accepted both for transformed and none transformed data.

I think that for untransformed data dividing

*MSE*by*LSM*goes back to Kem Phillips, who wrote*_{R}“*… σ being expressed as a percentage of a reference mean, that is, as a coefficient of variation; values of the difference in means are expressed as percentages of the same reference mean.*”

*That is not only not right; it is not even wrong!*”). Again: The mean and variance are*independent*. So, the more I think about it: Even my idea of using the weighted global mean does not make sense. Paraphrasing Stephen Senn:*Proving that apples are oranges by comparing the weight.*- Phillips KM.
*Power of the Two One-Sides Tests Procedure in Bioequivalence.*J Pharmacokinet Biopharm. 1990; 18(2): 137–44. doi:10.1007/BF01063556.

—

Cheers,

Helmut Schütz

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

Science Quotes

Cheers,

Helmut Schütz

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

Science Quotes

### Complete thread:

- Lack of IntersubjectCV in PHX - yicaoting, 2017-09-01 11:09
- CVs for untransformed data - mittyri, 2017-09-02 15:46
- CVs for untransformed data - Helmut, 2017-09-02 15:57
- CVs for untransformed data - yicaoting, 2017-09-02 17:50
- CVs for untransformed data - Helmut, 2017-09-02 19:20
- CVs for untransformed data - yicaoting, 2017-09-02 23:26
- N(μ, σ²) - Helmut, 2017-09-04 13:32
- N(μ, σ²) - yicaoting, 2017-09-05 02:46

- N(μ, σ²) - Helmut, 2017-09-04 13:32

- CVs for untransformed data - yicaoting, 2017-09-02 23:26

- CVs for untransformed data - Helmut, 2017-09-02 19:20

- CVs for untransformed data - yicaoting, 2017-09-02 17:50
- CVs for untransformed data - yicaoting, 2017-09-03 08:19
- CVs for untransformed data - mittyri, 2017-09-03 08:41
- CVs for untransformed data - yicaoting, 2017-09-04 11:35

- CVs for untransformed data - mittyri, 2017-09-03 08:41

- CVs for untransformed data - Helmut, 2017-09-02 15:57

- CVs for untransformed data - mittyri, 2017-09-02 15:46