# NLME Tip:  How do I obtain the intersubject CV%?

**URL:** <https://forum.certara.com/t/nlme-tip-how-do-i-obtain-the-intersubject-cv/2446>\
**Category:** Phoenix WNL basics\
**Created:** [July 9, 2012, 8:28pm UTC](https://forum.certara.com/t/nlme-tip-how-do-i-obtain-the-intersubject-cv/2446 "2012-07-09T20:28:06Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![ana.henry](https://sea1.discourse-cdn.com/certara/user_avatar/forum.certara.com/ana.henry/32/2578_2.png) [@ana.henry](https://forum.certara.com/u/ana.henry)\
**Post date:** [July 9, 2012, 8:28pm UTC](https://forum.certara.com/t/nlme-tip-how-do-i-obtain-the-intersubject-cv/2446/1 "2012-07-09T20:28:06Z")

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Q: How do I obtain the intersubject CV% for structural parameters from NLME output? A: In the core output (text output) there is a matrix printed called Omega5chol which contains the approximate CV (not in %) as the square root of the variances (diagonal elements).

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**Author:** ![Samer\_Mouksassi](https://avatars.discourse-cdn.com/v4/letter/s/ce7236/32.png) [@Samer\_Mouksassi](https://forum.certara.com/u/Samer_Mouksassi)\
**Post date:** [August 8, 2017, 3:26pm UTC](https://forum.certara.com/t/nlme-tip-how-do-i-obtain-the-intersubject-cv/2446/2 "2017-08-08T15:26:41Z")

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Some colleagues have pointed out this tip/topic and we need to clarify for new users:

a cholesky is just a decomposition of a positive definite matrix that has some nice uses in optimization and simulations.  
[https://en.wikipedia.org/wiki/Cholesky\_decomposition](https://en.wikipedia.org/wiki/Cholesky_decomposition).

what does it mean a Clearance with log normal distribution CL=tvCL \*exp(nCL) that has a BSV of 40 % ? this is not really intuitive and we know that the distribution is not symmetric

suppose you have an output like this:

omegaCL\<-0.098784 # variance of CL random effects

iivCL\<-100\*sqrt(exp(omegaCL)-1) # formula for CV % of log normal  
iivCL 32.22233 %

Still this number is hard to interpret what I need to know as a clinician is how much fold increase or decrease of CL I can expect with random variation ?

for the above model: CL=tvCL \*exp(nCL)  
we can compute where does say 90 % of the population is

> exp(qnorm(c(0.05, 0.95), 0, sqrt(omegaCL)))  
> [1] 0.596321 1.676949

where does say 50 % of the population is ?

> exp(qnorm(c(0.25, 0.75), 0, sqrt(omegaCL)))  
> [1] 0.8089715 1.2361375

this tells us that 90 % of patients will be within 0.6-1.68 and that 50 % will be within 0.8-1.24

We can even draw the distribution and show limits of interest.

for other models:  
EC50 =tvEC50 + nEC50

or

F = ilogit(F+ nF)  
or  
V =exp(tvV+nV)

I leave it as an exercise to the user the same concepts apply when in doub use simulations !