# Inflating clearance %CV for monte carlo simulation of off-diagonal omega matrix

**URL:** <https://forum.certara.com/t/inflating-clearance-cv-for-monte-carlo-simulation-of-off-diagonal-omega-matrix/3440>\
**Category:** Modelling and Simulation\
**Created:** [September 27, 2019, 5:49pm UTC](https://forum.certara.com/t/inflating-clearance-cv-for-monte-carlo-simulation-of-off-diagonal-omega-matrix/3440 "2019-09-27T17:49:34Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![dan.hines](https://avatars.discourse-cdn.com/v4/letter/d/76d3ee/32.png) [@dan.hines](https://forum.certara.com/u/dan.hines)\
**Post date:** [September 27, 2019, 5:49pm UTC](https://forum.certara.com/t/inflating-clearance-cv-for-monte-carlo-simulation-of-off-diagonal-omega-matrix/3440/1 "2019-09-27T17:49:34Z")

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I am trying to use a healthy volunteer population PK model in a monte carlo simulation to calculate a probability of target attainment analysis. In order to do this I need to inflate the variability of my clearance value to be more representative of a patient population. This is standard practice and easy for me when I have a diagonal omega matrix. But in this model, my omega matrix (covariance matrix) has off diagonal omega values associated with clearnace. So if I want to double the %CV value for clearance, and then in turn omega values, how do I calculate the impact of this clearance inflation on the off diagonal omega values?

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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:** [September 28, 2019, 3:42am UTC](https://forum.certara.com/t/inflating-clearance-cv-for-monte-carlo-simulation-of-off-diagonal-omega-matrix/3440/2 "2019-09-28T03:42:14Z")

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you can keep the correlation matrix as is and inflate the stdev part:

> <https://stats.stackexchange.com/questions/164471/generating-a-simulated-dataset-from-a-correlation-matrix-with-means-and-standard>

this works if your assumptions is to keep the correlation between random effects unaffected while inflating the variances

[user R on any other software to compute your "new " var cov matrix based on:](https://stats.stackexchange.com/questions/164471/generating-a-simulated-dataset-from-a-correlation-matrix-with-means-and-standard)

[inflationfactor ← 1.15](https://stats.stackexchange.com/questions/164471/generating-a-simulated-dataset-from-a-correlation-matrix-with-means-and-standard)

[mu ← c(0, 0, 0)](https://stats.stackexchange.com/questions/164471/generating-a-simulated-dataset-from-a-correlation-matrix-with-means-and-standard) # eta means

# this is your correlation matrix of omega

corMat ← matrix(c(1, 0.78, 0.23,

0.78, 1, 0.27,  
0.23, 0.27, 1),  
ncol = 3)

# you diagonals squareroots

stddev ← c(1.23, 0.92, 1.32) \* inflationfactor

covMat ← stddev %\*% t(stddev) \* corMat

plug the new covMat into your pml code