Add+Mult Error model feature

Phoenix Certara Forums Modelling and Simulation
1

Can anyone explain to me how to correctly parameterize the additive + multiplicative (combined error model). I understand how to integrate the additive portion of the error model in PML, however I am getting confused by the following “sqrt(1 + C^2 * (CMultStdev/sigma())^2))”.

Just as an example, if my proportional error is 30% what is the value of CmultStdev? 0.30? sqrt(0.30).

I am asking because I have a model already fit in NONMEM and I would like to transfer this over and use NLME to run some simulations?

Thanks!

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Hi Lance,

When you use this you get model code:

error(CEps = 1)
observe(CObs = C + CEps * sqrt(1 + C^2 * (CMultStdev/sigma())^2))

in model results outputs you will get:

Stdev0: (square root of CEps variance) additive error on concentration scale say you got : 2 mg/L
CMultStdev: proportional error on percent scale say you got: 0.20 ( 20%)

if you are coming from nonmem model with

Y=F +EPS(1) + FEPS(2)
then
$SIGMA
4 ; variance of additive var
0.04; variance of proportional part
VAR(Y) = VAR (EPS(1)) + F^2VAR(EPS(2))

var of eps(1) is sigma and so on

now if you want to deouble check here is the derivation:

Variance of CObs= Variance of (CEps * sqrt(1 + C^2 * (CMultStdev/sigma())^2))); we remove C since not a random variable

= Variance of (CEPS) *(1 + C^2 * (CMultStdev/sigma())^2))
( we square the second term variance rules, then sqrt is removed)

= Variance of (CEPS) + Variance of (CEPS)* C^2*(CMultStdev/sigma())^2

=Variance of (CEPS) + Variance of (CEPS)* C^2*(CMultStdev)^2/Variance of (CEPS)

=Variance of (CEPS)+ C^2*(CMultStdev)^2

so additive part variance is CEPS and porportional part variance is C^2*(CMultStdev)^2

we typically report square root of CEPS ( stdev0) and the proportional part in percent Cmultstdev