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ERROR MODELS

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#1 fogueri

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Posted 20 December 2017 - 04:05 PM

Can anyone explain what the error models mean -? multiplicative, additive, proportional errors?



#2 Simon Davis

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Posted 20 December 2017 - 04:31 PM

Hi Fogueri, this has been discussed a few times along with some associated topics; try looking at/following these threads;

 

https://support.cert...=multiplicative

 

https://support.cert...cative#entry121

 

https://support.cert...ative#entry4664

 

and maybe review http://onlinelibrary.../psp4.12161/pdf

 

https://support.cert...ative#entry4168

 

among others.

 

SImon



#3 fogueri

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Posted 20 December 2017 - 04:45 PM

Hi Fogueri, this has been discussed a few times along with some associated topics; try looking at/following these threads;

 

https://support.cert...=multiplicative

 

https://support.cert...cative#entry121

 

https://support.cert...ative#entry4664

 

and maybe review http://onlinelibrary.../psp4.12161/pdf

 

https://support.cert...ative#entry4168

 

among others.

 

SImon

Thank You Simon!



#4 serge guzy

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Posted 29 December 2017 - 04:33 PM

Can anyone explain what the error models mean -? multiplicative, additive, proportional errors?

Suppose you make an hypothetical experiment and you observe 1000 times(not possible in reality) drug levels at the same time, let say during the absorption phase of an extravascular single dose. You will get 1000 different observations and therefore you can compute the standard deviation based on these 1000 values. You try to attach a model to explain these data and you call the model prediction C and the 1000 observations(CObs) can be mathematically expressed as:

CObs=C+N(0,sigma)  where N(0,sigma) is a normal distribution with mean 0 and standard deviation sigma.

We say that CObs is a random variable because it is sampled from a distribution(N(0,sigma) plus the prediction C.

Suppose C=10 and sigma has been estimated to be 1.

Suppose now that we perform the same experiment near the peak and that C=1000 and sigma=100. You can see that sigma increased by 10 when C increased by 10. It means that the sigma is proportional to C. It means that the observation around the peak has less precision than the none at the beginning of the absorption phase.

Writing CObs=C+N(0,sigma) is in fact the expression of the error model but where we need to define a function for sigma.

 

If sigma is proportional to C, we say that the error model is multiplicative and we can write.

 

CObs=C+N(0,sigma) but sigma=a*C as it is proportional to C and we get

CObs=C+N(0,a*C)

The basis rules for normal distributions are that N(0,a*C)=C*N(0,a) and therefore we get

CObs=C+C*N(0,a)) where N(0,a) is a normal distribution with mean 0 and standard deviation =a

or CObs=C*(1+N(0,a)) where N(0,a) is defined in Phoenix NLME as CEps, CEps=N(0,a)

CObs=C*(1+CEps)

a for multiplicative error is in fact the coefficient of variation and for example if it is 0.1 means 10% variability or imprecision if you want

 

if the standard deviation is constant, we get

CObs=C+N(0,a)=C+CEps

 

 

Multiplicative and proportional is the same (synonyms)

Hope it helps

Serge Guzy



#5 shekhar.udct@gmail.com

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Posted 30 April 2018 - 08:34 AM

Hi Serge, 

 

Thanks for this valuable information. Your illustration really helped me to understand the multiplicative error model. 

 

Regards

 

Shekhar

 

 

Suppose you make an hypothetical experiment and you observe 1000 times(not possible in reality) drug levels at the same time, let say during the absorption phase of an extravascular single dose. You will get 1000 different observations and therefore you can compute the standard deviation based on these 1000 values. You try to attach a model to explain these data and you call the model prediction C and the 1000 observations(CObs) can be mathematically expressed as:

CObs=C+N(0,sigma)  where N(0,sigma) is a normal distribution with mean 0 and standard deviation sigma.

We say that CObs is a random variable because it is sampled from a distribution(N(0,sigma) plus the prediction C.

Suppose C=10 and sigma has been estimated to be 1.

Suppose now that we perform the same experiment near the peak and that C=1000 and sigma=100. You can see that sigma increased by 10 when C increased by 10. It means that the sigma is proportional to C. It means that the observation around the peak has less precision than the none at the beginning of the absorption phase.

Writing CObs=C+N(0,sigma) is in fact the expression of the error model but where we need to define a function for sigma.

 

If sigma is proportional to C, we say that the error model is multiplicative and we can write.

 

CObs=C+N(0,sigma) but sigma=a*C as it is proportional to C and we get

CObs=C+N(0,a*C)

The basis rules for normal distributions are that N(0,a*C)=C*N(0,a) and therefore we get

CObs=C+C*N(0,a)) where N(0,a) is a normal distribution with mean 0 and standard deviation =a

or CObs=C*(1+N(0,a)) where N(0,a) is defined in Phoenix NLME as CEps, CEps=N(0,a)

CObs=C*(1+CEps)

a for multiplicative error is in fact the coefficient of variation and for example if it is 0.1 means 10% variability or imprecision if you want

 

if the standard deviation is constant, we get

CObs=C+N(0,a)=C+CEps

 

 

Multiplicative and proportional is the same (synonyms)

Hope it helps

Serge Guzy






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