# additive + proportional residual error

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### #1 mario sampson

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Posted 31 May 2012 - 02:33 PM

Hi,

Is it possible to use an additive + proportional residual error model in NLME? I tried such a model, but it was unclear if it was being interpreted as intended.

Thanks,

Mario

### #2 Emily Colby

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Posted 31 May 2012 - 04:59 PM

Choose Mixed from the Residual Error drop-down menu in the model selection structural tab.

â€¢ Mixed is Proportional + Additive: CObs = C + CEps + C*CEps*CMixRatio

â€¢ CEps is the additive error

â€¢ Standard deviation of the additive error = Stdev(CEps)

â€¢ CEps*CMixRatio is the proportional error

â€¢ Standard deviation of the proportional error = sqrt(var(CEps*CMixRatio) ) =

sqrt(Var(CEps)*CMixRatio^2 )=Stdev(CEps)*|CMixRatio|

â€¢ CMixRatio is the ratio of the standard deviation of the proportional error to the standard deviation of the additive error, and it is a parameter that is estimated

â€¢ Stdev(proportional error)/Stdev(additive error) = Stdev(CEps)*|CMixRatio|/ Stdev(CEps)= CMixRatio

â€¢ Example: Mixed Stdev of 0.1 with CMixRatio of 1.5 means we have an additive component of 0.1 (Âµg/L for example) and a proportional part of: 0.1*1.5 = 0.15 = 15% CV

### #3 Richard Knapp

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Posted 20 September 2012 - 07:09 PM

I know it is possible to estimate additive and proportional error with the mix Ratio + Stdev residual error tool. What I cannot (cannot!) do is identify any estimate for these two parameters that will allow convergence. I allways get the "There was an error while executing Workflow..." I am working with a data set that is well fitted by a 1 or 2 compartment model with a multiplicative residual error. The residual error for the 1-compartment model is about 0.52 and is reduced to about 0.25 with the 2-compartment model. There does not seem to be any problem with the data nor the models. There is no problem with the multiplicative residual error or a simple additive residual error either. Can you please offer a strategy to make mix ratio estimates?

### #4 Emily Colby

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Posted 20 September 2012 - 08:07 PM

Dear Richard,

If you're able to get estimates of Stdev with the additive and multiplicative models, do that, and then use a simple calculation to get the estimate for CmixRatio.

and Stdev in the mixed case = AddStdev

Emily

### #5 Richard Knapp

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Posted 20 September 2012 - 08:20 PM

Emily:

I tried that. Add residual = 23. Multip residual error = 0.53. Calculated Ratio = 0.023. Result, program failed to converge.

Richard

### #6 Richard Knapp

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Posted 20 September 2012 - 08:40 PM

Same problem with the 2-compartment model. Here the multiplicative residual was 0.26 but the additive was a huge 332. My ratio calculation was 0.0008. I really don't believe the additive residual result.

### #7 Emily Colby

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Posted 20 September 2012 - 08:42 PM

We should first try to get a good model fit in the additive or multiplicative case. If your residual standard deviations are that high, there seems to be something else wrong with the model. Check your model structure and initial estimates. Send your project to support@pharsight.com if you would like more detailed assistance and we will go from there.

### #8 Richard Knapp

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Posted 20 September 2012 - 09:44 PM

I have attached the project file here.

The residual error for the 1-compartment model is high (0.5) but that for the 2-compartment model seems moderate (0.2). I was able to get an additive (0.0405, SD = 0.201) plus proportional (0.0664, CV = 25.8) residual error model from NONMEM via PDxPop. The Phoenix parameter errors are generally good for the 2-C model and worse for the 1-C model. Note that the file sent has clearance parameters for the 1-C and microconstants for the 2-C. Not my idea. You cannot directly compare them for this reason.

Richard [file name=MixedRatio_Problem.phxproj size=2510949]http://pharsight.com/extranet/media/kunena/attachments/legacy/files/MixedRatio_Problem.phxproj[/file]

### #9 Emily Colby

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Posted 20 September 2012 - 10:19 PM

Richard,

I started with the 2 cpt model because it fit better. I guessed initial values of 25 and 100 for Stdev and CmixRatio. I used FOCE LB to refine those a little (but the fit was bad because LB is not well set up for mixed error models). Then I used ELS and it converged.

Emily [file name=MixedRatio_Problem-20120920.phxproj size=3182036]http://pharsight.com/extranet/media/kunena/attachments/legacy/files/MixedRatio_Problem-20120920.phxproj[/file]

### #10 Richard Knapp

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Posted 21 September 2012 - 11:55 AM

Well I guess I understand a little more....

The separation of the Stdev estimate entry in the structural window and the CMixRatio estimate entry in the Fixed effect window is not very intitutive. However, this still does not address the original question of how to estimate these parameters. Can you give me some insight into how you "guessed" the initial values?

### #11 Samer Mouksassi

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Posted 21 September 2012 - 04:54 PM

Hello,

You can note you assay limit of quantitative and use it as an initial estimate for you additive part.

A general proportional part will be ~20 %

In Phoenix: PROPORTIONAL PART = CmixRatio * STDEV (additive part)

Assuming we want an intial of 20 % then 0.2 = Cmixratio *stdev (additive)

0.2 = Cmixratio * lloq

Cmixratio = 0.2 / lloq

suppose your lloq = 0.5 as minimum concentration reported was 0.775

Cmixratio = 0.2 /0.5 = 2/5 = 0.4

Samer

### #12 Lisa Liao1412845455

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Posted 19 October 2012 - 03:26 AM

Pls see attached file --> Base model Mixed Err (Phoenix model)

I tried doing a mixed residual error model and finally got it to run. However, some questions still remain. I set additive error=.02 in the Structure tab in stdev box then left CMIXRatio above that as the label. (Model will not run if I put prop err: add err ratio there)

Next I entered in the parameters; Fixed Effect tab Cmixratio= 10 because I assumed initial estimate of prop err = .2

I ran FOCE ELS.

Does NLME for population pk model estimate additive and proportional error separately or is additive fixed and only proportional error is estimated? If so where in the Results tab can I find both error estimates?

Pls advise! Thanks [file name=Pop_PK5.phxproj size=5727322]http://pharsight.com/extranet/media/kunena/attachments/legacy/files/Pop_PK5.phxproj[/file]

### #13 serge guzy

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Posted 19 October 2012 - 04:08 AM

The program will estimate the standard deviation stdev0 (2.36615 here) and tvCMixRatio (0.0346797 here).

Now your observation is assumed to have 3 cmponents, the prediction part (C from the model), an additive error standard deviation part which is CEps and a proportional error part which is CEps*C*CmixRatio.

error(CEps = 0.02)

observe(CObs = C + CEps * (1 + C * CMixRatio), bql)

Therefore, the additive error standard deviation part is CEps which is 2.36615 and the proportional error part is CEps*CMixRatio *C which is 2.36615*0.0346797 * C.

It means that the %cv (linked to the proportional error part) is about 8.2% (2.36615*0.0346797 *100) .

In summary theta has all the information and you just need to x CEps by Cmixratio to get the cv (proportional error component)where CEps is the sd for the additive error part.

Best Regards;

Serge

### #14 serge guzy

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Posted 19 October 2012 - 04:15 AM

Dear colleague

I responded to you but for some reason it did not go through.

The information is in theta.

The additive error component is stdev0 and the proportional error (CV) is

CEps * CMixRatio .

It comes from the error model defined (look at model text tab).

error(CEps = 0.02)

observe(CObs = C + CEps * (1 + C * CMixRatio), bql)

Copy your model to the workflow, then accept all fixed and random (parameters/fixed/accept all fixed and random), then click on model etxt tab and you will see now.

error(CEps = 2.36615)

You can see that stdev0 is in fact the sd associated with the additive error component.

Best Regards;

Serge

### #15 Charlie Brindley1412845450

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Posted 20 November 2012 - 12:53 PM

Using a naive-pooled approach, I get the following theta output:

Parameter Estimate SE

tvA 248.131 48.272145

tvAlpha 0.307973 0.078062155

tvB 169.605 52.438535

tvBeta 0.0468184 0.018048823

stdev0 58.3376 1.9960461

The CVs of the fixed parameters are clearly quite low at ~20 to 40%

I understand that stdev0 represents the additive error, but how should I interpret this value of 58.3?

Is this value relatively low or high?

### #16 Simon Davis

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Posted 20 November 2012 - 02:01 PM

Charlie - as I understand it, with an additive error model you are looking at a number analogous absolute amount of conc. so depending on concentrations seen in your experiment you can assess how high it is relative to those.

Simon.

### #17 Charlie Brindley1412845450

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Posted 20 November 2012 - 03:30 PM

Thanks Simon,

This makes sense.

Charlie

### #18 serge guzy

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Posted 20 November 2012 - 05:14 PM

To get a better assessmen of the real % error, I strongly suggest you to shift to proportional error or mixed error mdoel. If you shift to proportional error which features most of the PK models, you will get stdev0 being the cv. that number x 100 is the % error and you get immeditately an assesment of big or small. The problem with additive error for PK responses that span over a large range is that the meaning depends on where you look in the time profile. Suppose you have concentrations going from 0.1 to 1000. Your 50 absolute value for the error standard deviation correspond to about 5% error for concentrations about 1000 but 50000% error for responses around 0.1. In that case you shift to mixed error model which has 2 components or just proporitonal error. PD responses span over a smaller range and often additive error is a good error model for PD responses but alsmot never for PK responses.

best

Serge

### #19 Lisa Liao1412845455

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Posted 11 January 2013 - 04:27 AM

Question on the CMixRatio...

I'd like to use a mix error model with additive error = .5 + prportional error = .2 for the residual error model. How do I FIX the additive error to .5 and allow the proportional part to fluctuate with each iteration?

Thanks

### #20 serge guzy

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Posted 11 January 2013 - 04:55 PM

Dear Lisa

I attached a simple project to show how to do it. The diea is first using the built in option. stdev is the constant part of your error model and stdev (CEps in the model) x Cmixratio is your cv.

Therefore you start with 0.5 for stdev (CEps) and 0.4 for cmixratio (0.5 x 0.4=0.2=cv you want to start with). Then you copy the model to the workflow and shift to edit as textual with your copied model. You original error model is error(CEps = 0.5) and instead of that code you just write error(CEps (freeze) = 0.5) . This will freeze the cste erorr term to 0.5.

A simple project is attached.

best Regards;

Serge [file name=mixrstio_cste_freeze.phxproj size=151240]http://pharsight.com/extranet/media/kunena/attachments/legacy/files/mixrstio_cste_freeze.phxproj[/file]

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