Re: How serious are negative eigenvalues?
Dieter,
You ask:
> My question: can we trust this fit?
The answer depends on why you are doing the modelling.
If your goal is to describe the time course of concentrations then the overall ability of the model to describe what you saw depends on the totality of the model and its parameters. The model may be overparameterized but it may still do what you want it to do i.e. describe (and predict) the time course of concentrations in each compartment. If you are satisfied with the VPC showing that simulations from the model appropriately describe the observed concentrations then I think the answer to your question is yes.
Quoted reply history
On the other hand if the goal is to estimate the size of one or more critical parameters then you will need to pay attention to how well these parameters are estimated. As Leonid has pointed out it seems that at least some of the model parameters are not well identified. This may be unimportant if the parameters you want to describe are robustly estimated.
For example, if you had a simple PK model with samples mainly taken at steady state with few observations during absorption then you may get a good estimate of clearance but a rather poor estimate of KA. You cannot simply remove a parameter such as KA (you have to describe the sparse absorption somehow) but it will have little impact on the clearance estimate. Thus the model can be trusted for the purpose of estimating clearance but not absorption rate.
Nick
On 7/09/2010 12:11 a.m., Dieter Menne wrote:
> Dear Nmusers,
>
> we have very rich data from MRI concentration measurements, with 11
> compartments and multiple compartments observed. The model is fit via SAEM
> (nburn=2000), and followed by an IMPMAP as in the described in the 7.1.2
> manual. OMEGA is band with pair-wise block correlations in the following
> style:
>
> $OMEGA BLOCK(2)
> .02 ;CL
> 0.01 0.06 ; VC
> $OMEGA BLOCK(2)
> 5.4 ; QMVP
> 0.001 0.05 ;VMVP
> $OMEGA BLOCK(2)
> 0.06 ; QTVP
> 0.001 0.25 ;VTPV
>
> $EST PRINT=1 METHOD=SAEM INTERACTION NBURN=2000 NITER=200 CTYPE=2 NSIG=2
> FILE=SAEM.EXT
> $EST METHOD=IMPMAP EONLY = 1 INTERACTION ISAMPLE=1000 NITER=5 FILE=IMP.EXT
> $COV PRINT=E UNCONDITIONAL
>
> Fits and CWRES diagnostics are perfect, and VPC checks are good.
>
> However, we have negative eigenvalues (the following example has been edited
> by removing digits)
>
> ETAPval = 0.2 0.2 0.3 0.04 0.8 0.95 0.003 0.1 0.6 0.4 0.9 0.1 0.5 0.4 0.2
> 0.8 0.3 0.3 0.4 0.01 0.8
> ETAshr% = 13. 0.4 38 20 23 33 46 30 18 41 54 22 2. 26. 49. 12. 0.07 24. 18.
> 35. 2.5
> EPSshr% = 7.5 8.1
> Number of Negative Eigenvalues in Matrix= 7
> Most negative value= -65339.
> Most positive value= 88796185.9
> Forcing positive definiteness
> Root mean square deviation of matrix from original= 1.37E-003
>
> My question: can we trust this fit?
>
> Dieter Menne
> Menne Biomed/University Hospital of Zürich
--
Nick Holford, Professor Clinical Pharmacology
Dept Pharmacology& Clinical Pharmacology
University of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand
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