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Re: [NMusers] User defined likelihood function in POSTHOC estimation

From: Tingjie Guo <iam_at_tingjieguo.com>
Date: Wed, 06 Nov 2019 14:29:39 +0100

Hi Shan,

Constant should have no influence on estimation, from my understanding. I've already omitted all constants terms. Thanks anyway for your information!

Warm regards,
Tingjie

On Wed, Nov 6, 2019, at 13:22, Shan Pan wrote:
> Dear Tingjie,
>
> I don't know the answer but this might be helpful: see the link below on slide 3 and annotation on the right side.
>
> http://holford.fmhs.auckland.ac.nz/docs/modelling-likelihoods-using-nonmem-vi.pdf
>
> "*Actually its not quite - 2LL but proportional to it. It is missing a constant (-NOBS/2*Ln(2*Pi)) but this is not needed in order to minimize - 2LL and obtain maximum likelihood estimates." *-- I don't know whether this constant made a difference to your ETA estimates.
> **
> Kind regards,
> Shan
>
> On Tue, Nov 5, 2019 at 2:02 PM Tingjie Guo <iam_at_tingjieguo.com> wrote:
>> Dear NMusers,
>>
>> I would like to reproduce POSTHOC estimation with manually defined likelihood (LL) function.
>>
>> This is the control stream of a standard POSTHOC for which I want to reproduce:
>> $PK
>> CL = THETA(1) * CLCR/100 * EXP(ETA(1))
>> V = THETA(2) * WGT * EXP(ETA(2))
>> S1 = V
>>
>> $ERROR
>> IPRED = F
>> Y = IPRED + IPRED*EPS(1) + EPS(2)
>>
>> $THETA
>> 4.58 ; TVCL (L/h)
>> 1.53 ; TVV (L/kg)
>>
>> $OMEGA
>> 0.151321 ; omega^2 CL
>> 0.139876 ; omega^2 V
>>
>> $SIGMA
>> 0.039601 ; Proportional
>> 5.76 ; Additive
>>
>> $EST METHOD=COND LAPLACE MAXEVAL=0 NOABORT SIG=3 PRINT=1
>>
>> And below is the control stream I used aiming to reproduce above POSTHOC estimation:
>>
>> $PK
>> CL = THETA(1) * CLCR/100 * EXP(ETA(1))
>> V = THETA(2) * WGT * EXP(ETA(2))
>> S1 = V
>>
>> $ERROR
>> IPRED = F ; Predicted DV
>> ADDI = 5.76 ; Variance of additive error
>> PROR = 0.039601 ; Variance of proportional error
>> VAR = ADDI + PROR*IPRED**2 ; Variance of combined error
>>
>> Y = LOG(W) + (DV-IPRED)**2/VAR ; -2 log Likelihood,
>>
>> $THETA
>> 4.58 ; TVCL (L/h)
>> 1.53 ; TVV (L/kg)
>>
>> $OMEGA
>> 0.151321 ; omega^2 CL
>> 0.139876 ; omega^2 V
>>
>> $EST METHOD=COND LAPLACE -2LL MAXEVAL=0 NOABORT SIG=3 PRINT=1
>>
>> The LL function was based on the minus twice log posterior distribution:
>> -2LPosterior = log(Var) + SUM{(DV-IPRED)^2/Var} + ETA^2/OMEGA^2
>>
>> I did not add eta/omega part (prior distribution) to the LL function in the code because NONMEM seems to apply them automatically in POSTHOC. The eta estimates using defined LL function were fairly close but not exactly same as what standard POSTHOC generated and I don't know why. Does anyone have ideas what might be going wrong in the code? Any input is appreciated!
>>
>> Yours sincerely,
>> Tingjie Guo
>>

Received on Wed Nov 06 2019 - 08:29:39 EST

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