Re: Incorporating standard deviation (SD) on fitted mean values
Paul,
I largely agree with your reply.
Ahmad says he is fitting "means of a parameter X". I suspect he really means the "means of a variable X".
A = THETA(1)*EXP(ETA(1)) ;ETA1 is between STUDY variability on A ALPHA = THETA(2)*EXP(ETA(2)) ;ETA2 is between STUDY variability on ALPHA
IPRED = (A)*exp(-ALPHA*TIME)
Y = IPRED *(1+EPS(1)/SQRT(NSUB))
I would say that the random effect ETA is describing the between study variability in the parameters (A and ALPHA) while EPS is describing the random unexplained variability (RUV) in the prediction of the DV (mean of X) using an exponential function of A, ALPHA and TIME.
Some of the RUV arises from within study between subject variability in A and ALPHA and some from the usual sort of RUV (model misspecification, measurement error, stochastic noise, etc).
The SD covariate in the data set
ID
NSUB
TIME
DV
SD
1
10
0.083333
4.776667
0.230317
is described by Ahmad as "the standard deviation of the observations in the subjects at TIME=t." The random contributions to SD seem to be similar to those contributing to RUV as described above.
Therefore it seems to me that SD could be used in the prediction of X as you suggested:
Y = IPRED + SD*EPS(1)/SQRT(NSUB)
The variance of EPS(1) should be fixed to 1 like this:
$SIGMA 1 FIX
Best wishes,
Nick
Quoted reply history
On 17-Nov-15 20:43, Paul Matthias Diderichsen wrote:
> Hi Ahmad,
> In your aggregate data, ETA describes between-study variability while
> EPS describes the between-subject variability. As such, EPS is not
> "unexplained" (as in RUV) but rather "explained" in the data.
>
> You can interpret the residual error in NONMEM as a weight of your data.
> If you have small sample size or large BSV for a given outcome, then you
> should not put as much weight on that data point = larger variance.
>
> Precision is a different beast altogether: this relates to the standard
> error of your estimates (= variance-covariance matrix), and depends
> (everything else being equal) on how much data you have.
>
> (I'm looping this back into NMUsers; maybe somebody else has comments)
>
> On 11/17/2015 0:34, Abu Helwa, Ahmad Yousef Mohammad - abuay010 wrote:
>
> > Hi Paul,
> >
> > Thank you for your input on this. However, in the case you presented, the
> > SD in the error model will then informs about the precision rather than between
> > subject variability? In my case, the parameter I am modelling (gastric pH) is
> > measured in X number of subjects and the mean and SD are reported. So, the SD
> > is not the precision of the measurement within a subjects (the measurement in
> > each subject was performed one time), rather, it is between subjects. The large
> > SDs for some of the reported means is due to the fact that BSV in gastric pH is
> > high.
> >
> > Ahmad.
> >
> > -----Original Message-----
> > From: Paul Matthias Diderichsen [mailto:[email protected]]
> > Sent: Monday, 16 November 2015 6:16 PM
> > To: Abu Helwa, Ahmad Yousef Mohammad - abuay010
> > <[email protected]>
> > Subject: Re: [NMusers] Incorporating standard deviation (SD) on fitted mean
> > values
> >
> > Hi Ahmad,
> >
> > On 11/15/2015 23:46, Abu Helwa, Ahmad Yousef Mohammad - abuay010 wrote:
> >
> > > Y = IPRED *(1+EPS(1)/SQRT(NSUB))
> > > 5) Is there any way where I can incorporate the SDs that I have to
> > > inform about the between SUBJECT variability in the model fitting?
> >
> > Include the reported SD (REPSD) in your residual error variance and fix
> > the sigma to 1 (the variance is defined in your data). I would probably
> > describe the mean as a normal distributed variable, so:
> >
> > Y = IPRED + EPS(1)*REPSD/SQRT(NSUB)
> > $SIGMA
> > 1 FIX
> >
> > Kind regards,
--
Nick Holford, Professor Clinical Pharmacology
Dept Pharmacology & Clinical Pharmacology, Bldg 503 Room 302A
University of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand
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Holford SD, Allegaert K, Anderson BJ, Kukanich B, Sousa AB, Steinman A, Pypendop,
B., Mehvar, R., Giorgi, M., Holford,N.H.G. Parent-metabolite pharmacokinetic models
- tests of assumptions and predictions. Journal of Pharmacology & Clinical
Toxicology. 2014;2(2):1023-34.
Holford N. Clinical pharmacology = disease progression + drug action. Br J Clin
Pharmacol. 2015;79(1):18-27.