Dear NONMEM users,
1) I am fitting Studies-reported means of a parameter X measured in human
subjects as a function of TIME. The studies report the mean plus/minus SD of
that parameter rather than the actual subject measurements.
2) A snapshot of the main columns in my nmdata is provided below. The "ID"
column represent the STUDY number, the "DV" column is the reported mean of
parameter X at TIME=t, the "SD" is the standard deviation of the observations
in the subjects at TIME=t.
3) I am using $PRED for fitting.
4) I am using one exponential decline function to fit the means~TIME. I am
weighting for the number of subjects in each study in the error model.
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))
My Question:
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?
I am able to get a very good model as described above; however, I haven't
included the SDs in anyway in the model fitting. I only accounted for the
number of subjects in the error model. I am not sure if there is a way to
account for SDs either in the error model or if there is a way to incorporate
them to the DVs?
I would appreciate any thoughts on this. Thank you.
ID
NSUB
TIME
DV
SD
1
10
0.083333
4.776667
0.230317
1
10
0.5
3.713333
0.355235
1
10
0.583333
3.556667
0.361091
1
10
0.75
3.2
0.339621
1
10
1.083333
2.816667
.
1
10
1.333333
2.613333
0.304487
1
10
1.416667
2.823333
0.290825
1
10
2
2.23
0.202992
2
5
0.5
6.36
0.329154
2
5
1
6
.
2
5
1.5
5.76
0.821635
2
5
2
5.18
0.973441
2
5
2.5
4.76
1.347797
2
5
3
4.13
1.680903
2
5
3.5
3.17
1.618905
Sincerely,
Ahmad Abuhelwa
Adelaide, South Australia
Australia
Email:
[email protected]<mailto:[email protected]>
Incorporating standard deviation (SD) on fitted mean values
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)
Quoted reply history
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,
>
--
Paul Matthias Diderichsen, PhD
Quantitative Solutions, a Certara company
+31 624 330 706
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
office:+64(9)923-6730 mobile:NZ+64(21)46 23 53
email: [email protected]
http://holford.fmhs.auckland.ac.nz/
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.
Hi Ahmad,
I agree with Nick, you will want to weight your precision by the inverse
standard error.
More generally, you are doing a model-based meta-analysis. When I was first
learning about it, a book that I found very informative and readable was
"Introduction to Meta-Analysis" by Borenstein, et al. It focuses on standard
meta-analysis and not model-based, but the foundation it lays is necessary for
both.
Thanks,
Bill
Quoted reply history
On Nov 19, 2015, at 4:43, "Nick Holford" <[email protected]> wrote:
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
> 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
office:+64(9)923-6730 mobile:NZ+64(21)46 23 53
email: [email protected]
http://holford.fmhs.auckland.ac.nz/
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.
On 11/19/2015 9:58, Nick Holford wrote:
> 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)
Agree.
In this case, I don't think it matters where the variability comes from.
It's part of the data, with each reported outcome defined by c(mean,sd).
sd incorporates both between- and within-subject variability. Separating
BSV and WSV is tricky when only aggregate data is available.
--
Paul Matthias Diderichsen, PhD
Quantitative Solutions, a Certara company
+31 624 330 706