I have previously conducted a meta-analysis of PK data that contained
extensive and sparse sampling from 330 patients with a run time of ~ 4
days. I know have data from another 200 patients with sparse data. I have
created the median and 95th PI from the previous model and overlaid the
current data. The results demonstrate that the new data is well described
by that model. When the new data is fit with that model, the data does not
support using the model as some parameters were unidentifiable. I could
conducted an analysis of all the data simultaneously but was interested in
another method. Therefore, I have implemented $PRIOR into the model and
noticed that with each successive increase of the df, the objective
function significantly decreases. However, the THETA values do not change
much and are different from the prior estimates used. The only other
things that changed besides the objective function were the estimates and
SE of the covariance terms and the BSV estimate of the peripheral volume of
distribution. These values become more in line with the those observed
previously, and the correlation values between them becomes stronger. My
question is it justifiable to use such a high df (df=330) based on these
significant decreases of objective function and covariance as the
information from this meta-analysi would be highly informative.
Thanks
PRIORS
Dear Charles,
When using $PRIOR, the df specifies the degrees of freedom for the
Inverse-Wishart prior distribution on the covariance matrix of the
individual random effects (OMEGA). In practical terms, the larger the df,
the more informative the prior will be. It's not surprising, then, that
your parameter estimates approach the results of the previous model when df
is large.
The choice to use an informative prior distribution should not be made
based on objective function changes. Instead, you might want to consider
the rationale for including the prior information in the first place. One
strategy would be to use informative priors only where necessary to support
components of a previously defined or otherwise known model. If the new
data alone do not support estimation of parameters required in this model
structure, then you might want to include informative prior distributions
on those specific components. Sensitivity to the "informativeness" of the
prior could be explored by varying the df (or prior variance for fixed
effects), and conclusions from your analysis should probably be viewed in
the context of this prior sensitivity.
As you indicate, for this particular example, you may not need to use
$PRIOR at all, and could simply pool the data in a single analysis.
Hope this is useful.
Marc
Quoted reply history
On Sun, Jan 29, 2012 at 5:02 PM, Charles Steven Ernest II <
[email protected]> wrote:
> I have previously conducted a meta-analysis of PK data that contained
> extensive and sparse sampling from 330 patients with a run time of ~ 4
> days. I know have data from another 200 patients with sparse data. I have
> created the median and 95th PI from the previous model and overlaid the
> current data. The results demonstrate that the new data is well described
> by that model. When the new data is fit with that model, the data does not
> support using the model as some parameters were unidentifiable. I could
> conducted an analysis of all the data simultaneously but was interested in
> another method. Therefore, I have implemented $PRIOR into the model and
> noticed that with each successive increase of the df, the objective
> function significantly decreases. However, the THETA values do not change
> much and are different from the prior estimates used. The only other
> things that changed besides the objective function were the estimates and
> SE of the covariance terms and the BSV estimate of the peripheral volume of
> distribution. These values become more in line with the those observed
> previously, and the correlation values between them becomes stronger. My
> question is it justifiable to use such a high df (df=330) based on these
> significant decreases of objective function and covariance as the
> information from this meta-analysi would be highly informative.
> Thanks
>
--
Marc R. Gastonguay, Ph.D. <[email protected]>
Scientific Director
Metrum Institute http://metruminstitute.org
*Metrum Institute is a 501(c)3 non-profit organization.*
Hi Charles
The choice of the df of the Wishart should be based on what your prior
information provides not on what the posterior distribution tells you. I
suspect, if your data is relatively uninformative then a sensitivity analysis
will show that the posterior is sensitive to the prior. It would then be a
matter of determining objectively how your subjective prior will influence your
current analysis and this depends on what you want to learn from your
analysis...
Regards
Steve
--
Quoted reply history
From: [email protected] [mailto:[email protected]] On
Behalf Of Gastonguay, Marc
Sent: Monday, 30 January 2012 12:03 p.m.
To: Charles Steven Ernest II
Cc: [email protected]
Subject: Re: [NMusers] PRIORS
Dear Charles,
When using $PRIOR, the df specifies the degrees of freedom for the
Inverse-Wishart prior distribution on the covariance matrix of the individual
random effects (OMEGA). In practical terms, the larger the df, the more
informative the prior will be. It's not surprising, then, that your parameter
estimates approach the results of the previous model when df is large.
The choice to use an informative prior distribution should not be made based on
objective function changes. Instead, you might want to consider the rationale
for including the prior information in the first place. One strategy would be
to use informative priors only where necessary to support components of a
previously defined or otherwise known model. If the new data alone do not
support estimation of parameters required in this model structure, then you
might want to include informative prior distributions on those specific
components. Sensitivity to the "informativeness" of the prior could be explored
by varying the df (or prior variance for fixed effects), and conclusions from
your analysis should probably be viewed in the context of this prior
sensitivity.
As you indicate, for this particular example, you may not need to use $PRIOR at
all, and could simply pool the data in a single analysis.
Hope this is useful.
Marc
On Sun, Jan 29, 2012 at 5:02 PM, Charles Steven Ernest II
<[email protected]<mailto:[email protected]>>
wrote:
I have previously conducted a meta-analysis of PK data that contained
extensive and sparse sampling from 330 patients with a run time of ~ 4
days. I know have data from another 200 patients with sparse data. I have
created the median and 95th PI from the previous model and overlaid the
current data. The results demonstrate that the new data is well described
by that model. When the new data is fit with that model, the data does not
support using the model as some parameters were unidentifiable. I could
conducted an analysis of all the data simultaneously but was interested in
another method. Therefore, I have implemented $PRIOR into the model and
noticed that with each successive increase of the df, the objective
function significantly decreases. However, the THETA values do not change
much and are different from the prior estimates used. The only other
things that changed besides the objective function were the estimates and
SE of the covariance terms and the BSV estimate of the peripheral volume of
distribution. These values become more in line with the those observed
previously, and the correlation values between them becomes stronger. My
question is it justifiable to use such a high df (df=330) based on these
significant decreases of objective function and covariance as the
information from this meta-analysi would be highly informative.
Thanks
--
Marc R. Gastonguay, Ph.D.<mailto:[email protected]>
Scientific Director
Metrum http://metruminstitute.org
Metrum Institute is a 501(c)3 non-profit organization.
Steve
Enclosed is a WinBugs file that simulates from a multivariate normal
distribution. The Wishart distribution is very sensitive to the degree of
freedom for the prior. Winbugs parameterizes in terms of precision i.e inverse
of the variance
Robert D. Johnson, Ph.D
Chemical Systems Modeling Section
Corporate R&D
Procter & Gamble
8256 Union Centre Blvd, IP-351
West Chester, OH 45069
[email protected]
(513) 634-9827
Quoted reply history
From: [email protected] [mailto:[email protected]] On
Behalf Of Stephen Duffull
Sent: Monday, January 30, 2012 1:12 PM
To: Gastonguay, Marc; Charles Steven Ernest II
Cc: [email protected]
Subject: RE: [NMusers] PRIORS
Hi Charles
The choice of the df of the Wishart should be based on what your prior
information provides not on what the posterior distribution tells you. I
suspect, if your data is relatively uninformative then a sensitivity analysis
will show that the posterior is sensitive to the prior. It would then be a
matter of determining objectively how your subjective prior will influence your
current analysis and this depends on what you want to learn from your
analysis...
Regards
Steve
--
From: [email protected] [mailto:[email protected]] On
Behalf Of Gastonguay, Marc
Sent: Monday, 30 January 2012 12:03 p.m.
To: Charles Steven Ernest II
Cc: [email protected]
Subject: Re: [NMusers] PRIORS
Dear Charles,
When using $PRIOR, the df specifies the degrees of freedom for the
Inverse-Wishart prior distribution on the covariance matrix of the individual
random effects (OMEGA). In practical terms, the larger the df, the more
informative the prior will be. It's not surprising, then, that your parameter
estimates approach the results of the previous model when df is large.
The choice to use an informative prior distribution should not be made based on
objective function changes. Instead, you might want to consider the rationale
for including the prior information in the first place. One strategy would be
to use informative priors only where necessary to support components of a
previously defined or otherwise known model. If the new data alone do not
support estimation of parameters required in this model structure, then you
might want to include informative prior distributions on those specific
components. Sensitivity to the "informativeness" of the prior could be explored
by varying the df (or prior variance for fixed effects), and conclusions from
your analysis should probably be viewed in the context of this prior
sensitivity.
As you indicate, for this particular example, you may not need to use $PRIOR at
all, and could simply pool the data in a single analysis.
Hope this is useful.
Marc
On Sun, Jan 29, 2012 at 5:02 PM, Charles Steven Ernest II
<[email protected]<mailto:[email protected]>>
wrote:
I have previously conducted a meta-analysis of PK data that contained
extensive and sparse sampling from 330 patients with a run time of ~ 4
days. I know have data from another 200 patients with sparse data. I have
created the median and 95th PI from the previous model and overlaid the
current data. The results demonstrate that the new data is well described
by that model. When the new data is fit with that model, the data does not
support using the model as some parameters were unidentifiable. I could
conducted an analysis of all the data simultaneously but was interested in
another method. Therefore, I have implemented $PRIOR into the model and
noticed that with each successive increase of the df, the objective
function significantly decreases. However, the THETA values do not change
much and are different from the prior estimates used. The only other
things that changed besides the objective function were the estimates and
SE of the covariance terms and the BSV estimate of the peripheral volume of
distribution. These values become more in line with the those observed
previously, and the correlation values between them becomes stronger. My
question is it justifiable to use such a high df (df=330) based on these
significant decreases of objective function and covariance as the
information from this meta-analysi would be highly informative.
Thanks
--
Marc R. Gastonguay, Ph.D.<mailto:[email protected]>
Scientific Director
Metrum http://metruminstitute.org
Metrum Institute is a 501(c)3 non-profit organization.
CDOo ñDocuments.StdDocumentDesc ñDocuments.DocumentDesc ñContainers.ViewDesc ñViews.ViewDesc ðStores.StoreDesc " ñDocuments.ModelDesc ñContainers.ModelDesc ñModels.ModelDesc ñStores.ElemDesc ò p
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4 *uTÈ ò e ò K ò 0 äW ô LY ¦ L ò+ ô *uTÈ ò e ò K ò 0 äW ô LY ¦ L ò+ å
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*uTÈ ò m ò S ò 8 äW ô LY ¦ L ò+ : >I 2 *uTÈ ò e ò K ò 0 äW ô LY ¦ L ò+ è ÿmodel {
theta[1:p] ~ dmnorm(theta.mean[1:p], omega.inv[1:p, 1:p])
theta.mean[1] <- mu[1]
theta.mean[2] <- mu[2]
theta.mean[3] <- mu[3]
theta.mean[4] <- mu[4]
tau ~ dgamma(tau.a, tau.b)
sigma <- 1 / sqrt(tau)
mu[1:p] ~ dmnorm(mu.prior.mean[1:p], mu.prior.precision[1:p, 1:p])
omega.inv[1:p, 1:p] ~ dwish(omega.inv.matrix[1:p, 1:p], omega.inv.dof)
omega[1:p, 1:p] <- inverse(omega.inv[1:p, 1:p])
}
list(
p = 4,
tau.a =345.8664, tau.b =308122.5,
mu.prior.mean = c(
9.772055, 9.358233, -2.137944, -1.853783),
mu.prior.precision = structure(
.Data = c(
328.729354, -46.8439167, -10.3345782, -1.851925,
-46.843917, 30.9111313, -0.4673475, -1.586074,
-10.334578, -0.4673475, 3.6007946, 1.403187,
-1.851925, -1.5860742, 1.4031872, 3.257598),
.Dim = c(4, 4)),
omega.inv.matrix = structure(
.Data = c(
5.779969, 8.999986, 13.30347, 4.736827,
8.999986, 54.138340, 23.23332, 31.882416,
13.303473, 23.233316, 146.86460, -42.607441,
4.736827, 31.882416, -42.60744, 432.706083),
.Dim = c(4, 4)),
omega.inv.dof =100.0
)
list(
theta = c(
9.772055, 9.358233, -2.137944, -1.853783),
tau = 0.001122,
mu = c(
9.772055, 9.358233, -2.137944, -1.853783),
omega.inv = structure(
.Data = c(
5.779969, 8.999986, 13.30347, 4.736827,
8.999986, 54.138340, 23.23332, 31.882416,
13.303473, 23.233316, 146.86460, -42.607441,
4.736827, 31.882416, -42.60744, 432.706083),
.Dim = c(4, 4))
)
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pk ~
Robert
Sure, it is expected that multivariate deviates from the Wishart will be
sensitive to df. However the issue with Charles's question is whether the
posterior parameter estimates from his analysis are sensitive to choice of the
prior value of df for a (inverse)Wishart used in NONMEM.
Regards
Steve
Quoted reply history
From: [email protected] [mailto:[email protected]] On
Behalf Of Johnson, Robert
Sent: Tuesday, 31 January 2012 9:31 a.m.
To: Charles Steven Ernest II
Cc: [email protected]
Subject: RE: [NMusers] PRIORS
Steve
Enclosed is a WinBugs file that simulates from a multivariate normal
distribution. The Wishart distribution is very sensitive to the degree of
freedom for the prior. Winbugs parameterizes in terms of precision i.e inverse
of the variance
Robert D. Johnson, Ph.D
Chemical Systems Modeling Section
Corporate R&D
Procter & Gamble
8256 Union Centre Blvd, IP-351
West Chester, OH 45069
[email protected]<mailto:[email protected]>
(513) 634-9827
From: [email protected]<mailto:[email protected]>
[mailto:[email protected]] On Behalf Of Stephen Duffull
Sent: Monday, January 30, 2012 1:12 PM
To: Gastonguay, Marc; Charles Steven Ernest II
Cc: [email protected]<mailto:[email protected]>
Subject: RE: [NMusers] PRIORS
Hi Charles
The choice of the df of the Wishart should be based on what your prior
information provides not on what the posterior distribution tells you. I
suspect, if your data is relatively uninformative then a sensitivity analysis
will show that the posterior is sensitive to the prior. It would then be a
matter of determining objectively how your subjective prior will influence your
current analysis and this depends on what you want to learn from your
analysis...
Regards
Steve
--
From: [email protected]<mailto:[email protected]>
[mailto:[email protected]] On Behalf Of Gastonguay, Marc
Sent: Monday, 30 January 2012 12:03 p.m.
To: Charles Steven Ernest II
Cc: [email protected]<mailto:[email protected]>
Subject: Re: [NMusers] PRIORS
Dear Charles,
When using $PRIOR, the df specifies the degrees of freedom for the
Inverse-Wishart prior distribution on the covariance matrix of the individual
random effects (OMEGA). In practical terms, the larger the df, the more
informative the prior will be. It's not surprising, then, that your parameter
estimates approach the results of the previous model when df is large.
The choice to use an informative prior distribution should not be made based on
objective function changes. Instead, you might want to consider the rationale
for including the prior information in the first place. One strategy would be
to use informative priors only where necessary to support components of a
previously defined or otherwise known model. If the new data alone do not
support estimation of parameters required in this model structure, then you
might want to include informative prior distributions on those specific
components. Sensitivity to the "informativeness" of the prior could be explored
by varying the df (or prior variance for fixed effects), and conclusions from
your analysis should probably be viewed in the context of this prior
sensitivity.
As you indicate, for this particular example, you may not need to use $PRIOR at
all, and could simply pool the data in a single analysis.
Hope this is useful.
Marc
On Sun, Jan 29, 2012 at 5:02 PM, Charles Steven Ernest II
<[email protected]<mailto:[email protected]>>
wrote:
I have previously conducted a meta-analysis of PK data that contained
extensive and sparse sampling from 330 patients with a run time of ~ 4
days. I know have data from another 200 patients with sparse data. I have
created the median and 95th PI from the previous model and overlaid the
current data. The results demonstrate that the new data is well described
by that model. When the new data is fit with that model, the data does not
support using the model as some parameters were unidentifiable. I could
conducted an analysis of all the data simultaneously but was interested in
another method. Therefore, I have implemented $PRIOR into the model and
noticed that with each successive increase of the df, the objective
function significantly decreases. However, the THETA values do not change
much and are different from the prior estimates used. The only other
things that changed besides the objective function were the estimates and
SE of the covariance terms and the BSV estimate of the peripheral volume of
distribution. These values become more in line with the those observed
previously, and the correlation values between them becomes stronger. My
question is it justifiable to use such a high df (df=330) based on these
significant decreases of objective function and covariance as the
information from this meta-analysi would be highly informative.
Thanks
--
Marc R. Gastonguay, Ph.D.<mailto:[email protected]>
Scientific Director
Metrum http://metruminstitute.org
Metrum Institute is a 501(c)3 non-profit organization.
The premise of conducting the analysis was to explore different dosages in
a population that displayed similar characteristics to that already
examined (a couple of dosages were the same also) and to evaluate the
effect of these different dosages on the efficacy markers over a longer
period of time as the previous trials were not of sufficient duration. A
comparison of the established PK model performance based on simulations to
the current data demonstrated that the new data is described well by that
model and there is little reason to believe that differences in the
populations would be expected. Therefore, I would have thought that
including informative priors for all parameters would have been the
quickest means to obtain these individual parameter estimates to proceed
with the PD modeling. I was assuming that the penalty objective function
would remain relatively the same despite increase in df and the objective
function could be used as a relative marker of fit. I also thought that
you could not use the objective function only when adding more or less
priors.by that model. I have conducted VPCs and relative comparison of
individual parameter estimates with low df compared to high df. The
individual estimates do not fluctuate that much with changes to df but the
VPC show some differences (whether sig or not still evaluating). This
seems to be based on the covariance estimates between the omegas for those
parameters that include those BLOCKs. These parameters and the omegas are
still slighly different from the previous modeling even with high df. I
would have thought that with such little data, they would have converged to
the priors estimates with a high df as noted earlier that they would not be
expected to be that different. The impact might become more important for
PK/PD simulations and future trial designs. Thank you for your comments.
Stephen Duffull
<stephen.duffull@
otago.ac.nz> To
"Johnson, Robert"
01/31/2012 03:23 <[email protected]>, Charles
PM Steven Ernest II
<[email protected]
>
cc
"[email protected]"
<[email protected]>
Subject
RE: [NMusers] PRIORS
Robert
Sure, it is expected that multivariate deviates from the Wishart will be
sensitive to df. However the issue with Charles’s question is whether the
posterior parameter estimates from his analysis are sensitive to choice of
the prior value of df for a (inverse)Wishart used in NONMEM.
Regards
Steve
Quoted reply history
From: [email protected] [mailto:[email protected]] On
Behalf Of Johnson, Robert
Sent: Tuesday, 31 January 2012 9:31 a.m.
To: Charles Steven Ernest II
Cc: [email protected]
Subject: RE: [NMusers] PRIORS
Steve
Enclosed is a WinBugs file that simulates from a multivariate normal
distribution. The Wishart distribution is very sensitive to the degree of
freedom for the prior. Winbugs parameterizes in terms of precision i.e
inverse of the variance
Robert D. Johnson, Ph.D
Chemical Systems Modeling Section
Corporate R&D
Procter & Gamble
8256 Union Centre Blvd, IP-351
West Chester, OH 45069
[email protected]
(513) 634-9827
From: [email protected] [mailto:[email protected]] On
Behalf Of Stephen Duffull
Sent: Monday, January 30, 2012 1:12 PM
To: Gastonguay, Marc; Charles Steven Ernest II
Cc: [email protected]
Subject: RE: [NMusers] PRIORS
Hi Charles
The choice of the df of the Wishart should be based on what your prior
information provides not on what the posterior distribution tells you. I
suspect, if your data is relatively uninformative then a sensitivity
analysis will show that the posterior is sensitive to the prior. It would
then be a matter of determining objectively how your subjective prior will
influence your current analysis and this depends on what you want to learn
from your analysis...
Regards
Steve
--
From: [email protected] [mailto:[email protected]] On
Behalf Of Gastonguay, Marc
Sent: Monday, 30 January 2012 12:03 p.m.
To: Charles Steven Ernest II
Cc: [email protected]
Subject: Re: [NMusers] PRIORS
Dear Charles,
When using $PRIOR, the df specifies the degrees of freedom for the
Inverse-Wishart prior distribution on the covariance matrix of the
individual random effects (OMEGA). In practical terms, the larger the df,
the more informative the prior will be. It's not surprising, then, that
your parameter estimates approach the results of the previous model when df
is large.
The choice to use an informative prior distribution should not be made
based on objective function changes. Instead, you might want to consider
the rationale for including the prior information in the first place. One
strategy would be to use informative priors only where necessary to support
components of a previously defined or otherwise known model. If the new
data alone do not support estimation of parameters required in this model
structure, then you might want to include informative prior distributions
on those specific components. Sensitivity to the "informativeness" of the
prior could be explored by varying the df (or prior variance for fixed
effects), and conclusions from your analysis should probably be viewed in
the context of this prior sensitivity.
As you indicate, for this particular example, you may not need to use
$PRIOR at all, and could simply pool the data in a single analysis.
Hope this is useful.
Marc
On Sun, Jan 29, 2012 at 5:02 PM, Charles Steven Ernest II <
[email protected]> wrote:
I have previously conducted a meta-analysis of PK data that contained
extensive and sparse sampling from 330 patients with a run time of ~ 4
days. I know have data from another 200 patients with sparse data. I have
created the median and 95th PI from the previous model and overlaid the
current data. The results demonstrate that the new data is well described
by that model. When the new data is fit with that model, the data does not
support using the model as some parameters were unidentifiable. I could
conducted an analysis of all the data simultaneously but was interested in
another method. Therefore, I have implemented $PRIOR into the model and
noticed that with each successive increase of the df, the objective
function significantly decreases. However, the THETA values do not change
much and are different from the prior estimates used. The only other
things that changed besides the objective function were the estimates and
SE of the covariance terms and the BSV estimate of the peripheral volume of
distribution. These values become more in line with the those observed
previously, and the correlation values between them becomes stronger. My
question is it justifiable to use such a high df (df=330) based on these
significant decreases of objective function and covariance as the
information from this meta-analysi would be highly informative.
Thanks
--
Marc R. Gastonguay, Ph.D.
Scientific Director
Metrum Institute
Metrum Institute is a 501(c)3 non-profit organization.