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From: Ken Kowalski <kgkowalski58_at_gmail.com>

Date: Thu, 14 Mar 2019 14:01:23 -0400

Hi All,

I know what Bill is trying to say but it is not quite accurate the way he s=

tates it.

A prediction interval makes inference on a statistic based on a future samp=

le such as a sample mean of a future set of data. In contrast, a confidenc=

e interval makes inference on a parameter such as the population mean which=

is a fixed number. A prediction interval takes into account both the unce=

rtainty in the existing data used to estimate the population parameter as w=

ell as the sampling variation to make inference on a sample statistic (e.g.=

, sample mean for a future trial). A confidence interval only takes into =

account the uncertainty in the existing data used to estimate the parameter=

. Based on the Law of Large Numbers, the population mean can be thought =

of as taking the sample mean of an infinite sample size (i.e., sampling the=

entire population). For this reason, a prediction interval with an infini=

te sample size will collapse to a confidence interval.

An interval based on VPCs is more akin to a prediction interval since it ta=

kes into account the sampling variation based on a finite sample size, howe=

ver, one cannot assign a valid coverage probability (confidence level) to t=

his interval unless it also takes into account the parameter uncertainty. =

With VPCs applied to existing data (i.e, an internal VPC) it is customary t=

o not take into account this parameter uncertainty so many refer to such pr=

ediction intervals as degenerate as they place 100% certainty on the model =

parameter estimates used to obtain the VPC predictions. One could potent=

ially call these intervals â€˜degenerate prediction intervalsâ€=

™ but I tend to just call them â€˜VPC intervalsâ€™ (e.g., a 9=

0% VPC interval) so as to avoid misperception that these prediction interva=

ls have a statistically valid coverage probability. However, when VPCs are=

applied to an independent dataset not used in the development of the model=

, it is often advised to take into account the parameter uncertainty when p=

erforming the VPCs to essentially reflect the trial-to-trial uncertainty of=

the independent data not used in the estimation of model (i.e., refitting =

the same model to a new set of trial data will not give the same set of est=

imates and hence reflects trial-to-trial variation). In this setting, wher=

e the VPCs take into account both the parameter uncertainty and sampling va=

riation to predict on an independent (e.g., future) dataset, then one is on=

more solid ground to refer to these VPC intervals as prediction intervals =

with valid coverage probabilities.

Kind regards,

Ken

Kenneth G. Kowalski

Kowalski PMetrics Consulting, LLC

Email: <mailto:kgkowalski58_at_gmail.com> kgkowalski58_at_gmail.com

Cell: 248-207-5082

From: owner-nmusers_at_globomaxnm.com [mailto:owner-nmusers_at_globomaxnm.com] On=

Behalf Of Bill Denney

Sent: Thursday, March 14, 2019 1:10 PM

To: Soto, Elena <elena.soto_at_pfizer.com>; nmusers_at_globomaxnm.com

Subject: RE: [NMusers] VPCs confidence intervals?

Hi Elena,

VPCs are accurately called prediction intervals not confidence intervals. =

The difference is that a prediction interval shows what you would expect fo=

r the next individual in a study while a confidence interval shows what you=

would expect for the result of a statistic (often confidence intervals of =

a mean are shown). With many VPCs, the confidence interval of the median a=

nd the confidence interval of the 5th and 95th percentiles are shown.

Also, when the lines indicate the median, 5th, and 95th percentiles of the =

simulations, that is the 90% prediction interval since it is the middle 90%=

of the data (not the 95% confidence interval).

Thanks,

Bill

From: owner-nmusers_at_globomaxnm.com <mailto:owner-nmusers_at_globomaxnm.com> <=

owner-nmusers_at_globomaxnm.com <mailto:owner-nmusers_at_globomaxnm.com> > On Beh=

alf Of Soto, Elena

Sent: Thursday, March 14, 2019 12:49 PM

To: nmusers_at_globomaxnm.com

Subject: [NMusers] VPCs confidence intervals?

Dear all,

I have a question regarding visual predictive checks (VPCs).

Most of VPCs used now, include a line representing the median and 5th and 9=

5th percentiles of the data values and an area around the same percentiles =

that is commonly define as the 95% confidence interval (of the simulations)=

.

But is it correct, from the statistical point of view, to call confidence i=

nterval to this area? And if this is not the case how should we define them=

?

Thanks,

Elena Soto

Elena Soto, PhD

Pharmacometrician

Pharmacometrics, Global Clinical Pharmacology

Global Product Development

Pfizer R&D UK Limited, IPC 096

CT13 9NJ, Sandwich, UK

Phone : +44 1304 644883

_____

Unless expressly stated otherwise, this message is confidential and may be =

privileged. It is intended for the addressee(s) only. Access to this e-mai=

l by anyone else is unauthorised. If you are not an addressee, any disclosu=

re or copying of the contents of this e-mail or any action taken (or not ta=

ken) in reliance on it is unauthorised and may be unlawful. If you are not =

an addressee, please inform the sender immediately.

Pfizer R&D UK Limited is registered in England under No. 11439437 with its =

registered office at Ramsgate Road, Sandwich, Kent CT13 9NJ

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Received on Thu Mar 14 2019 - 14:01:23 EDT

Date: Thu, 14 Mar 2019 14:01:23 -0400

Hi All,

I know what Bill is trying to say but it is not quite accurate the way he s=

tates it.

A prediction interval makes inference on a statistic based on a future samp=

le such as a sample mean of a future set of data. In contrast, a confidenc=

e interval makes inference on a parameter such as the population mean which=

is a fixed number. A prediction interval takes into account both the unce=

rtainty in the existing data used to estimate the population parameter as w=

ell as the sampling variation to make inference on a sample statistic (e.g.=

, sample mean for a future trial). A confidence interval only takes into =

account the uncertainty in the existing data used to estimate the parameter=

. Based on the Law of Large Numbers, the population mean can be thought =

of as taking the sample mean of an infinite sample size (i.e., sampling the=

entire population). For this reason, a prediction interval with an infini=

te sample size will collapse to a confidence interval.

An interval based on VPCs is more akin to a prediction interval since it ta=

kes into account the sampling variation based on a finite sample size, howe=

ver, one cannot assign a valid coverage probability (confidence level) to t=

his interval unless it also takes into account the parameter uncertainty. =

With VPCs applied to existing data (i.e, an internal VPC) it is customary t=

o not take into account this parameter uncertainty so many refer to such pr=

ediction intervals as degenerate as they place 100% certainty on the model =

parameter estimates used to obtain the VPC predictions. One could potent=

ially call these intervals â€˜degenerate prediction intervalsâ€=

™ but I tend to just call them â€˜VPC intervalsâ€™ (e.g., a 9=

0% VPC interval) so as to avoid misperception that these prediction interva=

ls have a statistically valid coverage probability. However, when VPCs are=

applied to an independent dataset not used in the development of the model=

, it is often advised to take into account the parameter uncertainty when p=

erforming the VPCs to essentially reflect the trial-to-trial uncertainty of=

the independent data not used in the estimation of model (i.e., refitting =

the same model to a new set of trial data will not give the same set of est=

imates and hence reflects trial-to-trial variation). In this setting, wher=

e the VPCs take into account both the parameter uncertainty and sampling va=

riation to predict on an independent (e.g., future) dataset, then one is on=

more solid ground to refer to these VPC intervals as prediction intervals =

with valid coverage probabilities.

Kind regards,

Ken

Kenneth G. Kowalski

Kowalski PMetrics Consulting, LLC

Email: <mailto:kgkowalski58_at_gmail.com> kgkowalski58_at_gmail.com

Cell: 248-207-5082

From: owner-nmusers_at_globomaxnm.com [mailto:owner-nmusers_at_globomaxnm.com] On=

Behalf Of Bill Denney

Sent: Thursday, March 14, 2019 1:10 PM

To: Soto, Elena <elena.soto_at_pfizer.com>; nmusers_at_globomaxnm.com

Subject: RE: [NMusers] VPCs confidence intervals?

Hi Elena,

VPCs are accurately called prediction intervals not confidence intervals. =

The difference is that a prediction interval shows what you would expect fo=

r the next individual in a study while a confidence interval shows what you=

would expect for the result of a statistic (often confidence intervals of =

a mean are shown). With many VPCs, the confidence interval of the median a=

nd the confidence interval of the 5th and 95th percentiles are shown.

Also, when the lines indicate the median, 5th, and 95th percentiles of the =

simulations, that is the 90% prediction interval since it is the middle 90%=

of the data (not the 95% confidence interval).

Thanks,

Bill

From: owner-nmusers_at_globomaxnm.com <mailto:owner-nmusers_at_globomaxnm.com> <=

owner-nmusers_at_globomaxnm.com <mailto:owner-nmusers_at_globomaxnm.com> > On Beh=

alf Of Soto, Elena

Sent: Thursday, March 14, 2019 12:49 PM

To: nmusers_at_globomaxnm.com

Subject: [NMusers] VPCs confidence intervals?

Dear all,

I have a question regarding visual predictive checks (VPCs).

Most of VPCs used now, include a line representing the median and 5th and 9=

5th percentiles of the data values and an area around the same percentiles =

that is commonly define as the 95% confidence interval (of the simulations)=

.

But is it correct, from the statistical point of view, to call confidence i=

nterval to this area? And if this is not the case how should we define them=

?

Thanks,

Elena Soto

Elena Soto, PhD

Pharmacometrician

Pharmacometrics, Global Clinical Pharmacology

Global Product Development

Pfizer R&D UK Limited, IPC 096

CT13 9NJ, Sandwich, UK

Phone : +44 1304 644883

_____

Unless expressly stated otherwise, this message is confidential and may be =

privileged. It is intended for the addressee(s) only. Access to this e-mai=

l by anyone else is unauthorised. If you are not an addressee, any disclosu=

re or copying of the contents of this e-mail or any action taken (or not ta=

ken) in reliance on it is unauthorised and may be unlawful. If you are not =

an addressee, please inform the sender immediately.

Pfizer R&D UK Limited is registered in England under No. 11439437 with its =

registered office at Ramsgate Road, Sandwich, Kent CT13 9NJ

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Received on Thu Mar 14 2019 - 14:01:23 EDT