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From: Åstrand, Magnus <Magnus.Astrand_at_astrazeneca.com>

Date: Wed, 30 Sep 2015 19:36:21 +0000

Hi Matts, I agree on your conclusions and think the issue of missing data i=

s a very similar problem. There the missing completely at random and missin=

g at random would match your examples a and b. For missing data there exist=

s litterature and also perhaps a better understanding among statistician. R=

ubins book I think is a good referece with results showing good properties =

of maximum likelihood.

Bw

Magnus

________________________________

Från: owner-nmusers_at_globomaxnm.com <owner-nmusers_at_globomaxnm.com> för M=

atts Kågedal <mattskagedal_at_gmail.com>

Skickat: den 30 september 2015 20:33:16

Till: nmusers_at_globomaxnm.com

Ämne: [NMusers] Ambiguous independence of independent variable.

Hi nonmem users!

I have troubles explaining to statisticians (and perhaps to myself) why it =

can be OK to model data where the dose is adjusted based on the dependent v=

ariable, and wonder if I could get some help.

This is a very relevant issue when planing for adaptive designs where the d=

ose is being adjusted based on the endpoint of interested or a correlated e=

ndpoint. It then becomes important to have a good understanding of the pote=

ntial impact and ideally some convincing references for any skeptical colle=

agues. Also in many cases doses are modified based on safety (e.g. in oncol=

ogy), and understanding how this can impact the analysis is important. Stat=

isticians can become very suspicious (which is their job) when there is any=

ambiguity in the independence of the independent variable.

A PK study example for illustration of the problem:

PK measured at day 1 and day 10. Patients with high AUC on day 1 dose reduc=

e before day 10.

example 1: If naively analyzing the relation between dose and PK on day 10 =

it will appear that the PK is not dose proportional, when it actually is. T=

his results when the supposedly independent variable (dose) is not independ=

ent of the DV. (In this example it will falsely appear that low dose will r=

esult in low clearance.)

example 2: If analyzed longitudinally using all data and a pop PK model, th=

is problem goes away, since the model will be informed also by day 1 PK and=

the PK-parameters will be unbiased.

example 3: If however no PK-measurements were taken on day one but dose red=

uction could still occur based AEs, we would get a biased dose proportional=

ity assessment if AEs are correlated with exposure. (pop-PK analysis would =

not help).

The above is a PK-example for illustration, but the question may probably b=

e more relevant when modeling safety and efficacy data.

Thinking along the same lines as for informative vs non-informative censori=

ng, the parameters of a longitudinal model based on data with dose modifica=

tions will be unbiased if:

a) the dose modifications are completely uncorrelated to the dependent vari=

able (DV). (We could call this non-informative dose modification or dose mo=

dification completely at random)

b) if the dose modification is based on an observed value of the DV where t=

his observation is included in the analysis (We could call this non-informa=

tive dose modification or dose modification at random) (corresponds to exam=

ple 2 above).

- The parameters will be biased if:

c) the dose modification is based on an unobserved value of the DV (Could c=

all this informative dose modification or modified not at random). (corresp=

onds to example 3 above)

In case C, the model would need to include a function that estimates the pr=

obability of dose reduction based on the endpoint of interest. E.g. for exa=

mple 3, one would need to estimate the probability of dose reduction as a f=

unction of exposure.

Coming back to my original question, is there any literature that could hel=

p understanding this issue? (Ideally in a language that can be understood a=

lso by the less statistically oriented pharmacometrician, I find statistica=

l literature hard to read sometimes).

Are there further/better arguments for why example 2 will result in unbias=

ed parameter estimates (in addition to explanation b). Any arguments agains=

t?

Are there any examples in the literature showing when failure to account fo=

r "informative dose adjustments" results in biased parameter estimates?

Best regards,

Matts

--

Matts Kagedal

Pharmacometrician, Genentech

Mobile: +1(650) 255 2534<tel:%2B1%28650%29%20255%202534>

________________________________

Confidentiality Notice: This message is private and may contain confidentia=

l and proprietary information. If you have received this message in error, =

please notify us and remove it from your system and note that you must not =

copy, distribute or take any action in reliance on it. Any unauthorized use=

or disclosure of the contents of this message is not permitted and may be =

unlawful.

Received on Wed Sep 30 2015 - 15:36:21 EDT

Date: Wed, 30 Sep 2015 19:36:21 +0000

Hi Matts, I agree on your conclusions and think the issue of missing data i=

s a very similar problem. There the missing completely at random and missin=

g at random would match your examples a and b. For missing data there exist=

s litterature and also perhaps a better understanding among statistician. R=

ubins book I think is a good referece with results showing good properties =

of maximum likelihood.

Bw

Magnus

________________________________

Från: owner-nmusers_at_globomaxnm.com <owner-nmusers_at_globomaxnm.com> för M=

atts Kågedal <mattskagedal_at_gmail.com>

Skickat: den 30 september 2015 20:33:16

Till: nmusers_at_globomaxnm.com

Ämne: [NMusers] Ambiguous independence of independent variable.

Hi nonmem users!

I have troubles explaining to statisticians (and perhaps to myself) why it =

can be OK to model data where the dose is adjusted based on the dependent v=

ariable, and wonder if I could get some help.

This is a very relevant issue when planing for adaptive designs where the d=

ose is being adjusted based on the endpoint of interested or a correlated e=

ndpoint. It then becomes important to have a good understanding of the pote=

ntial impact and ideally some convincing references for any skeptical colle=

agues. Also in many cases doses are modified based on safety (e.g. in oncol=

ogy), and understanding how this can impact the analysis is important. Stat=

isticians can become very suspicious (which is their job) when there is any=

ambiguity in the independence of the independent variable.

A PK study example for illustration of the problem:

PK measured at day 1 and day 10. Patients with high AUC on day 1 dose reduc=

e before day 10.

example 1: If naively analyzing the relation between dose and PK on day 10 =

it will appear that the PK is not dose proportional, when it actually is. T=

his results when the supposedly independent variable (dose) is not independ=

ent of the DV. (In this example it will falsely appear that low dose will r=

esult in low clearance.)

example 2: If analyzed longitudinally using all data and a pop PK model, th=

is problem goes away, since the model will be informed also by day 1 PK and=

the PK-parameters will be unbiased.

example 3: If however no PK-measurements were taken on day one but dose red=

uction could still occur based AEs, we would get a biased dose proportional=

ity assessment if AEs are correlated with exposure. (pop-PK analysis would =

not help).

The above is a PK-example for illustration, but the question may probably b=

e more relevant when modeling safety and efficacy data.

Thinking along the same lines as for informative vs non-informative censori=

ng, the parameters of a longitudinal model based on data with dose modifica=

tions will be unbiased if:

a) the dose modifications are completely uncorrelated to the dependent vari=

able (DV). (We could call this non-informative dose modification or dose mo=

dification completely at random)

b) if the dose modification is based on an observed value of the DV where t=

his observation is included in the analysis (We could call this non-informa=

tive dose modification or dose modification at random) (corresponds to exam=

ple 2 above).

- The parameters will be biased if:

c) the dose modification is based on an unobserved value of the DV (Could c=

all this informative dose modification or modified not at random). (corresp=

onds to example 3 above)

In case C, the model would need to include a function that estimates the pr=

obability of dose reduction based on the endpoint of interest. E.g. for exa=

mple 3, one would need to estimate the probability of dose reduction as a f=

unction of exposure.

Coming back to my original question, is there any literature that could hel=

p understanding this issue? (Ideally in a language that can be understood a=

lso by the less statistically oriented pharmacometrician, I find statistica=

l literature hard to read sometimes).

Are there further/better arguments for why example 2 will result in unbias=

ed parameter estimates (in addition to explanation b). Any arguments agains=

t?

Are there any examples in the literature showing when failure to account fo=

r "informative dose adjustments" results in biased parameter estimates?

Best regards,

Matts

--

Matts Kagedal

Pharmacometrician, Genentech

Mobile: +1(650) 255 2534<tel:%2B1%28650%29%20255%202534>

________________________________

Confidentiality Notice: This message is private and may contain confidentia=

l and proprietary information. If you have received this message in error, =

please notify us and remove it from your system and note that you must not =

copy, distribute or take any action in reliance on it. Any unauthorized use=

or disclosure of the contents of this message is not permitted and may be =

unlawful.

Received on Wed Sep 30 2015 - 15:36:21 EDT