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SV: Ambiguous independence of independent variable.

From: Åstrand, Magnus <Magnus.Astrand>
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.

Frn: owner-nmusers
atts Kgedal <mattskagedal
Skickat: den 30 september 2015 20:33:16
Till: nmusers
mne: [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=

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


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

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