From: Matts Kågedal <*mattskagedal*>

Date: Wed, 30 Sep 2015 11:33:16 -0700

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

variable, and wonder if I could get some help.

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

dose is being adjusted based on the endpoint of interested or a correlated

endpoint. It then becomes important to have a good understanding of the

potential impact and ideally some convincing references for any skeptical

colleagues. Also in many cases doses are modified based on safety (e.g. in

oncology), and understanding how this can impact the analysis is important.

Statisticians 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

reduce 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. This results when the supposedly independent variable (dose) is not

independent of the DV. (In this example it will falsely appear that low

dose will result in low clearance.)

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

this 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

reduction could still occur based AEs, we would get a biased dose

proportionality 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

be more relevant when modeling safety and efficacy data.

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

censoring, the parameters of a longitudinal model based on data with dose

modifications will be *unbiased* if:

a) the dose modifications are completely uncorrelated to the dependent

variable (DV). (We could call this non-informative dose modification or

dose modification completely at random)

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

this observation is included in the analysis (We could call this

non-informative dose modification or dose modification at random)

(corresponds to example 2 above).

- The parameters will be *biased* if:

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

call this informative dose modification or modified not at random).

(corresponds to example 3 above)

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

probability of dose reduction based on the endpoint of interest. E.g. for

example 3, one would need to estimate the probability of dose reduction as

a function of exposure.

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

help understanding this issue? (Ideally in a language that can be

understood also by the less statistically oriented pharmacometrician, I

find statistical literature hard to read sometimes).

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

unbiased parameter estimates (in addition to explanation b). Any arguments

against?

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

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

Best regards,

Matts

--

Matts Kagedal

Pharmacometrician, Genentech

Mobile: +1(650) 255 2534

Received on Wed Sep 30 2015 - 14:33:16 EDT

Date: Wed, 30 Sep 2015 11:33:16 -0700

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

variable, and wonder if I could get some help.

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

dose is being adjusted based on the endpoint of interested or a correlated

endpoint. It then becomes important to have a good understanding of the

potential impact and ideally some convincing references for any skeptical

colleagues. Also in many cases doses are modified based on safety (e.g. in

oncology), and understanding how this can impact the analysis is important.

Statisticians 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

reduce 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. This results when the supposedly independent variable (dose) is not

independent of the DV. (In this example it will falsely appear that low

dose will result in low clearance.)

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

this 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

reduction could still occur based AEs, we would get a biased dose

proportionality 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

be more relevant when modeling safety and efficacy data.

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

censoring, the parameters of a longitudinal model based on data with dose

modifications will be *unbiased* if:

a) the dose modifications are completely uncorrelated to the dependent

variable (DV). (We could call this non-informative dose modification or

dose modification completely at random)

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

this observation is included in the analysis (We could call this

non-informative dose modification or dose modification at random)

(corresponds to example 2 above).

- The parameters will be *biased* if:

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

call this informative dose modification or modified not at random).

(corresponds to example 3 above)

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

probability of dose reduction based on the endpoint of interest. E.g. for

example 3, one would need to estimate the probability of dose reduction as

a function of exposure.

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

help understanding this issue? (Ideally in a language that can be

understood also by the less statistically oriented pharmacometrician, I

find statistical literature hard to read sometimes).

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

unbiased parameter estimates (in addition to explanation b). Any arguments

against?

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

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

Best regards,

Matts

--

Matts Kagedal

Pharmacometrician, Genentech

Mobile: +1(650) 255 2534

Received on Wed Sep 30 2015 - 14:33:16 EDT