Dose-proportionality versus dose-linearity [PK / PD]

posted by martin  – Austria, 2018-08-03 10:25  – Posting: # 19131
Views: 2,810

Dear Colleagues,

I would like to re-open again the never ending discussion regarding the concepts of dose-proportionality versus dose-linearity. Based on some internal discussion I tried to summarize my current understanding of this topic in bullet points where I would be happy to get the opinion of the form members on these considerations.

Concept:
The concept of dose-proportionality is based on the premise that a dose of zero leads to an exposure of zero (i.e. line going through the origin). In contrast, the concept of dose-linearity does not require having a line going through the origin.

Currently I am aware of only two situations where the concept of dose-linearity is favored over the concept of dose-proportionality namely

Situation 1: Endogenous substances (e.g. estradiol) where the individual PK metrics are not adjusted for the endogenous background prior evaluation of the dose-response relationship. This means a dose of zero leads to an AUC > 0 due to the endogenous background

Situation 2: A compounds that is invariably lost upon administration which would result also in a line not going through the origin.

Statistical considerations:
Typically, dose-proportionality is an equivalence problem and can be evaluated based on the work of Smith et al (2000). In contrast, dose-linearity is sometimes evaluated by fitting a quadratic equation and evaluate whether or not this model provided a better fit than just a straight line.

In addition, I became aware of cases where dose-proportionality was not shown but dose-linearity was claimed based on the approach above. I think this approach is flawed as the 1) quadratic model approach is also driven by precision and sample size and not necessarily just by degree of non-linearity and 2) the absence of evidence is not the evidence of absence.

My summary:
I am having serious troubles thinking of a situation which fails to show dose proportionality (for lack of evidence) and yet still shows linear PK and therefore:

I would recommend using the concept of dose-proportionality (e.g. Smith et al, 2000) unless there is biological reason not to do so (e.g. endogenous substances or substances that are invariably lost upon administration). If you have to stick with the concept of dose-linearity and the fitted line of the quadratic model does not go through the origin and there is no underlying rationale for that (e.g. endogenous substance) than I would consider this as an inadequate model for the data at hand (e.g. internal validation failed).

Best regards & looking for an interesting discussion

Martin

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