Bioequivalence and Bioavailability Forum

Hi Martin!

❝ consider the following situation:

❝ - parallel group design with k study arms

❝ - all concentrations over time are <LOQ for ca. 40% of subjects (no

❝   C_max available)

Oops!

❝ what do you suggest for statistical comparison of C_max values

❝ between study arms?

❝ - set C_max at LOQ for these subjects

❝ - no statistical evaluation

❝ - statistical evaluation only for the subset of subjects with

❝   C_max > LOQ which may bias results

❝ - ...

To get into the right mood read this goody again.
Did you anticipate something like this in the SAP? If not, it's not too late - but stop now and take a deep breath. It's important not to play around with the data until you have developed a statistical contingency plan (ideally an amended SAP). Now let's see:

1. Massive bias of the estimates, I would say - even if these 40 % <LOQ are evenly spread across groups. On the other hand, if (and only if) these values are evenly distributed, the absolute mean values of C_max of the treatments will have a positive bias - the ratio between groups should not be hit (that much). Suboptimal, but possible. Problematic is also the influence on the variance (should be smaller, right?).
   Once I did something similar in a safety study, where we expected the majority of subjects to show values <LOQ. Since this was a one-sided test situation, replacing these values with LOQ was conservative and preserved the patient's risk better than any other method.
   
2. Probably the best, but your boss will not like that.
   Modifying Ludwig Wittgenstein: »Wovon man nicht rechnen kann, darüber muss man schweigen.«*
   
3. This is essentially the opposite of #1.

I have no solution; if you have a little time, fire up a simulation. And don't forget to generate one dataset with C_max=LOQ/2. Black magic, but who knows?

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* Tractatus Logico-Philosophicus (1921), Section 7: »Wovon man nicht sprechen kann, darüber muss man schweigen.« (Whereof one cannot speak, thereof one must be silent.)