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?

---

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

Dear Martin,

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

❝   C_max available)

It is not clear what the purpose of the trial is but I am willing to bet a monthly salary on the fact that the study report when reviewed by an assessor will not do much for you, whatever you do.

The 40% being <LOQ is extremely unexpected unless everybody in your team had had a stroke the day the trial was planned (which I think is unlikely, but feel free to comment).
For this reason, send out an auditor; do a for-cause audit to look at the trial itself and the bioanalysis. Make sure the auditor comes home to give you a really qualified idea of whether the observed problem is a real problem. I highly recommend you to use an auditor that looks for more than just missing signatures or misspelling on training records.

Dear Martin,

I was thinking a little further about this. OK, admittedly, my moments of thinkings are typically the moments when things go seriously pear-shaped for me.
Anyways, how about this: do nothing out of the ordinary.

You have a system for your chromatography, recording of data, getting data into your spreadsheet, getting the data analysed and getting the results printed, saved, documented. Each of these steps is (should be) an objective process. In the first steps your output is not of the 71.93-kind but of the "<LOQ"-kind (or NA or BLQ or DOA or whateever) for some of the data.
Unless you have pre-specified otherwise, I think it you should at least consider inputting exactly what comes out of the first steps and into the next steps. I know this is brutal and perhaps brainless, all depending on your coding, but it might be per protocol. All validated software has default methods to handle missing or unexpected inputs. You might not get anything meaningful out of it, but you have handled it objectively as prescribed and cannot be nailed for attempts to prune the data prior to analysis.
As someone once said: Garbage in, garbage out.

After you obtain garbage out, I think you have pretty free hands to apply other types of common sense to your problem. I could be wrong, but I think I would do this with a new protocol/sap rather than trying to modify the old one(s).

Let it be known, I am not a fan of garbage in but it is darn hard to plan against all types of eventualities.