Bioequivalence and Bioavailability Forum

Dear all,

with the increasing number of studies designed for RSABE (FDA) or ABEL (EMA) the question about con­servatism in sample size estimation pops up. ICH E9 tells us:

The number of subjects in a clinical trial should always be large enough to provide a reliable answer to the questions addressed.

Well roared, lion! In other words, that’s not a playground for gamblers. Too small sample sizes are unethical because the power might be too low. Many of us have put a lot of efforts in the past teaching “The Guy in the Armani-suit” (© ElMaestro) that there is no point playing games and be conservative instead (i.e., assume a higher CV in estimating the sample size of pivotal studies).
Apart from the splendid – and widespread – “Let’s fake a CV and ratio which gives a sample size matching our budget!" I have seen three approaches/arguments:

1. The Gambler’s
   After the pilot study the CRO has learned to deal with the drug, the bioanalytical method is routine, the CV will be lower.
   
2. The Believer’s
   What we have seen in the pilot will be reproduced in the pivotal. Also known as the “carved in stone”-approach.
   
3. The Conservative’s
   The CV is just an estimate. In the pivotal study it might be higher. Let’s assume that. If the assumption is not correct, we lost money but still have a study which demonstrates BE. Further­more, with a lower CV we have a higher chance of passing if the T/R-ratio is further away from 1.

Which category does your boss belong to?

Let’s start with a simple example (ABE). In a reasonably sized pilot study we have found a CV of 30%. We plan for a T/R-ratio of 0.90 and 90% power. Since the sample sizes in a conventional 2×2 are large, we ex­plore a fully replicated design as well.
───────────────────────
              CV%      
         ──────────────
         25  30  35  40
───────────────────────
2×2×2 n  78 108 146 186
2×2×4 n  38  54  72  94
───────────────────────

What happens (% power) in the pivotal studies with the different approaches?
─────────────────────────────────────────────────────────
               2×2×2                        2×2×4        
─────────────────────────────────────────────────────────
                CV%                          CV%         
     ───────────────────────      ───────────────────────
 n     25    30    35    40   n     25    30    35    40 
─────────────────────────────────────────────────────────
 78  90.59 79.91 69.13 59.76  38  90.07 79.19 68.36 59.01
108  96.77 90.05 81.19 72.15  54  96.82 90.16 81.34 72.31
146  99.23 96.14 90.35 83.02  72  99.18 95.98 90.07 82.67
186  99.84 98.65 95.39 90.19  94  99.86 98.73 95.60 90.53
─────────────────────────────────────────────────────────
Trivial. If the assumption is correct we achieve the planned power (blue). If the CV is is lower, power will be higher (as a side effect allowing the T/R to deviate more; green). The gambler (red) might still get 80% power, but may fail terribly in many cases.

So far, so good. But what happens if we decide to go with re­­ference-scaling? Similar like above (CV 30%, T/R-ratio 0.90, and 90% power), but this time FDA’s method in a fully replicated design.
─────────────────
        CV%      
   ──────────────
   25  30  35  40
─────────────────
n  40  44  38  34
─────────────────
At the border for scaling (CV 30%) we need the largest sample size. That’s well known, but may take novices by surprise. The sample size is lower for 25%. Sure, but smaller ones are also needed for CVs >30% because scaling cuts in. At CVs >50% we have to increase the sample size again. Al­though we are still allowed to scale (there is no cap at 50% like in EMA’s ABEL), the GMR-restriction cuts in.

What does that mean for study planning?
────────────────────────────
                CV%         
     ───────────────────────
 n     25    30    35    40 
────────────────────────────
 40  91.00 87.70 91.97 94.27
 44  93.25 90.02 93.85 94.50
 38  89.84 86.63 90.85 93.73
 34  86.75 83.38 87.90 91.04
────────────────────────────
The pattern almost reverses. In many cases you get more power if the CV is higher than expected. Try to teach that to your boss (“Let’s assume a lower CV in order to be conservative…”) However, the drop in power is nowhere as pronounced as in ABE.