## Deficiencies or not [Study As­sess­ment]

Hi zizou,

❝ The statistically significant formulation effect for AUC(0-t) is quite common. The sample size is usually estimated with intra-subject CV of Cmax (as it is usually higher than of AUC(0-t)).

Correct.

❝ To continue with your example:

❝ Assumed intra-subject CV of Cmax = 25% -> with assumed PE of 95% for target power 90%: n = 38

❝ Assumed intra-subject CV of AUC(0-t) e.g. 10%

❝ When assumed parameters used for sample size estimation will be theoretically observed in the study, i.e. the observed GMR will be 95% and observed intra-subect CV will be 10%, we will get 90% CI equal to 91.40-98.74% and statistically significant formulation effect (at a 10% significance level).

Correct as well. A study should be powered for the worst case combination (assumed CV, PE) of PK metrics. Naturally, PK metrics with ‘better combinations’ will have higher power.

❝ If the 90% CI does not contain 100%, the p value will always be <0.1 but how it could further exacerbated the uncertainty about fulfillment of the bioequivalence criteria? (Question for regulators.)

❝ ❝

  100% not within CI           :  5.76% (∆ stat. significant)

❝ I just want to point that it's observed more often for AUC(0-t) than for Cmax and it would be interesting to know the percentage of that also for AUC(0-t) with lower variability. ;)

Your wish is my command I (-script upon request).

Assumed CV (Cmax)    : 25.00% Assumed CVs (AUC)    : 25.00%, 20.00%, 15.00%, 10.00% Assumed PE           : 95.00% Target power         : 90.00% Sample size          : 38 (based on Cmax) Achieved power (Cmax): 90.89% Achieved powers (AUC): 90.89%, 98.05%, 99.95%, 100.00% Dosed                : 44 (anticipated dropout-rate of 10%)   100,000 simulated 2×2×2 studies   n: 28 – 37 (median 34)   Cmax (25.00%)     CV       : 13.87 –  40.66% (geom. mean  24.62%)     PE       : 83.65 – 107.59% (geom. mean  94.99%)     passed BE: 98.61% (‘empiric power’)     passing studies with ‘post hoc’ power of <50%:  0.03%                                        ≥50 – <60%:  3.11%                                        ≥60 – <70%:  7.99%                                        ≥70 – <80%: 16.74%                                        ≥80 – <90%: 30.51%                                              >90%: 41.63%     100% not within CI (∆ stat. significant)     :  5.76%    AUC (25.00%)     CV       :  12.22 –  41.01% (geom. mean  24.60%)     PE       :  82.68 – 107.20% (geom. mean  95.00%)     passed BE:  98.63% (‘empiric power’)     passing studies with ‘post hoc’ power of <50%:   0.03%                                        ≥50 – <60%:   3.10%                                        ≥60 – <70%:   7.74%                                        ≥70 – <80%:  16.78%                                        ≥80 – <90%:  30.30%                                              >90%:  42.05%     100% not within CI (∆ stat. significant)     :   5.82%    AUC (20.00%)     CV       :   9.77 –  31.70% (geom. mean 19.68%)     PE       :  84.80 – 105.86% (geom. mean 95.00%)     passed BE:  99.98% (‘empiric power’)     passing studies with ‘post hoc’ power of <50%:   0.00%                                        ≥50 – <60%:   0.13%                                        ≥60 – <70%:   0.62%                                        ≥70 – <80%:   2.87%                                        ≥80 – <90%:  12.47%                                              >90%:  83.92%     100% not within CI (∆ stat. significant)     :  13.06%    AUC (15.00%)     CV       :   7.24 –  24.83% (geom. mean  14.77%)     PE       :  88.31 – 102.73% (geom. mean  95.01%)     passed BE: 100.00% (‘empiric power’)     passing studies with ‘post hoc’ power of <50%:   0.00%                                        ≥50 – <60%:   0.00%                                        ≥60 – <70%:   0.00%                                        ≥70 – <80%:   0.01%                                        ≥80 – <90%:   0.23%                                              >90%:  99.75%     100% not within CI (∆ stat. significant)     :  31.35%    AUC (10.00%)     CV       :   4.77 –  15.32% (geom. mean   9.85%)     PE       :  90.25 – 100.03% (geom. mean  95.00%)     passed BE: 100.00% (‘empiric power’)     passing studies with ‘post hoc’ power of <50%:   0.00%                                        ≥50 – <60%:   0.00%                                        ≥60 – <70%:   0.00%                                        ≥70 – <80%:   0.00%                                        ≥80 – <90%:   0.00%                                              >90%: 100.00%     100% not within CI (∆ stat. significant)     :  79.43%

❝ ❝

2. Lack of a posteriori data on the power...

❝ The only good thing on this point is that the regulators believe that test and reference IMPs are bioequivalent. (As they deal with power.)

❝ Posteriori power is never ending story. The question on the power should be raised to the protocol, if it is addressed to the report, it is just a suggestion for future projects.

❝ Additionaly You can remind them what the low power means: With lower power, the type II error (sponsor's risk) is higher - it means that the bioequivalent preparations could be assessed wrongly as not bioequivalent with higher probability. The regulators should sleep well with higher type II error (unless the study was designed for e.g. 50% power from the start - but such protocols should be rejected).

Agree, though in the statistical sense we assume (i.e., believe) that products are not bioequivalent (that’s the Null) and hope that it will rejected.

❝ I wish the regulators would be interested also in the type I error - …

So do I. Inflated Type I Error in reference-scaling – another issue generally ignored.

❝ … it would mean that regulators do not believe that test and reference IMPs are bioequivalent. The probability of approving non-bioequivalent test product should be up to 5%.

Correct.

❝ I noticed several studies which suprised me more than this deficiency letter…

Funny stories! Assessors of the MHRA are a strange bunch.
1. Pilot:
Not particularly nice PE though BE seems to be possible in a pivotal study.
2. Pivotal:
CV similar to the pilot study but the PE moved further away from 100% than in the pilot. Study failed and repeating in a larger sample size (like in your example) was considered futile. Product reformulated and →
1. Pilot:
CV similar to the others, PE promising this time.
2. Pivotal:
Passed BE with flying colors.
Submitted #2.b. to the MHRA. Synopses of the others as well to document the product development.

The MHRA wanted to see a pooled (pooled ‼) analysis of all four studies. What the heck?

The applicant replied that the first formulation went into the waste bin and hence, only market authorization of the second one was sought. The purpose of #2.a. was just to design #2.b. – which stands on its own. Refused to pool any of the studies. Pointed also out that the studies were evaluated with α 0.05 and by pooling the consumer risk cannot be controlled by any means.

Then the MHRA insisted to get a pooled analysis of #2 (with a 95% CI II). Passed AUC, failed Cmax (by a small margin).
Accepted and market authorization granted…

PT Frustration - not related to vaccine

Yep.

1. Homework (not for an initiated like you but interested readers): Why pass in the simulations more studies than what we expect for the sample size, or – in other words – why is the ‘empiric power’ higher than planned?
2. Oh dear, Bonferroni misused post mortem!
Nonsense cause the entire α was already spent.

Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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