Bioequivalence and Bioavailability Forum

• Nasty drug, only steady state in patients possible, parallel design (cross-over would take more than one year, disease often not stable (needs dose-adjustment – exclusion of subjects, etc.), expected drop­out-rate 20%. Given that, the agency’s PK-expert was fine with waiving the (more sensitive) single dose study and accepted the proposed parallel design.
  
• Little known about the variability, but likely >50%. The company suggested a TSD and was referring to Anders’ paper.* Since the variability was expected to be high, the company followed the advice of the two Lászlós and assumed a T/R-ratio of 0.90. Not covered in Anders’ paper, simulations required.
  
• I started with equal group sizes (62 to 125 per group = n₁ 124 to 250; step size 1/group) and CV 24% to 100% (step size 2%) ~2.7·10⁹ simulations.
  Repeated for unequal group sizes, covering slight unbalance to the extreme scenario of 50.4% drop­outs in one group and none in the other (n₁: 124/125 to 62/125).
  So far, so good.
  
• But I had to assess heteroscedasticity in the combination of unequal group sizes as well. I explored 32 different CV-ratios (CV_G1/CV_G2: 0.262 to 3.87). The set was centered around CV 58% (the location of the maximum TIE). With current technology it is not feasible to simulate all possible combinations, i.e., 1.1·10⁶×2,496² = 6.853·10¹² (~seven trillion!) BE studies. The runtime would be approximately three to four years. Hence, I assessed eight scenarios (all based on the Welch-test adjusting for heterogenicity and unequal group sizes):
  • Equal group sizes
    • No dropouts (n₁ 250).
      
    • Expected dropout rate of ~30%, resulting in 88 eligible subjects in stage 1 (n₁ 176).
      
    • High dropout rate of ~38%, resulting in 77 subjects in stage 1 (n₁ 154). This is the location of the maximum observed TIE.
      
    • Extreme dropout rate of ~50%, resulting in 62 eligible subjects in stage 1 (n₁ 124).
      
  • Unequal group sizes
    • No dropouts in group 1 (n_G1 125) and dropout rate ~30% in group 2 (n_G2 88), resulting in 213 subjects in stage 1. Overall dropout rate ~15%.
      
    • Dropout rate ~30% in group 1 (n_G1 88) and no dropouts in group 2 (n_G2 125), resulting in 213 subjects in stage 1. Overall dropout rate ~15%.
      
    • No dropouts in group 1 (n_G1 125) and extreme dropout rate ~50% in group 2 (n_G2 62), resulting in 187 subjects in stage 1. Overall dropout rate ~25%.
      
    • Extreme dropout rate ~30% in group 1 (n_G1 62) and no dropouts in group 2 (n_G2 125), resulting in 187 subjects in stage 1. Overall dropout rate ~25%.

• “According to the BE guideline Two-Stage Designs are acceptable in principle. Primary concern is preserving the TIE.”
  In principle‽ Sounds like Radio Yerevan.
  
• “I did not read the report in its entirety.”
  The company sent my report to the agency one month in advance. Leaving the title page, formulas, tables, and graphs aside the text covers 4 (four!) pages.
  
• “According to a recommendation of the Biostatistics Working Party TSDs similar to Potvin et al. are not acceptable because they are only based on simulations and lack a statistical proof.”
  Although both my report and the briefing package referred to Anders’ paper she had only Potvin’s paper with her. I told her that I’m aware of such rumours but since this recommendatoon of the BSWP is not public available companies performed such studies in the past and plan similar ones as well. The quality assessor of the agency was quite surprised and asked me “This statement was not made public‽”. I replied yes and the statistician confirmed that. After that the other assessors groaned loudly…
  I pointed out that these methods were published in peer-reviewed journals with high impact factors and co-authored by veteran statisticians like Donald Schuirmann and Walter Hauck. She replied:
  
• “The BSWP does not agree with their conclusions. There are alternative methods containing a proof available.”
  I asked her which methods but she was unable to name a single one. The very next day I’ve sent her an e-mail asking for references and didn’t get an answer so far.
  
• “The method might be [sic] acceptable if the outcome is unambigous (i.e., the CI not too close to the acceptance range).”

Type I error control in two-stage designs in bioequivalence studies
Action: Continue work related to type I error control in two-stage designs in bioequivalence studies.
Comments: This is done in collaboration with the Pharmacokinetics Working Party.

• Fuglsang A. Sequential Bioequivalence Approaches for Parallel Designs. AAPS J. 2014;16(3):373–8.
  doi:10.1208/s12248-014-9571-1.