Bioequivalence and Bioavailability Forum

Hi BE-proff,

❝ I have always thought that PASS calculates via simulation. Am I mistaken?

Yes. The documentation of PASS refers to Julious¹ (see esp. pp1961–2). Given that, the approxi­ma­tion by the noncentral t-distribution is used. Example 2 from PASS’ manual: 2×2 crossover, target power 0.90, α 0.05, acceptance range 0.80–1.25, θ₀ 1, CV 0.25:

═══════════════════════════════════════════════════
                    n     power     method
═══════════════════════════════════════════════════
Table VII¹         28  ≥0.90     noncentral t
───────────────────────────────────────────────────
PASS 14            28   0.9023   noncentral t
───────────────────────────────────────────────────
PowerTOST 1.2-07   28   0.902260 exact
                   28   0.902260 noncentral t
                   30   0.918776 shifted central t
───────────────────────────────────────────────────
FARTSSIE 1.7       28   0.902260 noncentral t
───────────────────────────────────────────────────
StudySize 2.01     28   0.90221  ?
                   28   0.9045   10,000 simulations
                   28   0.9023   100,000 sim’s
                   28   0.9022   1,000,000 sim’s
                   28   0.9022   9,999,000 sim’s
───────────────────────────────────────────────────
EFG 2.01           28   0.9023   noncentral t
                   28   0.9008   10,000 sim’s
                   28   0.9026   100,000 sim’s
                   28   0.9023   1,000,000 sim’s
                   28   0.9024   9,999,000 sim’s
═══════════════════════════════════════════════════

For common ranges the noncentral t is a very good approximation of the exact method (Owen’s Q-func­tions)². The latter were used in Diletti’s paper³. The shifted central t-distribution⁴ gives some­times lower power and therefore, higher samples sizes⁵. Unnecessarily conservative.
Only StudySize and ElMaestro’s EFG have the option to simulate studies (see here) which should asymp­totically approach the true value.

---

1. Julious SA. Sample sizes for clinical trials with Normal data. Stat Med. 2004;23(12):1921–86. doi:10.1002/sim.1783.
   
2. Owen DB. A special case of a bivariate non-central t-distribution. Biometrika. 1965;52(3/4):437–46. doi:10.1093/biomet/52.3-4.437.
   
3. Diletti E, Hauschke D, Steinijans VW. Sample size determination for bioequivalence assessment by means of confidence intervals. Int J Clin Pharm Ther Toxicol. 1991;29(1):1–8. PMID 2004861.
   
4. Kraemer HC, Paik M. A Central t Approximation to the Noncentral t Distribution. Technometrics. 1979;21(3):357–60. doi:10.1080/00401706.1979.10489781.
   
5. Hauschke D, Steinijans VW, Diletti E, Burke M. Sample Size Determination for Bioequivalence Assessment Using a Multi­pli­ca­tive Model. J Pharmacokin Biopharm. 1992;20(5):557–61. PMID 1287202