Bioequivalence and Bioavailability Forum

Hi Uday,

welcome to the club!

❝ What is the null and alternative hypothesis in bioequivalence studies.

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The Null hypothesis is bioinequivalence; generally based on the 1–2α confidence interval of the ratio of log-transformed adjusted (aka least squares) means compared to the acceptance range (AR). Therefore:

1. CI ⊂ AR: H₀ rejected, H_a of BE accepted.*
   
2. CI not entirely within the AR, but CL_lo < AR_hi ∩ CL_hi > AR_lo: indecisive
   (e.g., CV higher and/or T/R more deviant from 1 than expected; more dropouts than anticipated).
   
3. CI ⊄ AR (CL_hi < AR_lo ∨ CL_lo > AR_hi): H₀ accepted, bioinequivalence proven.

If you prefer this notation:\begin{matrix}
H_0:\mu_T/\mu_R < \theta_1 \vee \mu_T/\mu_R > \theta_2 \\
H_a:\theta_1\leq\mu_T/\mu_R\leq\theta_2
\end{matrix} where \(\theta_1\) and \(\theta_2\) are the lower and upper boundaries of AR based on a clinically not relevant difference \(\Delta\). With the common \(\Delta\) of 20% you get \(\theta_1=1-\Delta=0.8\) and \(\theta_2=(1-\Delta)^{-1}=1.25\).

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• In the special case that the CI does not contain 1 formulations are statistically different (p <α), but this difference is considered clinically not relevant (e.g., CV lower and/or T/R less deviant from 1 than expected, fewer dropouts than anticipated, for drugs with low CV high power due to the regulatory minimum sample size). For an example see here.