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# Average Bioequivalence

This calculator uses the 2 x 2 crossover design recommended by FDA guidelines. The test of average bioequivalence is a the same as testing the equivalence for means. If another design is used, the two sample crossover calculator for hypotheses on means can be used.

Letting $$y_{ijk}$$ be the PK response of interest (in log transfored or in original units) of the $$i^{th}$$ subject in the $$k^{th}$$ sequence in the $$j^{th}$$ dosing period, the model used to test average bioequivalence is given by:

$y_{ijk} = \mu + F_l + P_j + Q_k + S_{ikl} + \epsilon_{ijk}$

where $$\mu$$ is the overall mean, $$P_j$$ is the fixed period effect, $$Q_k$$ is the fixed sequence effect, $$F_l$$ is the fixed effect of the $$l^{th}$$ formulation ($$l = T, R$$), and $$S_{ikl}$$ is the random effect of the $$i^{th}$$ subject in the $$k^{th}$$ sequence using the $$l^{th}$$ formulation (see Chow et at. and the FDA guidance for a more detailed specification of the model).

To test average bioequivalence, we test the hypothesis:

$H_0: \delta \le \delta_L \text{ or } \delta \ge \delta_U \text{ versus } H_1: \delta_L \lt \delta \lt \delta_U$

where $$\delta = F_{T} - F_{R}$$ and $$\delta_L$$ and $$\delta_U$$ are bioequivalence limits.

To perform this calculation, we need to estimate the standard deviation of the intersubject comparison: $$\sigma_{1,1}$$. The value can be estimated by:

$\hat{\sigma}_{1,1} = \frac{1}{2(n - 1)} \sum^2_{k=1} \sum^n_i=1 (y_{i1k} - y_{i2k} - \bar{y}_{\cdot1k} + \bar{y}_{\cdot2k})^2$

## Power Calculation Parameters

To input multiple values, seperate them by a comma.

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## Power Calculation Explanation

Solve For
The unknown you are interested in solving for.
N
The sample size used to test the hypothesis.
Alpha
The $$\alpha$$ (Type I error rate) level of the hypothesis test.
Power
The power (1 - Type II error rate) of the hypothesis test.
$$\delta$$
The difference of the fixed effects.
Standard Deviation ($$\sigma_{1,1}$$)
The standard deviation for the inter-subject comparison.
Bioequivalence Margin
The difference between the upper (lower) bioequivalence limit and $$\delta$$ (i.e. $$\delta_U - \delta$$). Note: for this calculator, we assume $$\delta_U - \delta = \delta - \delta_L$$
Known Standard Deviation
If the standard deviation is known or estimated (usually it is estimated).

## Calculation Results

No calculation has been generated yet.

Known Standard Deviation

Unknown Standard Deviation

N Alpha Power $$\delta$$ Standard Deviation Margin
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