# Testing bioequivalence statistically using FDA guidance

I need to statistically test whether a drug is bioequivalent to another drug by using the pharmacokinetic parameters AUC (area under the curve of a plasma concentration curve) and Cmax (maximum concentration). According to the FDA one should calculate the 90% confidence interval (CI) of the proportion of test drug and reference (test/reference) for both parameters. In my case the data are unpaired, meaning that a few persons took drug X and a few persons took drug Y and the mean AUC and Cmax were calculated for both groups. So this means that if the group that took drug X had a mean AUC of 2.7 and the group that took drug Y had a mean AUC of 5.5, the 90% confidence interval would be for the proportion $\frac{2.7}{5.5}$. Now my question is, how can I calculate this 90% confidence interval? According to the FDA one should first log transform the data and calculate the 90% CI for the difference of the logarithm of both parameters, so the 90% CI of differences for: ln AUC$_1$ - ln AUC$_2$ and ln Cmax$_1$ - ln Cmax$_2$. And then transform the lower and upper bounds back by taking $e$ to the power of the boundaries to get the lower and upper bounds of the proportion since $ln(x) - ln( y) = ln (x/y)$. The only example I got was with paired data so I assumed it worked for unpaired data too. However when I tried this with my unpaired data the confidence intervals I got were way off way since I got CIs boundaries with way higher values than the maximum observed values. I first calculated group means for both groups and then took the Ln of both. Then subtracted the log transformed parameters like I referenced before (ln AUC$_1$ - ln AUC$_2$). And then calculated the pooled standard deviation. And lastly the 90% CI for the difference of the log transformed parameters using the formula $(Ln(AUC_1)-Ln(AUC_2)) ± t_{0.10} * s_p * \sqrt{1/n_1 +1/n_2}$ Sorry for the somewhat long and vague question. Thanks in advance to anyone who can help me with this though. If further explaination needed I can elaborate or if the data are needed I could post them .

• "So this means that if the group that took drug X had a mean AUC of 2.7 and the group that took drug Y had a mean AUC of 5.5, the 90% confidence interval would be for the proportion $\frac{2.7}{5.5}$." That number is not a proportion, but a ratio of two mean AUCs. Mar 15 '19 at 17:14