For any bioequivalence study done using a crossover design, the output also includes for each test formulation a table of differences and ratios of the original data computed individually for each subject.
Let test be the value of the dependent variable measured after administration of the test formulation for one subject. Let ref be the corresponding value for the reference formulation, for the case in which only one dependent variable measurement is made. If multiple test or reference values exist for the same subject, then let test be the mean of the values of the dependent variable measured after administration of the test formulation, and similarly for ref, except for the cases of ‘ln-transform’ and ‘log10-transform’ where the geometric mean should be used:
where Xi are the measurements after administration of the test formulation, and similarly for ref. For each subject, for the cases of no transform, ln-transform, or log10-transform, the ratios table contains:
Difference=test – ref
Ratio(%Ref)=100*test/ref
For data that was specified to be ‘already ln-transformed,’ these values are back-transformed to be in terms of the original data:
Difference=exp(test) – exp(ref)
Ratio(%Ref)=100*exp(test – ref)=100*exp(test)/exp(ref)
Similarly, for data that was specified to be ‘already log10-transformed’:
Difference=10test – 10ref
Ratio(%Ref)=100*10test – ref=100*10test/10ref
Note: For ‘already transformed’ input data, if the mean is used for test or ref, and the antilog of test or ref is taken above, then this is equal to the geometric mean.