Power of the two one-sided t-tests procedure
Power_TOST in the output is the power of the two one-sided t-tests procedure described in the previous section. Refer to the previous section for the definitions of t1 and t2 for the transformation that was used and recall from previous sections that df is the degrees of freedom for the difference of the test and reference least squares means. Define the critical t-value as:
where 2a=(100 – Confidence Level/100) and Confidence Level is specified in the user interface.
In general:
PowerOfTest=1 – (probTypeIIError) = probRejectingH0, when H1 is true
For the two one-sided t-tests procedure, H1 is bioequivalence (concluded when both of the one-sided tests pass) and H0 is nonequivalence. The power of the two one-sided t-tests procedure is (Phillips, K. F. (1990), or Diletti, E., Hauschke, D., and Steinijans, V. W. (1991)):
Power = Prob{t1 ³ tcrit and t2 £ –tcrit | bioequivalence}
This power is closely approximated by the difference of values from a non-central t-distribution (Owen, D. B. (1965)):
Power_TOST = p(–tcrit,df,t2) – p(tcrit,df,t1)
This is the formula used in the Bioequivalence module (power is set to zero if this results in a negative), and the non-central t should be accurate to 1e–8. If it fails to achieve this accuracy, the non-central t-distribution is approximated by a shifted central t-distribution (again, power is set to zero if this results in a negative):
Power_TOST = p(–tcrit,–t2,df) – p(tcrit,–t1,df)
Power of the two one-sided t-tests procedure is more likely to be of use with simulated data, such as when planning for sample size, rather than for drawing conclusions for observed data.