Bioequivalence and Bioavailability Forum

Dear AB!

THX for bringing this inaccuracy to my attention. I will write in the future ~75% and ~50%. Actual sample sizes depend on the design (3-way / 4-way, number of subjects & sequences / periods ⇒ degrees of freedom). For the dfs see here. Furthermore in designing the study we have to consider complete sequences (which are a multiple of 3 in the partial replicate TRR|RTR|RRT and a multiple of 4 in TRTR|RTRT|TTRR|RRTT – compared to the multiple of 2 in RT|TR).

❝ could you provide the rationale to consider the sample size as 75% & 50% (of 2×2×2 study) for 3 period & 4 period replicate designs respectively?

Power stays roughly the same keeping the number of treatments across designs. Sample sizes obtained by D. Labes’ famous PowerTOST (α 0.05, AR 80–125%, CV 50%, θ₀ 95%, target power 80%):

Design alpha  CV theta0 theta1 theta2 Sample size Achieved power Target power % of 2×2
   2x2  0.05 0.5   0.95    0.8   1.25          98      0.8032172          0.8
 2x2x3  0.05 0.5   0.95    0.8   1.25          74      0.8076842          0.8    75.75
 2x3x3  0.05 0.5   0.95    0.8   1.25          75      0.8128304          0.8    75.53
 2x2x4  0.05 0.5   0.95    0.8   1.25          50      0.8128063          0.8    51.02
 2x4x4  0.05 0.5   0.95    0.8   1.25          52      0.8274094          0.8    53.06

It’s even possible to get the target power with sample sizes <75% or <50% in the case of drop-outs (unequal sequences) – but you cannot plan for that.
First 3-way replicate from above, balanced (37/37) and 1 drop-out (37/36).
power2.TOST(alpha=0.05, logscale=TRUE, CV=0.5, n=c(37,37), design="2x2x3", robust=TRUE)
0.8076842 74 subjects = 75.75% of 2×2
power2.TOST(alpha=0.05, logscale=TRUE, CV=0.5, n=c(36,37), design="2x2x3", robust=TRUE)
0.8023176 73 subjects = 74.49% of 2×2
Or the last design: 1 drop-out in three of the four sequences each:
power2.TOST(alpha=0.05, logscale=TRUE, CV=0.5, n=c(12,12,12,13), design="2x4x4", robust=TRUE)
0.8045673 49 subjects = 50.00% of 2×2