Bioequivalence and Bioavailability Forum

Hi Balaji,

❝ Can anyone tell me how to calculate Inter subject variability for parallel design…

That’s a common misconception. The fact that you administered products only once does not mean that the intra-subject variability does not exist (you observed only one occasion). You can calculate the inter-subject variability only in a crossover design. In a parallel design you get only the total (or pooled) vari­abi­li­ty, which con­sists of both inter- and intra-subject components. Talking of inter-subject variability in paral­lel designs is sloppy terminology.

❝ … using phoenix winnonlin or manually i can find only Var(Residual) in final variance parameters sheet in Winnonlin while calculating average bioequivalence

Correct. I would not suggest to assume equal variances in groups (see the FDA’s 2001 guidance). Example dataset:

subj trt  var
  1   T  2.52
  2   T  8.87
  3   T  0.79
  4   T  1.68
  5   T  6.95
  6   T  1.05
  7   T  0.99
  8   T  5.60
  9   T  3.16
 10   R  4.98
 11   R  7.14
 12   R  1.81
 13   R  7.34
 14   R  4.25
 15   R  6.66
 16   R  4.76
 17   R  7.16
 18   R  5.52

With PHX/WNL’s default method (fixed: trt) you get
PE 48.58% (90% CI: 27.15–86.94%).
Levene’s test for equality of variances is significant (p 0.0229). The conventional t-test is liberal in the case of unequal variances and even more sensitive to unequal group sizes. Personally I would not apply pre-test­ing and use the Welch-Satterthwaite adjustment in all cases. In PHX/WNL add a column “period” to the data (containing 1 in all rows). Map trt to Formulation, var to Dependent, subj and period to Classification. Keep trt as the fixed effect and add a repeated specification to the variance structure: repeated = period, variance blocking variables = subj, group = trt, type = variance components. This specification gives:
PE 48.58% (90% CI: 26.78–88.14%) – which is wider (conservative).

In the conventional analysis the total CV is \(\small{100\sqrt{\exp{(Var(Residual))}-1}=80.54\%}\).
In the modified analysis you can estimate the total CV separately for T and R, where in PHX/WNL Var(period*trt*subj)_11 is the one of R and Var(period*trt*subj)_12 the one of T. From these variances we get a total CV of 46.23% for R and 111.34% for T.
Variances (but not CVs) are additive. Since group sizes are equal, we don’t have to worry about weighting by the degrees of freedom. The residual variance in the default model is 0.5000. The one of R is 0.1937 and the one of T 0.8063. Hence, (0.1937+0.8063)/2=0.5000. ∎