## Inter-subject variability in Full replicate design [RSABE / ABEL]

Hi MGR,

like ElMaestro I’m not a SASian and my knowledge is limited.

❝ […] I am not able to calculate the inter-subject variabilities for test and reference treatments. Please help me with this calculation.

With the EMA’s example ‘Data set I’ (download CSV) you should get sumfink like:

        Covariance Parameter Estimates Cov Parm     Subject    Group    Estimate FA(1,1)      SUBJ                0.8530 FA(2,1)      SUBJ                0.8284 FA(2,2)      SUBJ                8.339e-07 Residual     SUBJ       TRT R    0.2021 Residual     SUBJ       TRT T    0.1174

In Phoenix/WinNonlin slightly different terms.

Final variance parameter estimates:            lambda(1,1)_11  0.852995            lambda(1,2)_11  0.828407            lambda(2,2)_11  8.33919e-007 Var(PER*TRT*SUBJ)_21       0.202118 Var(PER*TRT*SUBJ)_22       0.117394

The first two lines give $$\small{\widehat{s_\textrm{bR}^2}}$$ and $$\small{\widehat{s_\textrm{bT}^2}}$$ and the last two $$\small{\widehat{s_\textrm{wR}^2}}$$ and $$\small{\widehat{s_\textrm{wT}^2}}$$. Ignore the third, which is the Subject-by-Formulation Interaction. Then as usual $$\small{100\sqrt{\exp \left ( \widehat{s_{\ldots}^2} \right )-1}}$$.
Here $$\small{CV_\textrm{bR}=116.0\%,\;CV_\textrm{bT}=113.6\%,\;CV_\textrm{wR}=47.3\%,\;CV_\textrm{wT}=35.3\%}$$.

As ElMaestro wrote, you can get the estimated between-subject variances also from Col1 of the estimated G matrix, where the 1st Row is for R and 2nd for T.

❝ But when I use the proc varcomp procedure in SAS, I am able to generate the Variabilities (Inter and Intra) for test and reference treatments.

Out of curiosity: Do they are agree with the results of Proc Mixed as outlined above?

❝ My doubt is that whether it is acceptable by FDA regulatory?

The between-subject variabilities are not required for RSABE (in the FDA’s Summary Table 3B you have to give only the within-subject variance and standard deviation of the reference). For ABE (Table 3A) variances are not required at all.

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