## Calculation of intra-subject CVs in replicate design [General Sta­tis­tics]

Hi Andrew,

It's a bit late for this reply, but I found the answer to your question. You don't need to run proc GLM. The replicate SAS output gives all of the information you need to calculate intra- and inter-CV, where it outputs the covariate matrix ("Covariate Parameter Estimates"). The SAS output might look like this:

Covariate Parameter Estimates
Cov Parm Subject Group Estimate
FA(1,1) Subject 0.5928 <---- (sig_BT, the between-subject standard deviation for the Test product)
FA(2,1) Subject 0.4968 <---- (sig_BR, the between-subject standard deviation for the Reference product)
FA(2,2) Subject 2E-17 <---- (sig_D, the subject-by-formulation interaction term)
Residual Subject Treatment A 0.124 <---- (sig_WT^2, the within-subject standard deviation for the Test product)
Residual Subject Treatment B 0.242 <---- (sig_WR^2, the within-subject standard deviation for the Reference product)

The intra-subject variabilities are still calculated from the residuals as in a 2-way crossover, using:
IntraCV_T = 100%*sqrt(exp(sig_WT^2)-1) (in this case, = 100*sqrt(exp(0.124)-1) = 36.3%
IntraCV_R = 100%*sqrt(exp(sig_WR^2)-1) (in this case, = 100*sqrt(exp(0.242)-1) = 52.3%

FA(1,1) and FA(2,1) are the inter-subject standard deviations for Test and Reference products, respectively:
InterCV_T = 100%*sqrt(exp(sig_BT^2)-1) = 100*sqrt(exp(0.5928^2)-1) = 64.9%
IntraCV_R = 100%*sqrt(exp(sig_BR^2)-1) = 100*sqrt(exp(0.4968^2)-1) = 52.9%

Hope this helps,
Dave

David Dubins, Ph.D., B.A.Sc.
Associate Professor, Teaching Stream
Director, Pharmaceutical Chemistry Specialist Program
Leslie Dan Faculty of Pharmacy
University of Toronto

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