Bioequivalence and Bioavailability Forum

Hi ANgus,

❝ How is it that the Sequence, Formulation and period are obtained in terms of AUC. Does this relate to matrix algebra? In general and in simple terms how should we think of that equation.

Look at it this way:

Your model is:
ln(AUC) = int + Subject + Sequence + Period + Treatment + error

and that means:
"Each observed log(AUC) is the sum of a constant called the intercept plus a constant for the subject plus a constant for the Sequence assigned to that subject plus a constant for the Period from which we got this observation plus a constant for the Treatment the Subject received plus some sort of error (residual)."


If you're telling me that this is an awful lot of constants then you are right. Of course some of these constants are constrained (=loss of df's) so our headache is not excruciating but it's still plenty bewildering.

Before the fit we only have our observations but not the errors or residuals. The residuals themselves depend, of course, on the constants. When we fit the model, we fiddle and tweak with all those constants until we have a situation where the sum of the squared residuals are at a minimum, because that's associated with the maximum likelihood.
All this can be expressed beautifully and simple by means of matrix algebra. You don't need to do it, but you can if you wish and to some this is very pleasing. Just like when your wife hints something about you doing the dishes after she has cooked a good dinner for you. You don't have to do it, but your life may be considerably less torturous if you do it.



[Note: The above applies when subject is modeled as a fixed effect. If you fit it as random then things get a little more complicated since minimisation of sums of squares doesn't result in maximum likelihood.]