Thanks Angus, I have used partial AUCs before, but generally we use non-overlapping windows (e.g. 0-15 min, 15-60 min, 1-2 hr, etc.) to characterize the different phases of the absorption profile. With overlapping windows (such as you described, the results get a bit muddy and comparisons can be confusing. In essence, each subsequent interval dilutes any response from the previous interval.
You are correct that total exposure is evaluated using 2 metrics (AUC and Cmax). These two metrics were chosen as the most accurate combination that describes an entire concentration time profile. The assumption is that if the AUCs match and the Cmax values match, than the overall "shape" of the PK profile should be similar (even identical). Now we all know cases where AUC and Cmax fall within prescribed equivalence ranges, yet the PK profiles are markedly different, however, the theory still exists that we can boil down an entire profile to 2 values.
Partial AUCs are an attempt to further characterize different portions of the concentration-time profile. Specifically, they are used to evaluate the absorption phase to identify differences in the rate of absorption which may affect efficacy for certain classes of drugs (e.g. methylphenidate HCl). AUC is used because it represents the average concentration over a defined period of time. Cmax is not used because it is a metric that is meaningless outside of the full PK profile. Interval-specific maximums do not provide information about the eventual maximum concentration, nor the timing of such a maximum. A ranked statistical test of Tmax would provide an equal amount of information as trying to interpret interval-specific maximum concentrations.
If the sponsor is trying to show more rapid efficacy (using absorption as a surrogate for efficacy), then I would compare Tmax values or pAUCs. If there are distinct peaks (e.g. multiphasic release compared to multiple doses) then perhaps multiple Cmax and Tmax values could be useful ... but that doesn't seem to apply for your situation. I think I'm with Helmut on this one, partial area Cmax's don't appear to be logical or useful.