## Partial AUC calculation [NCA / SHAM]

Dear Astea,

» 1. There were time deviations in the first point (that is instead of t0=0, we have, for example, t0=1 hour)
I didn't get this. Does that mean the deviation in dosing time or what?

» 2. There were time deviations in the last sample point (that is instead of tlast=72 h we have tlast=71 h or tlast=73 h). Additionally what if we have concentrations below LLOQ in the several last points (agree it is strange for drugs with long half-life but who knows..)?
» 3. There were abscent samples (NA) at the last time point 72 h

I think all options are described in WNL Guide:
• If a start or end time falls within the range of the data but does not coincide with an observed data point, then a linear or logarithmic interpolation is done to estimate the corresponding Y, according to the AUC Calculation method selected in the NCA Options. (See “NCA Options tab” on page 42.) Note that logarithmic interpolation is overridden by linear interpolation in the case of a non-positive endpoint.
• If a start or end time occurs after the last numeric observation (i.e., not “missing” or “BQL”) and λz is estimable, λz is used to estimate the corresponding Y:

Y = exp(alpha – λz * t)
= exp(alpha – λz * tlast) * exp(–λz * (t-tlast))
= (predicted concentration at tlast) * exp(–λz * (t-tlast))

The values alpha and λz are those values found during the regression for λz The value for alpha is not given in the normal output, but can be obtained by selecting the Intermediate Output checkbox on the Options tab, and finding the alpha in the Core Output. Note that a last observation of zero will be used for linear interpolation, i.e., this rule does not apply prior to a last observation of zero.
• If a start or end time falls after the last numeric observation and λz is not estimable, the partial area will not be calculated.
• If both the start and end time for a partial area fall at or after the last positive observation, then the log trapezoidal rule will be used. However, if any intervals used in computing the partial area have non-positive endpoints or equal endpoints (for example, there is an observation of zero that is used in computing the partial area), then the linear trapezoidal rule will override the log trapezoidal rule.

» The question arises: is it not strange to calculate the last part by log trapezoid method while the whole curve is calculated via untransformed trapezoid? Of course log interpolation is more preferable for the elimination part of the curve but we initially stated to use untransformed method.

Then we need to use another lambda for 'linear regression', right? How to calculate it? Should we use some rules for it? How many points do we need?
So many questions as you see...
Think about WNL Partial Areas rules as about huge combination of compromises.
You're free to create your own rules in WNL or in R or other data management/plotting tool.

» Why does the situations 2) and 3) have different solution methods?

Different ClastPreds, different Lambdas, different solutions

Kind regards,
Mittyri

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