## Partial AUC calculation [NCA / SHAM]

Dear all!

Sorry for reviving the battered topic but for validation purposes I need to understand the methods of calculating partial areas in some nasty cases. I have a premonition that it would be hard to understand my question so I’ll try to use more illustrations…

Suppose we have to calculate AUC

To compare different methods I used the following concentration-time table:

1. Let us start with the first case: as it is intuitevily simple we just use a linear approximation to zero point. It is hard to invent an alternative approach because it is difficult to approximate by a known function the absorbtion part of the curve. Only if there was a non-zero concentration in the first sample (not enough wash-out or some unsufficient endogenous calculation) the results would differ.

AUC

2. To calculate AUC

For t

But when we deal with t

a). rude linear approximation (over the two last values or over the elimination period)

For t

b). log-linear interpolation (over the elimination period)

For t

( AUC

After assessing the concentration at 72 h we have to calculate the area under the last curve.

It can be done via:

- linear trapezoid method

(С

AUC

- log trapezoid method

(С

AUC

I can’t imagine what else there could be done. What method does WinNonLin use if it gets a value 8379.421 (very close to linear interpolation but not equal to it)

3. If there were no samples at t=72 h, the last point can be approximated by linear or log-linear interpolation and area can be calculated via linear or log trapezoid as in the previous case.

Comparing the results of the calculation I conclude that in this case WinNonLin use:

- Log-linear interpolation and log trapezoid method to calculate AUC

AUC

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.

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

Sorry for reviving the battered topic but for validation purposes I need to understand the methods of calculating partial areas in some nasty cases. I have a premonition that it would be hard to understand my question so I’ll try to use more illustrations…

Suppose we have to calculate AUC

_{0-72}. The biggest problem is to decide: to extrapolate or nor to extrapolate. Let us follow the first scene. Suppose that the protocol states to use a simple**linear**trapezoid method to calculate AUC. How to calculate AUC_{0-72}in the following situations?- There were time deviations in the first point (that is instead of t
_{0}=0, we have, for example, t_{0}=1 hour)

- There were time deviations in the last sample point (that is instead of t
_{last}=72 h we have t_{last}=71 h or t_{last}=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..)?

- There were abscent samples (NA) at the last time point 72 h

^{®}presents itself as a golden standard of NCA, I tried to understand what methods does it use in the uppermentioned cases.To compare different methods I used the following concentration-time table:

```
time Conc.
```

----------------------------------

0 0 (NA)

1 3

2 17

3 55

4 87

5 190

6 250

7 315

8 330

10 230

12 185

16 115

18 100

24 125

48 100

72(71,73) 77 (NA)

----------------------------------

1. Let us start with the first case: as it is intuitevily simple we just use a linear approximation to zero point. It is hard to invent an alternative approach because it is difficult to approximate by a known function the absorbtion part of the curve. Only if there was a non-zero concentration in the first sample (not enough wash-out or some unsufficient endogenous calculation) the results would differ.

AUC

_{last}=AUC_{all}=AUC_{0-72}=83912. To calculate AUC

_{0-72}(AUC truncated) for the cases with t_{last}>72 h we can just truncate (cut down) at the time t=72 h (see the upper picture).For t

_{last}=73: AUC_{last}=AUC_{all}=8479.5; AUC_{0-72}=8402.0But when we deal with t

_{last}<72 h there appear different opportunities to get the value at t=72 h:a). rude linear approximation (over the two last values or over the elimination period)

For t

_{last}=71: C_{72}=76b). log-linear interpolation (over the elimination period)

For t

_{last}=71: C_{72}=76.84( AUC

_{last}=AUC_{all}=8302.5);After assessing the concentration at 72 h we have to calculate the area under the last curve.

It can be done via:

- linear trapezoid method

(С

_{1}+C_{2})/2*(t_{2}-t_{1})AUC

_{0-72}=8379.0- log trapezoid method

(С

_{1}-C_{2})/(ln С_{1}-lnC_{2})*(t_{2}-t_{1})AUC

_{0-72}=8376.9I can’t imagine what else there could be done. What method does WinNonLin use if it gets a value 8379.421 (very close to linear interpolation but not equal to it)

3. If there were no samples at t=72 h, the last point can be approximated by linear or log-linear interpolation and area can be calculated via linear or log trapezoid as in the previous case.

Comparing the results of the calculation I conclude that in this case WinNonLin use:

- Log-linear interpolation and log trapezoid method to calculate AUC

_{0-72}.AUC

_{last}=AUC_{all}=6267; AUC_{0-72}=7983.3The 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.

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

—

"Being in minority, even a minority of one, did not make you mad"

"Being in minority, even a minority of one, did not make you mad"

### Complete thread:

- Calculation of AUC0-72 Sasi 2008-06-10 10:44
- Calculation of AUC0-72 Jaime_R 2008-06-10 12:18
- Calculation of AUC0-72 Ohlbe 2008-06-10 17:28
- Calculation of AUC0-72 Jaime_R 2008-06-10 18:45
- Regulators truncated d_labes 2009-06-18 09:26
- Regulators truncated Ohlbe 2009-06-18 10:37
- Regulators truncated Helmut 2009-06-18 14:49
- Regulators truncated d_labes 2009-06-18 15:26
- Regulators truncated Helmut 2009-06-18 15:44
- Regulators truncated ElMaestro 2009-06-19 22:16
- Regulators truncated Helmut 2009-06-19 22:35

- Regulators truncated ElMaestro 2009-06-19 22:16

- Regulators truncated Helmut 2009-06-18 15:44

- Regulators truncated d_labes 2009-06-18 15:26
- Luke 23:34 ElMaestro 2009-06-18 14:50

- Regulators truncated d_labes 2009-06-18 09:26
- Calculation of AUC0-72 d_labes 2008-09-05 15:00
- Calculation of AUC0-72 Helmut 2009-01-26 16:24
- Calculation of AUC0-72 d_labes 2009-01-26 16:57
- Calculation of AUC0-72 Helmut 2009-01-26 17:20
- The missing 72h d_labes 2009-01-27 11:48
- The missing 72h Ohlbe 2009-01-28 00:00
- sensitivity analyses ? martin 2009-01-28 08:26
- Regulators ways are inscrutable d_labes 2009-01-28 09:54
- Regulators ways are inscrutable (at least the French) Ohlbe 2009-01-28 10:16

- The missing 72h ElMaestro 2009-01-28 14:32
- Page 3848 of 221 d_labes 2009-01-28 14:51

- Partial AUC calculationAstea 2017-03-11 20:14
- Partial AUC calculation mittyri 2017-03-16 19:46

- The missing 72h Ohlbe 2009-01-28 00:00

- The missing 72h d_labes 2009-01-27 11:48

- Calculation of AUC0-72 Helmut 2009-01-26 17:20

- Calculation of AUC0-72 d_labes 2009-01-26 16:57

- Calculation of AUC0-72 Helmut 2009-01-26 16:24

- Calculation of AUC0-72 Jaime_R 2008-06-10 18:45

- Calculation of AUC0-72 Ohlbe 2008-06-10 17:28

- Calculation of AUC0-72 Jaime_R 2008-06-10 12:18