Bioequivalence and Bioavailability Forum • Steady state PK calculation

ratnakar1811
★

India,
2011-10-03 12:14
(4962 d 00:52 ago)

Posting: # 7408
Views: 7,395

Steady state PK calculation [NCA / SHAM]

Dear All,
I have a little confusion in the calculation of the steady state study data, my study is of 5 days once daily dosing with following parameters to be evaluated:
Primary Parameters: Cmin, Cmaxss and AUCtau
Secondary Parameters: Tmax & %fluctuations

Now my query is how do we arrange data? I tried it with the following data set (1) but it is not giving any out put and I require converting it to hrs from the first dosing day like data set (2)?
1. Which is the right format of data set?
Data set 1

Subject Sequence period formulation Day Time point (hr) Concentration

1         BA       1        T        1    Predose          0

1         BA       1        T        2    Predose         35.38

1         BA       1        T        3    Predose         49.792

1         BA       1        T        4    Predose         60.015

1         BA       1        T        5    Predose         51.224

1         BA       1        T        5      1             51.224

1         BA       1        T        5      1.5           58.255

1         BA       1        T        5      3             86.012

1         BA       1        T        5      3.5          142.207

1         BA       1        T        5      4            138.1

1         BA       1        T        5      4.5          148.922

1         BA       1        T        5      5            143.729

1         BA       1        T        5      5.5          139.647

1         BA       1        T        5      6            126.951

Continued……till 24 hrs

OR

Data Set 2:

Subject Sequence period formulation Day Time point (hr) Concentration

1         BA       1        T        1      0              0

1         BA       1        T        2     24             35.38

1         BA       1        T        3     48             49.792

1         BA       1        T        4     72             60.015

1         BA       1        T        5     96             51.224

1         BA       1        T        5     97             51.224

1         BA       1        T        5     97.5           58.255

1         BA       1        T        5     99             86.012

1         BA       1        T        5     99.5          142.207

1         BA       1        T        5    100            138.1

1         BA       1        T        5    100.5          148.922

1         BA       1        T        5    101            143.729

1         BA       1        T        5    101.5          139.647

1         BA       1        T        5    102            126.951

Continued……till 110 hrs

2. How do we take into account deviations occurred in pre-dose (which was to be collected with in 5 minutes) in case of data set (1)?

3. Also how do we conclude whether steady state is achieved or not?

Your guidance will be highly appreciated.

Regards,

Ratnakar

Edit: Category changed. [Helmut]

Helmut
★★★

Vienna, Austria,
2011-10-03 17:04
(4961 d 20:01 ago)

@ ratnakar1811
Posting: # 7411
Views: 6,422

Steady state PK calculation

Post reply

Dear Ratnakar,

I think you have two problems:

software related
dealing with time deviations

❝ Now my query is how do we arrange data? I tried it with the following data set (1) but it is not giving any out put

Which software are you using? Non-numeric time points cannot be used in calculations.

❝ […] I require converting it to hrs from the first dosing day like data set (2)?

Better but not optimal, IMHO.

❝ 1. Which is the right format of data set?

There’s no right or wrong here. I can only give you my preferred coding. I set the administration time point in steady state to zero and code time points in the saturation phase accordingly. With -5 min for each predose sample I would get:

   t         C

-48.0833   49.792

-24.0833   60.015

 -0.08333  51.224

  1        51.224

  1.5      58.255

   …         …

 23.91667    ?

BTW, was it a copy&paste error that the concentration after one hour in SS is exactly the same like the predose value? I’m not sure whether it makes sense to report concentrations to as many significant digits. A value of 148.922 implies that the analytical method can distinguish between 148.9215 and 148.9224 (rounding!). Are you sure that the precision of the method is 0.0004%?

❝ 2. How do we take into account deviations occurred in pre-dose (which was to be collected with in 5 minutes) in case of data set (1)?

I give you the example I use in my steady state protocols – a multiphasic formulation: calculation of partial AUCs (pAUC_0-4, pAUC_4-τ), t_75%, HVD. A picture tells more than a thousand words and helps regulators understanding the NCA methods.
[image]

I use the lin-up (blue sections) / log-down (orange sections) trapezoidal rule. Green lines demonstrate the calculation of t_75% (plateau time; interval where C ≥75 % of C_max) and HVD (half value duration; interval where C ≥50 % of C_max). Concentrations at exactly t=0, at the truncation time point t=4, and at t=τ are inter-/extrapolated (orange circles). The interpolation in the linear section is trivial. For the estimation of C_τ (=C_min according to EMA’s definition) and AUC_τ we need a reliable estimate of λ_z. Don’t use the global minimum concentration within the dosage interval – which is standard output of commercial software; the same applies to %PTF. C_τ = C_z·e^{-λ_z(τ–t_z)}. Note that if t_z = τ no correction is done, since τ–t_z = 0 and e⁰ = 1; therefore C_τ = C_z. If you want to avoid the estimation of C_τ you may also take the last sample in the second period at 23:55 instead of 24:00 hours and use C_z. Otherwise you are comparing apples to oranges.

❝ 3. Also how do we conclude whether steady state is achieved or not?

Depends on the regulation. FDA’s/EMA’s veterinary guidelines call for a formal proof by linear regression of predose values. In steady state the slope should no differ significantly from zero. With your data (assuming all predose values were sampled exactly five minutes before administration) I got a slope of 0.0298 (95% confidence interval -3.7439 to +3.8036). Since zero is included in the CI, steady state was achieved. In Taiwan you have to estimate λ_z and assess whether the dosing was suitable (if I recall it correctly ≥5×t_½). You may state in your protocol to exclude subjects who were not in steady state.
No formal test is required for EMA.

P.S.: See my note at the end of this post. Take your time and use the Preview. Your post contained a funny mixture of multiple blanks and tabs. Please avoid that in the future. THX.

—
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
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ratnakar1811
★

India,
2011-10-04 07:17
(4961 d 05:49 ago)

@ Helmut
Posting: # 7419
Views: 6,093

Steady state PK calculation

Post reply

Dear HS,
Thanks a lot for your prompt reply as always!

❝ Which software are you using? Non-numeric time points cannot be used in calculations.

I am using winNonlin, I have written as pre-dose instead of 0 hr for the sake of understanding.

❝ Better but not optimal, IMHO.

I think the format of data set proposed by you can take care of all issues, I will revert back to you on rest of the queries after my home work is done as per you suggestions.

❝ P.S.: See my note at the end of this post. Take your time and use the Preview. Your post contained a funny mixture of multiple blanks and tabs. Please avoid that in the future. THX.

I will take care of this.

Once again thanking you for your guidance,

Ratnakar

Helmut
★★★

Vienna, Austria,
2011-10-04 15:59
(4960 d 21:07 ago)

@ ratnakar1811
Posting: # 7421
Views: 6,500

Steady state NCA (WinNonlin)

Post reply

Dear Ratnakar!

❝ I am using winNonlin, I have written as pre-dose instead of 0 hr for the sake of understanding.

❝ I think the format of data set proposed by you can take care of all issues, I will revert back to you on rest of the queries after my home work is done as per you suggestions.

In WinNonlin the setup of NCA is easy. With my coding enter the "Time of dose" as 0 and "Tau" as 24. In the ASCII/Core output you find a documentation about extra-/interpolated values (check "Intermediate Output").
Example (steady state profile):

t [hh:mm]   t [h]   C [ng/mL]

 -00:05   -0.08333    0.264

← 5 minutes predose

  00:30    0.50000    0.473

    …        …         …

  07:10    7.16667    7.845

  08:30    8.50000    5.985

  10:00   10.00000    4.132

  12:00   12.00000    2.726

  16:00   16.00000    0.917

  23:55   23.91667    0.232

← 5 minutes predose (switch to other formulation)

gives (rearranged for clarity):

Model:  Plasma Data, Extravascular Administration

Steady state interval Tau: 24.00

Dose time:                  0.00

Calculation method:  Linear Trapezoidal Rule for for Increasing Values,

                     Log Trapezoidal Rule for Decreasing Values

Weighting for lambda_z calculations:  Uniform weighting

Lambda_z method:  User-specified lambda_z range,  Log regression

User's lambda_z bounds:   7.17,  23.92



Intermediate Output

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

  Value for Lambda_z:   0.2142, and intercept:   3.5563



Summary Table

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

      Time         Conc.      Pred.    Residual      AUC

        h         ng/mL       ng/mL      ng/mL     h*ng/mL

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

     0.0000 @     0.2320                             0.0000

     0.5000       0.4730                             0.1763



     7.167 *      7.845      7.550     0.2951       63.58

     8.500 *      5.985      5.675     0.3104       72.75

    10.00  *      4.132      4.116     0.01647      80.25

    12.00  *      2.726      2.682     0.04428      87.01

    16.00  *      0.9170     1.139    -0.2216       93.65

    23.92  *      0.2320     0.2090    0.02303      97.60



@) Note - the concentration at dose time was added for extrapolation purposes.

*) Starred values were included in the estimation of Lambda_z.



Intermediate Output: Partial Areas

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

Computing partial area from 0.000000 to 24.000000:

piece from ( 0.000000, 0.232) to ( 0.50000, 0.473) = 0.176250

…

piece from ( 7.166667, 7.845) to ( 8.50000, 5.985) = 9.164138

piece from ( 8.500000, 5.985) to (10.00000, 4.132) = 7.502130

piece from (10.000000, 4.132) to (12.00000, 2.726) = 6.760814

piece from (12.000000, 2.726) to (16.00000, 0.917) = 6.641681

piece from (16.000000, 0.917) to (23.91667, 0.232) = 3.945747

piece from (23.916667, 0.232) to (24.00000, 0.205) = 0.018197

Partial area from 0.000000 to 24.000000 = 97.616587



Final Parameters

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

Rsq_adjusted                 0.9912

Lambda_z            1/h      0.2142

Tlast                 h     23.9167

Clast             ng/mL      0.2320

AUClast         h*ng/mL     97.5984

AUC_TAU         h*ng/mL     97.6166

Tmin                  h     23.9167

Cmin              ng/mL      0.2320

Note the differences between AUClast and AUC_TAU. Cmin by chance was observed at the last sampling time point, but in true steady state there’s a 50 % chance to observe it at t=0! Therefore in WinNonlin (and Phoenix as well) don’t use this value if you want to go with EMA’s definition. Use either Clast – or better IMHO – the estimate at t=24:

C_τ = C_z·e^{-λ_z(τ–t_z)} = 0.232·e^{–0.2142·(24–23.9167)} = 0.228.

WinNonlin uses exp(intercept-Lambda_z*TAU) = e^{(3.5563–0.2142·24)} = 0.205 to add the last trapezoid to AUClast in order to get AUC_TAU.

The plot shows both estimated values (upper: the estimated C_τ, lower: the one used by WinNonlin in the calculation of AUC_TAU):
[image]

—
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
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