Bioequivalence and Bioavailability Forum

pjs
★

India,
2017-05-21 17:57
(2895 d 05:17 ago)

Posting: # 17379
Views: 9,468

AUC calculation in bear [🇷 for BE/BA]

Hi all,

I have just started using bear. Thanks to the developers for this wonderful freeware.

Following is the AUC calculation done in bear for one subject data.

 subj  time    conc AUC(0-t) AUMC(0-t)

    1  0.00   0.000    0.000     0.000

    1  1.00   0.000    0.000     0.000

    1  1.50   0.000    0.000     0.000

    1  2.00   0.000    0.000     0.000

    1  2.50   0.000    0.000     0.000

    1  3.00   0.000    0.000     0.000

    1  3.50   0.000    0.000     0.000

    1  4.00   1.518    0.380     1.518

    1  4.33   5.027    1.459     6.111

    1  4.67  12.700    4.473    19.894

    1  5.00  22.210   10.233    48.004

    1  5.33  18.013   16.846    82.120

    1  5.67  22.332   23.704   119.967

    1  6.00  30.500   32.422   171.055

    1  6.33  24.290   41.423   226.493

    1  6.67  31.676   50.937   288.549

    1  7.00  32.647   61.551   361.117

    1  7.50  45.512   81.091   503.584

    1  8.00  95.827  116.425   780.573

    1 10.00 120.261  332.513  2749.799

    1 12.00  89.598  540.870  5031.520

    1 16.00  41.572  791.036  8470.430

    1 24.00  24.576 1049.699 13553.463

    1 36.00   9.237 1237.802 19015.333

    1 48.00   4.897 1319.870 22410.463

    1 72.00   1.976 1397.115 26906.872

    1 96.00   1.287 1435.682 30113.526

Now if i do manual calculation of AUC by trapezoid rule by formula, AUC is coming to 1478.681 instead of 1435.682 by bear.

Can anyone pls explain the reason for this difference.

Regards
Pjs

Edit: BBcoded; see also this post #6. [Helmut]

Helmut
★★★

Vienna, Austria,
2017-05-21 19:32
(2895 d 03:42 ago)

@ pjs
Posting: # 17380
Views: 8,690

lin-up/log-down is bear’s default

Post reply

Dear Pjs,

❝ […] this wonderful freeware

bear = free software (open source) ≠ freeware. :-D

❝ […] if i do manual calculation of AUC by trapezoid rule by formula, AUC is coming to 1478.681 instead of 1435.682 by bear.

Note that the lin-up/log-down trapezoidal method is the default in bear – and for good reasons (IMHO, the linear rule should abandoned since it overestimates the AUC in the distribution/elimination phase). I got:

 time    conc     bear   incr/equal  linear   lin/log

 0.00    0.000     0.000    yes      0.000      0.000

 1.00    0.000     0.000    yes      0.000      0.000

 1.50    0.000     0.000    yes      0.000      0.000

 2.00    0.000     0.000    yes      0.000      0.000

 2.50    0.000     0.000    yes      0.000      0.000

 3.00    0.000     0.000    yes      0.000      0.000

 3.50    0.000     0.000    yes      0.000      0.000

 4.00    1.518     0.380    yes      0.380      0.380

 4.33    5.027     1.459    yes      1.459      1.459

 4.67   12.700     4.473    yes      4.473      4.473

 5.00   22.210    10.233    no      10.233     10.088

 5.33   18.013    16.846    yes     16.870     16.725

 5.67   22.332    23.704    yes     23.729     23.583

 6.00   30.500    32.422    no      32.446     32.231

 6.33   24.290    41.423    yes     41.486     41.271

 6.67   31.676    50.937    yes     51.000     50.785

 7.00   32.647    61.551    yes     61.614     61.398

 7.50   45.512    81.091    yes     81.154     80.938

 8.00   95.827   116.425    yes    116.488    116.273

10.00  120.261   332.513    no     332.576    331.437

12.00   89.598   540.870    no     542.435    539.794

16.00   41.572   791.036    no     804.775    789.960

24.00   24.576  1049.699    no    1069.367   1048.623

36.00    9.237  1237.802    no    1272.245   1236.725

48.00    4.897  1319.870    no    1357.049   1318.793

72.00    1.976  1397.115    no    1439.525   1396.039

96.00    1.287  1435.682    no    1478.681   1434.606

Lin-up/log-down trapezoidal method:
If concentrations are increasing or equal in the interval [1, 2] use the linear trapezoidal, i.e.,

AUC_1–2 = 0.5(t₂–t₁)(C₂+C₁)

If concentrations are decreasing in the interval [1, 2] use the log trapezoidal, i.e.,

AUC_1–2 = (t₂–t₁)(C₂–C₁)∕log(C₂∕C₁)

1435.682 ≠ 1434.606. Close, but… Is it possible that in your original data set times and/or concentrations are given with more significant digits than you posted here? Please check.

If you have to use the linear trapezoidal method (stupid SAP, SOP, boss), see this post and change the Setting for trapezoidal AUC from 0 to 1.

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

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes

pjs ★ India, 2017-05-21 21:08 (2895 d 02:06 ago) @ Helmut Posting: # 17381 Views: 8,294	lin-up/log-down any regulatory recommendation? Post reply
	Dear Helmut, Thanks for the explanation . Is there any regulatory requirement for the use of linup-logdown method. As u explained there could be more bias in the AUC estimation in case of missing samples. Do this needs to be defined in the Protocol? This could become crucial incase of borderline study results for AUC. Regards pjs

Helmut
★★★

Vienna, Austria,
2017-05-21 21:14
(2895 d 02:00 ago)

@ pjs
Posting: # 17382
Views: 8,302

lin-up/log-down any regulatory recommendation?

Post reply

Hi Pjs,

❝ Thanks for the explanation :-) .

Would you mind answer my question from above? Did you use more significant digits?

❝ Is there any regulatory requirement for the use of linup-logdown method.

No. Was recommended in the previous version of the WHO’s GL.

❝ Do this needs to be defined in the Protocol?

Exactly. Go ahead and update your SOP.

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

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes

pjs ★ India, 2017-05-21 21:33 (2895 d 01:41 ago) @ Helmut Posting: # 17383 Views: 8,231	lin-up/log-down any regulatory recommendation? Post reply
	Hi Helmut ❝ Would you mind answer my question from above? Did you use more significant digits? No similar digits were used for the data incorporation in bear. ❝ ❝ Is there any regulatory requirement for the use of linup-logdown method. ❝ No. Was recommended in the previous version of the WHO’s GL. Ok Thanks. Regards Pjs

yjlee168
★★★

Kaohsiung, Taiwan,
2017-05-21 22:08
(2895 d 01:05 ago)

@ Helmut
Posting: # 17384
Views: 8,392

lin-up/log-down is bear’s default

Post reply

Dear Helmut,

Thanks for your help. :ok:

The following step can be done also simply from GUI as shown in the picture.

❝ If you have to use the linear trapezoidal method (stupid SAP, SOP, boss), see this post and change the Setting for trapezoidal AUC from 0 to 1.

—
All the best,
-- Yung-jin Lee
bear v2.9.2:- created by Hsin-ya Lee & Yung-jin Lee
Kaohsiung, Taiwan https://www.pkpd168.com/bear
Download link (updated) -> here

Yura ★ Belarus, 2017-05-25 14:52 (2891 d 08:21 ago) @ yjlee168 Posting: # 17415 Views: 8,147	lin-up/log-down is bear’s default Post reply
	Dear yjlee168 Do I understand correctly that it is necessary to set zero when entering data into a bear if there are concentrations below the lower detection level at the end of sampling? Regards

yjlee168 ★★★ Kaohsiung, Taiwan, 2017-05-25 16:38 (2891 d 06:36 ago) @ Yura Posting: # 17416 Views: 8,165	zero (0), missing (NA), or BLLOQ (0 or NA) in bear (II) Post reply
	Dear Yura, You can enter BBLOQ as 'NA' or zero depending on your SOP. Please have a look at this. Edit: Changed to internal link; see also this post #7. [Helmut] — All the best, -- Yung-jin Lee bear v2.9.2:- created by Hsin-ya Lee & Yung-jin Lee Kaohsiung, Taiwan https://www.pkpd168.com/bear Download link (updated) -> here

Yura ★ Belarus, 2017-05-25 17:17 (2891 d 05:56 ago) @ yjlee168 Posting: # 17417 Views: 8,069	zero (0), missing (NA), or BLLOQ (0 or NA) in bear (II) Post reply
	Dear yjlee168 Thank you

Astea
★★

Russia,
2017-05-22 04:12
(2894 d 19:02 ago)

@ Helmut
Posting: # 17385
Views: 8,320

lin-up/log-down is bear’s default

Post reply

Dear Helmut!

Please check the data you've posted in the column "lin/log". Accidently you've summed a previous to the "down" number instead: pay attention, every "no" follows the moment previous to that of falling the concentration (like 22.210 to 18.013). The data in the "bear" column is correct. It also coincides with that of the "linear up log down" method in WinNonLin (1435.6823). For "linear trapezoidal linear interpolation" I've got 1478.6813 in WinNonLin and 1478.7 in bear.

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

Helmut
★★★

Vienna, Austria,
2017-05-22 15:19
(2894 d 07:55 ago)

@ Astea
Posting: # 17386
Views: 8,438

Never use Excel

Post reply

Dear Astea,

❝ Please check the data you've posted in the column "lin/log".

THX, I stand corrected! I should have observed Martin’s advice:

❝ never never never never use excel for any statistical calculations

Plain R

time <- c(0.00, 1.00, 1.50, 2.00, 2.50, 3.00, 3.50, 4.00, 4.33, 4.67, 5.00, 5.33, 5.67, 6.00, 6.33, 6.67, 7.00, 7.50, 8.00, 10.00, 12.00, 16.00, 24.00, 36.00, 48.00, 72.00, 96.00) conc <- c(0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 1.518, 5.027, 12.700, 22.210, 18.013, 22.332, 30.500, 24.290, 31.676, 32.647, 45.512, 95.827, 120.261, 89.598, 41.572, 24.576, 9.237, 4.897, 1.976, 1.287) data <- data.frame(time, conc, lin=0, linlog=0) delta.t <- diff(data$time) delta.c <- diff(data$conc) for (j in seq_along(delta.t)) { # linear trapezoidal method data$lin[j] <- 0.5*delta.t[j]*sum(data$conc[j+1], data$conc[j]) # lin-up/log-down trapezoidal method if (delta.c[j] < 0) { # decreasing : log trapezoidal method data$linlog[j] <- delta.t[j]*delta.c[j]/log(data$conc[j+1]/data$conc[j]) } else { # increasing or equal: linear trapezoidal method data$linlog[j] <- data$lin[j] } } data$lin <- cumsum(data$lin) data$linlog <- cumsum(data$linlog) print(round(data, 4), row.names=FALSE)

gives

time conc lin linlog 0.00 0.000 0.0000 0.0000 1.00 0.000 0.0000 0.0000 1.50 0.000 0.0000 0.0000 2.00 0.000 0.0000 0.0000 2.50 0.000 0.0000 0.0000 3.00 0.000 0.0000 0.0000 3.50 0.000 0.0000 0.0000 4.00 1.518 0.3795 0.3795 4.33 5.027 1.4594 1.4594 4.67 12.700 4.4730 4.4730 5.00 22.210 10.2332 10.2332 5.33 18.013 16.8700 16.8458 5.67 22.332 23.7286 23.7045 6.00 30.500 32.4459 32.4217 6.33 24.290 41.4862 41.4232 6.67 31.676 51.0005 50.9375 7.00 32.647 61.6138 61.5508 7.50 45.512 81.1535 81.0905 8.00 95.827 116.4883 116.4253 10.00 120.261 332.5763 332.5133 12.00 89.598 542.4353 540.8702 16.00 41.572 804.7753 791.0362 24.00 24.576 1069.3673 1049.6994 36.00 9.237 1272.2453 1237.8016 48.00 4.897 1357.0493 1319.8698 72.00 1.976 1439.5253 1397.1153 96.00 1.287 1478.6813 1435.6823

Sorry for the confusion caused.

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

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes

AUC calculation in bear [🇷 for BE/BA]

lin-up/log-down is bear’s default

lin-up/log-down any regulatory recommendation?

lin-up/log-down any regulatory recommendation?

lin-up/log-down any regulatory recommendation?

lin-up/log-down is bear’s default

lin-up/log-down is bear’s default

zero (0), missing (NA), or BLLOQ (0 or NA) in bear (II)

zero (0), missing (NA), or BLLOQ (0 or NA) in bear (II)

lin-up/log-down is bear’s default

Never use Excel