ivivc for R v0.2.1 - A Tool for “in vitro-in vivo Correlation" Exploration with  (demo)

originally created by Hsin-ya Lee and Yung-jin Lee (mobilepk@gmail.com)
Kaohsiung Veterans General Hospital (HY) &
ptpc, inc. (YJ),
Kaohsiung, Taiwan 807

Introduction
In vitro-in vivo correlation (IVIVC) is defined as the correlation between in-vitro drug dissolution profile and in vivo drug absorption profile.  The main purpose of conducting an IVIVC study is to utilize in vitro dissolution profiles as a surrogate for in vivo bioequivalence and to support biowaivers.  In order to prove the validity of a new formulation, which is bioequivalent with a target formulation, a considerable amount of efforts is required to study bioequivalence/bioavailability.  Thus, data analysis of IVIVC attracts great attention from the pharmaceutical industry.  The purpose of this study is to develop an IVIVC tool (ivivc) running in R.

Installation & Upgrade: ivivc for R is one of R packages.  Thus, users have to download and install R first, and then run it.  Under R Console, users can click "Packages" from the menu then ->"Install package(s)..." --> select a CRAN mirror site near you and you will see the list of currently available R packages.  Just select "ivivc" from the list and click "OK" to start installation.  Then it's done!  If you want to upgrade from previous version of ivivc for R when a new version is released, please go to the menu and click "Packages", and then select "Update packages...".  then select a CRAN mirror site near you and click "OK".  Done!  Pretty easy to upgrade.  If you're running Linux PC or Mac OS X, you may not see the menu but the R Console.  You can read this R Installation and Administration (pdf ) for detailed information.  You can also type help("INSTALL") or help("install.packages") in R Console for information on how to install packages from this directory.  Don't worry about this. You only need to do this once.  After these installation, you now can run ivivc by simply typing "library(ivivc) (enter)" under R Console.

Remove ivivc for R: Simply go to the directory of R where you installed and then go to the sub-directory of /library, delete ivivc.


Methods

Development and validation are 2 critical steps in the evaluation of an IVIVC model.  In the first, the development of level A IVIVC model is usually estimated by a two-stage process.  (1) Deconvolution:  the observed fraction of the drug absorbed is estimated based on the Wagner-Nelson method.  IV, IR or oral solution was attempted as the reference.  Then, the pharmacokinetic parameters will be estimated using a nonlinear regression tool or obtained from literatures reported previously.  The IVIVC model is developed using the observed fraction of the drug absorbed and that of the drug dissolved.  Based on the IVIVC model, the predicted fraction of the drug absorbed is calculated from the observed fraction of the drug dissolved.  (2) Convolution: the predicted fraction of the drug absorbed is then convolved to the predicted plasma concentrations by using the convolution method.  In the second stage, evaluating the predictability of a level A correlation focuses on estimating the percent prediction error (%PE) between the observed and predicted plasma concentration profiles, such as the difference in pharmacokinetic parameters (Cmax, and the area under the curve from time zero to infinity, AUC). Here is .pdf sample file for the plots.
    This package was performed together with several R packages.  "PKfit" package is used to fit the reference data such as IV, IR or oral solution by fitting an one-compartment model.  Moreover, we use "reshape" package to rearrange some data format in "ivivc" package.  Then, "sciplot" package assists us to plot the mean values and standard error (or other summary statistics) of observed or predicted
concentrations.



























      Sample output file
ps. The following output may be obtained from previous ver.

..................................................

 This report was generated using ivivc for R v0.1.7
 on:- Tue May 07 05:43:50 2013 

 ivivc dor R was developed by Hsin-ya Lee & Yung-jin Lee.
 contact: Yung-jin Lee  
 Kaohsiung Veterans General Hospital (HY) &
 ptpc inc. (YJ),
 Kaohsiung City, Taiwan

..................................................

Enter the dose of ER formulations:

 ER Dose = 200 

 Load PK parameter data file automatically as follows.

  subj        ka       kel       Vd
1    1 0.4609453  4.824635 42.25891
2    2 0.6040652  7.531070 37.34740
3    3 0.7525116 14.472986 21.56361


****************************************************************************
* Next:                                                                    *
*      calculate AUCobs(0~t), AUCobs(0~inf), Fobs(t), FABobs               *
*--------------------------------------------------------------------------*
* AUCobs(0~t): area under the observed plasma concentration time curve     *
*              (time = 0 to t)                                             *
* AUCobs(0~inf): area under the observed plasma concentration time curve   *
*               (time = 0 to infinity)                                     *
* Fobs(t): observed absorption rate                                        *
* FABobs: observed cumulative absorption fraction(%)                       *
* FRD: cumulative released fraction(%)                                     *
****************************************************************************

<< Output >>
    pH subj formula. time conc.obs AUCobs(0~t)   Fobs(t)     FABobs   FRD
1  1.2    1        F  0.0  0.00000   0.0000000 0.0000000   0.000000  0.00
2  1.2    1        F  0.5  0.11026   0.0275650 0.2432511   6.415222 11.14
3  1.2    1        F  1.0  0.11617   0.0841725 0.5222716  13.773787 13.86
4  1.2    1        F  1.5  0.13020   0.1457650 0.8334629  21.980788 18.84
5  1.2    1        F  2.0  0.14577   0.2147575 1.1818965  31.169973 19.79
6  1.2    1        F  3.0  0.12375   0.3495175 1.8100443  47.736018 25.97
7  1.2    1        F  4.0  0.12305   0.4729175 2.4047043  63.418892 32.09
8  1.2    1        F  5.0  0.08235   0.5756175 2.8594943  75.412998 37.16
9  1.2    1        F  6.0  0.04862   0.6411025 3.1417055  82.855710 41.44
10 1.2    1        F  8.0  0.02651   0.7162325 3.4820704  91.832099 50.12
11 1.2    1        F 10.0  0.00304   0.7457825 3.6011683  94.973051 54.28
12 1.2    1        F 12.0  0.00287   0.7516925 3.6295119  95.720552 59.81
13 1.2    1        F 24.0  0.00274   0.7853525 3.7917791 100.000000 84.53

<< AUCobs(0~inf) is computed with trapezoidal method >>

[1] 0.7859204


****************************************************************************
* Next:                                                                    *
*      calculate AUCobs(0~t), AUCobs(0~inf), Fobs(t), FABobs               *
*--------------------------------------------------------------------------*
* AUCobs(0~t): area under the observed plasma concentration time curve     *
*              (time = 0 to t)                                             *
* AUCobs(0~inf): area under the observed plasma concentration time curve   *
*               (time = 0 to infinity)                                     *
* Fobs(t): observed absorption rate                                        *
* FABobs: observed cumulative absorption fraction(%)                       *
* FRD: cumulative released fraction(%)                                     *
****************************************************************************

<< Output >>
    pH subj formula. time conc.obs AUCobs(0~t)   Fobs(t)     FABobs   FRD
1  6.8    1        F  0.0  0.00000   0.0000000 0.0000000   0.000000  0.00
2  6.8    1        F  0.5  0.11044   0.0276100 0.2436482   4.427523  8.83
3  6.8    1        F  1.0  0.15988   0.0951900 0.6191370  11.250825 14.09
4  6.8    1        F  1.5  0.13663   0.1693175 0.9535251  17.327255 17.69
5  6.8    1        F  2.0  0.15370   0.2419000 1.3207792  24.000918 20.79
6  6.8    1        F  3.0  0.06338   0.3504400 1.7541251  31.875586 25.71
7  6.8    1        F  4.0  0.06718   0.4157200 2.0728772  37.667883 31.34
8  6.8    1        F  5.0  0.08396   0.4912900 2.4542549  44.598196 35.67
9  6.8    1        F  6.0  0.12941   0.5979750 3.0144211  54.777417 40.20
10 6.8    1        F  8.0  0.08863   0.8160150 4.0256045  73.152426 48.40
11 6.8    1        F 10.0  0.01732   0.9219650 4.4654646  81.145469 55.72
12 6.8    1        F 12.0  0.01718   0.9564650 4.6317745  84.167617 61.48
13 6.8    1        F 24.0  0.01306   1.1379050 5.5030362 100.000000 81.08

<< AUCobs(0~inf) is computed with trapezoidal method >>

[1] 1.140612


****************************************************************************
* Next:                                                                    *
*      calculate AUCobs(0~t), AUCobs(0~inf), Fobs(t), FABobs               *
*--------------------------------------------------------------------------*
* AUCobs(0~t): area under the observed plasma concentration time curve     *
*              (time = 0 to t)                                             *
* AUCobs(0~inf): area under the observed plasma concentration time curve   *
*               (time = 0 to infinity)                                     *
* Fobs(t): observed absorption rate                                        *
* FABobs: observed cumulative absorption fraction(%)                       *
* FRD: cumulative released fraction(%)                                     *
****************************************************************************

<< Output >>
    pH subj formula. time conc.obs AUCobs(0~t)   Fobs(t)     FABobs    FRD
1  1.2    1        M  0.0  0.00000   0.0000000 0.0000000   0.000000   0.00
2  1.2    1        M  0.5  0.10740   0.0268500 0.2369414   2.539983  16.70
3  1.2    1        M  1.0  0.15168   0.0916200 0.5937131   6.364531  21.24
4  1.2    1        M  1.5  0.18293   0.1752725 1.0285558  11.025993  27.10
5  1.2    1        M  2.0  0.21175   0.2739425 1.5334226  16.438102  35.42
6  1.2    1        M  3.0  0.14171   0.4506725 2.3160403  24.827668  41.53
7  1.2    1        M  4.0  0.13102   0.5870375 2.9632616  31.765802  49.33
8  1.2    1        M  5.0  0.14073   0.7229125 3.6285189  38.897278  56.06
9  1.2    1        M  6.0  0.14073   0.8636425 4.3074898  46.175763  53.36
10 1.2    1        M  8.0  0.08957   1.0939425 5.3674432  57.538334  71.22
11 1.2    1        M 10.0  0.05584   1.2393525 6.0352634  64.697285  80.03
12 1.2    1        M 12.0  0.07919   1.3743825 6.7100838  71.931277  84.48
13 1.2    1        M 24.0  0.01353   1.9307025 9.3284648 100.000000 100.22

<< AUCobs(0~inf) is computed with trapezoidal method >>

[1] 1.933507


****************************************************************************
* Next:                                                                    *
*      calculate AUCobs(0~t), AUCobs(0~inf), Fobs(t), FABobs               *
*--------------------------------------------------------------------------*
* AUCobs(0~t): area under the observed plasma concentration time curve     *
*              (time = 0 to t)                                             *
* AUCobs(0~inf): area under the observed plasma concentration time curve   *
*               (time = 0 to infinity)                                     *
* Fobs(t): observed absorption rate                                        *
* FABobs: observed cumulative absorption fraction(%)                       *
* FRD: cumulative released fraction(%)                                     *
****************************************************************************

<< Output >>
    pH subj formula. time conc.obs AUCobs(0~t)   Fobs(t)     FABobs   FRD
1  6.8    1        M  0.0  0.00000   0.0000000 0.0000000   0.000000  0.00
2  6.8    1        M  0.5  0.11418   0.0285450 0.2518992   3.885225 16.94
3  6.8    1        M  1.0  0.16072   0.0972700 0.6300122   9.717138 22.85
4  6.8    1        M  1.5  0.15228   0.1755200 0.9990999  15.409846 27.10
5  6.8    1        M  2.0  0.12505   0.2448525 1.3063739  20.149157 35.17
6  6.8    1        M  3.0  0.11897   0.3668625 1.8889476  29.134616 41.03
7  6.8    1        M  4.0  0.12326   0.4879775 2.4775733  38.213419 48.59
8  6.8    1        M  5.0  0.14346   0.6213375 3.1411866  48.448811 56.06
9  6.8    1        M  6.0  0.13700   0.7615675 3.8112852  58.784229 60.76
10 6.8    1        M  8.0  0.09148   0.9900475 4.8680978  75.084220 69.28
11 6.8    1        M 10.0  0.05246   1.1339875 5.5235357  85.193517 77.14
12 6.8    1        M 12.0  0.01539   1.2018375 5.8138172  89.670740 83.04
13 6.8    1        M 24.0  0.00800   1.3421775 6.4835165 100.000000 98.36

<< AUCobs(0~inf) is computed with trapezoidal method >>

[1] 1.343836


****************************************************************************
* Next:                                                                    *
*      calculate AUCobs(0~t), AUCobs(0~inf), Fobs(t), FABobs               *
*--------------------------------------------------------------------------*
* AUCobs(0~t): area under the observed plasma concentration time curve     *
*              (time = 0 to t)                                             *
* AUCobs(0~inf): area under the observed plasma concentration time curve   *
*               (time = 0 to infinity)                                     *
* Fobs(t): observed absorption rate                                        *
* FABobs: observed cumulative absorption fraction(%)                       *
* FRD: cumulative released fraction(%)                                     *
****************************************************************************

<< Output >>
    pH subj formula. time conc.obs AUCobs(0~t)   Fobs(t)     FABobs   FRD
1  1.2    1        S  0.0  0.00000   0.0000000 0.0000000   0.000000  0.00
2  1.2    1        S  0.5  0.02265   0.0056625 0.0499695   1.050154 17.17
3  1.2    1        S  1.0  0.03262   0.0194800 0.1266039   2.660694 19.63
4  1.2    1        S  1.5  0.05025   0.0401975 0.2441883   5.131835 24.81
5  1.2    1        S  2.0  0.05025   0.0653225 0.3654072   7.679360 30.38
6  1.2    1        S  3.0  0.13061   0.1557525 0.8820590  18.537259 35.01
7  1.2    1        S  4.0  0.12923   0.2856725 1.5074955  31.681368 40.60
8  1.2    1        S  5.0  0.12883   0.4147025 2.1296182  44.755833 47.86
9  1.2    1        S  6.0  0.07619   0.5172125 2.5715515  54.043457 54.07
10 1.2    1        S  8.0  0.04683   0.6402325 3.1357181  65.899923 64.59
11 1.2    1        S 10.0  0.02390   0.7109625 3.4540345  72.589628 72.49
12 1.2    1        S 12.0  0.02043   0.7552925 3.6644406  77.011500 78.66
13 1.2    1        S 24.0  0.01746   0.9826325 4.7583031 100.000000 98.05

<< AUCobs(0~inf) is computed with trapezoidal method >>

[1] 0.9862514


****************************************************************************
* Next:                                                                    *
*      calculate AUCobs(0~t), AUCobs(0~inf), Fobs(t), FABobs               *
*--------------------------------------------------------------------------*
* AUCobs(0~t): area under the observed plasma concentration time curve     *
*              (time = 0 to t)                                             *
* AUCobs(0~inf): area under the observed plasma concentration time curve   *
*               (time = 0 to infinity)                                     *
* Fobs(t): observed absorption rate                                        *
* FABobs: observed cumulative absorption fraction(%)                       *
* FRD: cumulative released fraction(%)                                     *
****************************************************************************

<< Output >>
    pH subj formula. time conc.obs AUCobs(0~t)    Fobs(t)     FABobs   FRD
1  6.8    1        S  0.0  0.00000   0.0000000  0.0000000   0.000000  0.00
2  6.8    1        S  0.5  0.09167   0.0229175  0.2022386   1.842393 13.46
3  6.8    1        S  1.0  0.21678   0.1000300  0.6993882   6.371426 19.60
4  6.8    1        S  1.5  0.17991   0.1992025  1.1409893  10.394412 24.80
5  6.8    1        S  2.0  0.18702   0.2909350  1.5906752  14.491049 30.63
6  6.8    1        S  3.0  0.17615   0.4725200  2.4558865  22.373124 36.51
7  6.8    1        S  4.0  0.17124   0.6462150  3.2889915  29.962709 42.59
8  6.8    1        S  5.0  0.15783   0.8107500  4.0694028  37.072255 49.35
9  6.8    1        S  6.0  0.14915   0.9642400  4.8012560  43.739437 56.04
10 6.8    1        S  8.0  0.14218   1.2555700  6.1998469  56.480599 66.31
11 6.8    1        S 10.0  0.10756   1.5053100  7.3701312  67.141888 74.42
12 6.8    1        S 12.0  0.08637   1.6992400  8.2845827  75.472540 81.06
13 6.8    1        S 24.0  0.00930   2.2732600 10.9769497 100.000000 99.69

<< AUCobs(0~inf) is computed with trapezoidal method >>

[1] 2.275188


****************************************************************************
* Next:                                                                    *
*      calculate AUCobs(0~t), AUCobs(0~inf), Fobs(t), FABobs               *
*--------------------------------------------------------------------------*
* AUCobs(0~t): area under the observed plasma concentration time curve     *
*              (time = 0 to t)                                             *
* AUCobs(0~inf): area under the observed plasma concentration time curve   *
*               (time = 0 to infinity)                                     *
* Fobs(t): observed absorption rate                                        *
* FABobs: observed cumulative absorption fraction(%)                       *
* FRD: cumulative released fraction(%)                                     *
****************************************************************************

<< Output >>
    pH subj formula. time conc.obs AUCobs(0~t)   Fobs(t)     FABobs   FRD
1  1.2    2        F  0.0  0.00000   0.0000000 0.0000000   0.000000  0.00
2  1.2    2        F  0.5  0.12571   0.0314275 0.3623927   4.899442  9.75
3  1.2    2        F  1.0  0.08260   0.0835050 0.7114820   9.619026 13.63
4  1.2    2        F  1.5  0.15150   0.1420300 1.2211379  16.509423 18.38
5  1.2    2        F  2.0  0.07328   0.1982250 1.5661264  21.173565 23.56
6  1.2    2        F  3.0  0.05693   0.2633300 2.0400867  27.581369 27.72
7  1.2    2        F  4.0  0.06357   0.3235800 2.5004737  33.805664 34.83
8  1.2    2        F  5.0  0.04843   0.3795800 2.9070736  39.302775 39.39
9  1.2    2        F  6.0  0.08606   0.4468250 3.4511304  46.658262 43.66
10 1.2    2        F  8.0  0.07116   0.6040450 4.6202653  62.464620 52.33
11 1.2    2        F 10.0  0.04743   0.7226350 5.4896449  74.218375 57.43
12 1.2    2        F 12.0  0.02257   0.7926350 5.9919598  81.009524 62.70
13 1.2    2        F 24.0  0.00882   0.9809750 7.3966116 100.000000 85.53

<< AUCobs(0~inf) is computed with trapezoidal method >>

[1] 0.9821461


****************************************************************************
* Next:                                                                    *
*      calculate AUCobs(0~t), AUCobs(0~inf), Fobs(t), FABobs               *
*--------------------------------------------------------------------------*
* AUCobs(0~t): area under the observed plasma concentration time curve     *
*              (time = 0 to t)                                             *
* AUCobs(0~inf): area under the observed plasma concentration time curve   *
*               (time = 0 to infinity)                                     *
* Fobs(t): observed absorption rate                                        *
* FABobs: observed cumulative absorption fraction(%)                       *
* FRD: cumulative released fraction(%)                                     *
****************************************************************************

<< Output >>
    pH subj formula. time conc.obs AUCobs(0~t)   Fobs(t)     FABobs   FRD
1  6.8    2        F  0.0  0.00000   0.0000000 0.0000000   0.000000  0.00
2  6.8    2        F  0.5  0.15918   0.0397950 0.4588789   7.019696  9.06
3  6.8    2        F  1.0  0.11120   0.1073900 0.9199616  14.073103 14.32
4  6.8    2        F  1.5  0.16542   0.1765450 1.4949928  22.869636 18.38
5  6.8    2        F  2.0  0.12595   0.2493875 2.0041048  30.657771 21.55
6  6.8    2        F  3.0  0.04238   0.3335525 2.5543873  39.075711 26.97
7  6.8    2        F  4.0  0.04280   0.3761425 2.8755556  43.988780 33.33
8  6.8    2        F  5.0  0.05870   0.4268925 3.2736574  50.078738 38.15
9  6.8    2        F  6.0  0.07521   0.4938475 3.7944102  58.044948 43.41
10 6.8    2        F  8.0  0.04670   0.6157575 4.6840130  71.653637 51.59
11 6.8    2        F 10.0  0.02065   0.6831075 5.1651805  79.014292 57.91
12 6.8    2        F 12.0  0.01819   0.7219475 5.4552273  83.451280 63.42
13 6.8    2        F 24.0  0.00602   0.8672075 6.5370205 100.000000 82.51

<< AUCobs(0~inf) is computed with trapezoidal method >>

[1] 0.8680069


****************************************************************************
* Next:                                                                    *
*      calculate AUCobs(0~t), AUCobs(0~inf), Fobs(t), FABobs               *
*--------------------------------------------------------------------------*
* AUCobs(0~t): area under the observed plasma concentration time curve     *
*              (time = 0 to t)                                             *
* AUCobs(0~inf): area under the observed plasma concentration time curve   *
*               (time = 0 to infinity)                                     *
* Fobs(t): observed absorption rate                                        *
* FABobs: observed cumulative absorption fraction(%)                       *
* FRD: cumulative released fraction(%)                                     *
****************************************************************************

<< Output >>
    pH subj formula. time conc.obs AUCobs(0~t)    Fobs(t)     FABobs   FRD
1  1.2    2        M  0.0  0.00000   0.0000000  0.0000000   0.000000  0.00
2  1.2    2        M  0.5  0.12390   0.0309750  0.3571749   2.889492 14.16
3  1.2    2        M  1.0  0.16241   0.1025525  0.9347401   7.561910 21.23
4  1.2    2        M  1.5  0.12500   0.1744050  1.4384563  11.636900 27.10
5  1.2    2        M  2.0  0.12500   0.2369050  1.9091482  15.444728 34.91
6  1.2    2        M  3.0  0.14800   0.3734050  2.9601393  23.947091 42.53
7  1.2    2        M  4.0  0.16100   0.5279050  4.1366896  33.465210 48.83
8  1.2    2        M  5.0  0.12800   0.6724050  5.1919292  42.001944 55.81
9  1.2    2        M  6.0  0.13200   0.8024050  6.1749684  49.954586 61.00
10 1.2    2        M  8.0  0.12800   1.0624050  8.1290466  65.762791 71.47
11 1.2    2        M 10.0  0.08904   1.2794450  9.7246301  78.670827 78.58
12 1.2    2        M 12.0  0.02400   1.3924850 10.5109023  85.031653 84.25
13 1.2    2        M 24.0  0.01710   1.6390850 12.3611642 100.000000 99.54

<< AUCobs(0~inf) is computed with trapezoidal method >>

[1] 1.641356


****************************************************************************
* Next:                                                                    *
*      calculate AUCobs(0~t), AUCobs(0~inf), Fobs(t), FABobs               *
*--------------------------------------------------------------------------*
* AUCobs(0~t): area under the observed plasma concentration time curve     *
*              (time = 0 to t)                                             *
* AUCobs(0~inf): area under the observed plasma concentration time curve   *
*               (time = 0 to infinity)                                     *
* Fobs(t): observed absorption rate                                        *
* FABobs: observed cumulative absorption fraction(%)                       *
* FRD: cumulative released fraction(%)                                     *
****************************************************************************

<< Output >>
    pH subj formula. time conc.obs AUCobs(0~t)    Fobs(t)     FABobs   FRD
1  6.8    2        M  0.0  0.00000   0.0000000  0.0000000   0.000000  0.00
2  6.8    2        M  0.5  0.12286   0.0307150  0.3541768   3.061372 15.55
3  6.8    2        M  1.0  0.11261   0.0895825  0.7872621   6.804799 21.93
4  6.8    2        M  1.5  0.19124   0.1655450  1.4379710  12.429283 21.83
5  6.8    2        M  2.0  0.16243   0.2539625  2.0750394  17.935864 36.17
6  6.8    2        M  3.0  0.17607   0.4232125  3.3633130  29.071218 44.53
7  6.8    2        M  4.0  0.18753   0.6050125  4.7439216  41.004682 49.08
8  6.8    2        M  5.0  0.15657   0.7770625  6.0086822  51.936799 55.32
9  6.8    2        M  6.0  0.09821   0.9044525  6.9097053  59.724905 61.49
10 6.8    2        M  8.0  0.09435   1.0970125  8.3560281  72.226378 69.52
11 6.8    2        M 10.0  0.04474   1.2361025  9.3539147  80.851736 76.65
12 6.8    2        M 12.0  0.02707   1.3079125  9.8770508  85.373528 83.04
13 6.8    2        M 24.0  0.01074   1.5347725 11.5692194 100.000000 98.83

<< AUCobs(0~inf) is computed with trapezoidal method >>

[1] 1.536199


****************************************************************************
* Next:                                                                    *
*      calculate AUCobs(0~t), AUCobs(0~inf), Fobs(t), FABobs               *
*--------------------------------------------------------------------------*
* AUCobs(0~t): area under the observed plasma concentration time curve     *
*              (time = 0 to t)                                             *
* AUCobs(0~inf): area under the observed plasma concentration time curve   *
*               (time = 0 to infinity)                                     *
* Fobs(t): observed absorption rate                                        *
* FABobs: observed cumulative absorption fraction(%)                       *
* FRD: cumulative released fraction(%)                                     *
****************************************************************************

<< Output >>
    pH subj formula. time conc.obs AUCobs(0~t)    Fobs(t)     FABobs    FRD
1  1.2    2        S  0.0  0.00000   0.0000000  0.0000000   0.000000   0.00
2  1.2    2        S  0.5  0.22248   0.0556200  0.6413581   4.253171  13.23
3  1.2    2        S  1.0  0.24437   0.1723325  1.5422182  10.227231  20.08
4  1.2    2        S  1.5  0.24437   0.2945175  2.4624020  16.329436  26.41
5  1.2    2        S  2.0  0.27090   0.4233350  3.4590656  22.938818  33.15
6  1.2    2        S  3.0  0.13900   0.6282850  4.8706584  32.299806  40.52
7  1.2    2        S  4.0  0.13900   0.7672850  5.9174772  39.241792  46.08
8  1.2    2        S  5.0  0.08430   0.8789350  6.7036212  44.455111  55.70
9  1.2    2        S  6.0  0.06942   0.9557950  7.2675792  48.195003  59.05
10 1.2    2        S  8.0  0.06991   1.0951250  8.3173732  55.156720  69.74
11 1.2    2        S 10.0  0.07202   1.2370550  9.3883680  62.259029  77.60
12 1.2    2        S 12.0  0.07862   1.3876950 10.5294484  69.826112  84.47
13 1.2    2        S 24.0  0.02330   1.9992150 15.0795285 100.000000 101.38

<< AUCobs(0~inf) is computed with trapezoidal method >>

[1] 2.002309


****************************************************************************
* Next:                                                                    *
*      calculate AUCobs(0~t), AUCobs(0~inf), Fobs(t), FABobs               *
*--------------------------------------------------------------------------*
* AUCobs(0~t): area under the observed plasma concentration time curve     *
*              (time = 0 to t)                                             *
* AUCobs(0~inf): area under the observed plasma concentration time curve   *
*               (time = 0 to infinity)                                     *
* Fobs(t): observed absorption rate                                        *
* FABobs: observed cumulative absorption fraction(%)                       *
* FRD: cumulative released fraction(%)                                     *
****************************************************************************

<< Output >>
    pH subj formula. time conc.obs AUCobs(0~t)    Fobs(t)      FABobs    FRD
1  6.8    2        S  0.0  0.00000   0.0000000  0.0000000   0.0000000   0.00
2  6.8    2        S  0.5  0.03946   0.0098650  0.1137540   0.8348257  14.62
3  6.8    2        S  1.0  0.02642   0.0263350  0.2247507   1.6494161  21.70
4  6.8    2        S  1.5  0.05992   0.0479200  0.4208089   3.0882610  28.70
5  6.8    2        S  2.0  0.09049   0.0855225  0.7345659   5.3908829  35.42
6  6.8    2        S  3.0  0.15998   0.2107575  1.7472095  12.8225409  43.79
7  6.8    2        S  4.0  0.17935   0.3804225  3.0443385  22.3420001  48.09
8  6.8    2        S  5.0  0.27032   0.6052575  4.8285567  35.4361425  54.83
9  6.8    2        S  6.0  0.15921   0.8200225  6.3348570  46.4906822  61.00
10 6.8    2        S  8.0  0.06918   1.0484125  7.9648481  58.4529726  70.98
11 6.8    2        S 10.0  0.05965   1.1772425  8.9255459  65.5034072  78.83
12 6.8    2        S 12.0  0.04659   1.2834825  9.7125868  71.2793968  84.73
13 6.8    2        S 24.0  0.04016   1.8039825 13.6260788 100.0000000 100.91

<< AUCobs(0~inf) is computed with trapezoidal method >>

[1] 1.809315


****************************************************************************
* Next:                                                                    *
*      calculate AUCobs(0~t), AUCobs(0~inf), Fobs(t), FABobs               *
*--------------------------------------------------------------------------*
* AUCobs(0~t): area under the observed plasma concentration time curve     *
*              (time = 0 to t)                                             *
* AUCobs(0~inf): area under the observed plasma concentration time curve   *
*               (time = 0 to infinity)                                     *
* Fobs(t): observed absorption rate                                        *
* FABobs: observed cumulative absorption fraction(%)                       *
* FRD: cumulative released fraction(%)                                     *
****************************************************************************

<< Output >>
    pH subj formula. time conc.obs AUCobs(0~t)    Fobs(t)    FABobs   FRD
1  1.2    3        F  0.0  0.00000   0.0000000  0.0000000   0.00000  0.00
2  1.2    3        F  0.5  0.16745   0.0418625  0.7733254   5.61673  9.75
3  1.2    3        F  1.0  0.12430   0.1148000  1.7857988  12.97041 13.86
4  1.2    3        F  1.5  0.13227   0.1789425  2.7221023  19.77087 17.92
5  1.2    3        F  2.0  0.11946   0.2418750  3.6201135  26.29320 21.55
6  1.2    3        F  3.0  0.06243   0.3328200  4.8793293  35.43900 26.47
7  1.2    3        F  4.0  0.04864   0.3883550  5.6692966  41.17660 32.59
8  1.2    3        F  5.0  0.06557   0.4454600  6.5127064  47.30236 36.91
9  1.2    3        F  6.0  0.05926   0.5078750  7.4097279  53.81750 40.94
10 1.2    3        F  8.0  0.04277   0.6099050  8.8699167  64.42298 49.63
11 1.2    3        F 10.0  0.03909   0.6917650 10.0509953  73.00126 53.07
12 1.2    3        F 12.0  0.02206   0.7529150 10.9189884  79.30557 58.84
13 1.2    3        F 24.0  0.01088   0.9505550 13.7682494 100.00000 81.53

<< AUCobs(0~inf) is computed with trapezoidal method >>

[1] 0.9513067


****************************************************************************
* Next:                                                                    *
*      calculate AUCobs(0~t), AUCobs(0~inf), Fobs(t), FABobs               *
*--------------------------------------------------------------------------*
* AUCobs(0~t): area under the observed plasma concentration time curve     *
*              (time = 0 to t)                                             *
* AUCobs(0~inf): area under the observed plasma concentration time curve   *
*               (time = 0 to infinity)                                     *
* Fobs(t): observed absorption rate                                        *
* FABobs: observed cumulative absorption fraction(%)                       *
* FRD: cumulative released fraction(%)                                     *
****************************************************************************

<< Output >>
    pH subj formula. time conc.obs AUCobs(0~t)    Fobs(t)    FABobs   FRD
1  6.8    3        F  0.0  0.00000   0.0000000  0.0000000   0.00000  0.00
2  6.8    3        F  0.5  0.16745   0.0418625  0.7733254   5.61673  9.99
3  6.8    3        F  1.0  0.12430   0.1148000  1.7857988  12.97041 13.40
4  6.8    3        F  1.5  0.13227   0.1789425  2.7221023  19.77087 17.23
5  6.8    3        F  2.0  0.11946   0.2418750  3.6201135  26.29320 18.78
6  6.8    3        F  3.0  0.06243   0.3328200  4.8793293  35.43900 24.46
7  6.8    3        F  4.0  0.04864   0.3883550  5.6692966  41.17660 30.34
8  6.8    3        F  5.0  0.06557   0.4454600  6.5127064  47.30236 34.92
9  6.8    3        F  6.0  0.05926   0.5078750  7.4097279  53.81750 38.96
10 6.8    3        F  8.0  0.04277   0.6099050  8.8699167  64.42298 47.42
11 6.8    3        F 10.0  0.03909   0.6917650 10.0509953  73.00126 54.98
12 6.8    3        F 12.0  0.02206   0.7529150 10.9189884  79.30557 60.51
13 6.8    3        F 24.0  0.01088   0.9505550 13.7682494 100.00000 81.53

<< AUCobs(0~inf) is computed with trapezoidal method >>

[1] 0.9513067


****************************************************************************
* Next:                                                                    *
*      calculate AUCobs(0~t), AUCobs(0~inf), Fobs(t), FABobs               *
*--------------------------------------------------------------------------*
* AUCobs(0~t): area under the observed plasma concentration time curve     *
*              (time = 0 to t)                                             *
* AUCobs(0~inf): area under the observed plasma concentration time curve   *
*               (time = 0 to infinity)                                     *
* Fobs(t): observed absorption rate                                        *
* FABobs: observed cumulative absorption fraction(%)                       *
* FRD: cumulative released fraction(%)                                     *
****************************************************************************

<< Output >>
    pH subj formula. time conc.obs AUCobs(0~t)    Fobs(t)     FABobs   FRD
1  1.2    3        M  0.0  0.00000    0.000000  0.0000000   0.000000  0.00
2  1.2    3        M  0.5  0.12700    0.031750  0.5865173   2.454328 13.69
3  1.2    3        M  1.0  0.14000    0.098500  1.5655891   6.551332 21.00
4  1.2    3        M  1.5  0.10400    0.159500  2.4124413  10.095051 26.41
5  1.2    3        M  2.0  0.10300    0.211250  3.1604183  13.225020 34.91
6  1.2    3        M  3.0  0.16631    0.345905  5.1725883  21.645105 43.53
7  1.2    3        M  4.0  0.16351    0.510815  7.5565285  31.620891 49.08
8  1.2    3        M  5.0  0.16351    0.674325  9.9230064  41.523605 55.07
9  1.2    3        M  6.0  0.11862    0.815390 11.9197482  49.879129 60.75
10 1.2    3        M  8.0  0.12589    1.059900 15.4658081  64.717897 69.03
11 1.2    3        M 10.0  0.06181    1.247600 18.1183076  75.817490 76.16
12 1.2    3        M 12.0  0.03234    1.341750 19.4514693  81.396211 81.84
13 1.2    3        M 24.0  0.01901    1.649850 23.8972663 100.000000 97.20

<< AUCobs(0~inf) is computed with trapezoidal method >>

[1] 1.651163


****************************************************************************
* Next:                                                                    *
*      calculate AUCobs(0~t), AUCobs(0~inf), Fobs(t), FABobs               *
*--------------------------------------------------------------------------*
* AUCobs(0~t): area under the observed plasma concentration time curve     *
*              (time = 0 to t)                                             *
* AUCobs(0~inf): area under the observed plasma concentration time curve   *
*               (time = 0 to infinity)                                     *
* Fobs(t): observed absorption rate                                        *
* FABobs: observed cumulative absorption fraction(%)                       *
* FRD: cumulative released fraction(%)                                     *
****************************************************************************

<< Output >>
    pH subj formula. time conc.obs AUCobs(0~t)    Fobs(t)     FABobs   FRD
1  6.8    3        M  0.0  0.00000   0.0000000  0.0000000   0.000000  0.00
2  6.8    3        M  0.5  0.20449   0.0511225  0.9443852   4.005884 13.69
3  6.8    3        M  1.0  0.25887   0.1669625  2.6753160  11.348130 20.31
4  6.8    3        M  1.5  0.14486   0.2678950  4.0221006  17.060909 25.95
5  6.8    3        M  2.0  0.13363   0.3375175  5.0185161  21.287495 33.65
6  6.8    3        M  3.0  0.16114   0.4849025  7.1791272  30.452355 42.03
7  6.8    3        M  4.0  0.14877   0.6398575  9.4094188  39.912784 46.83
8  6.8    3        M  5.0  0.19937   0.8139275 11.9793315  50.813816 52.83
9  6.8    3        M  6.0  0.10678   0.9670025 14.1021939  59.818554 58.28
10 6.8    3        M  8.0  0.04773   1.1215125 16.2793650  69.053658 67.79
11 6.8    3        M 10.0  0.05063   1.2198725 17.7058279  75.104415 76.63
12 6.8    3        M 12.0  0.04617   1.3166725 19.1023530  81.028182 83.02
13 6.8    3        M 24.0  0.00580   1.6284925 23.5749495 100.000000 98.12

<< AUCobs(0~inf) is computed with trapezoidal method >>

[1] 1.628893


****************************************************************************
* Next:                                                                    *
*      calculate AUCobs(0~t), AUCobs(0~inf), Fobs(t), FABobs               *
*--------------------------------------------------------------------------*
* AUCobs(0~t): area under the observed plasma concentration time curve     *
*              (time = 0 to t)                                             *
* AUCobs(0~inf): area under the observed plasma concentration time curve   *
*               (time = 0 to infinity)                                     *
* Fobs(t): observed absorption rate                                        *
* FABobs: observed cumulative absorption fraction(%)                       *
* FRD: cumulative released fraction(%)                                     *
****************************************************************************

<< Output >>
    pH subj formula. time conc.obs AUCobs(0~t)    Fobs(t)     FABobs    FRD
1  1.2    3        S  0.0  0.00000   0.0000000  0.0000000   0.000000   0.00
2  1.2    3        S  0.5  0.05093   0.0127325  0.2352073   1.720962  13.46
3  1.2    3        S  1.0  0.06240   0.0410650  0.6567332   4.805177  21.23
4  1.2    3        S  1.5  0.11309   0.0849375  1.3423893   9.821977  27.78
5  1.2    3        S  2.0  0.07568   0.1321300  1.9879957  14.545742  34.41
6  1.2    3        S  3.0  0.15707   0.2485050  3.7536794  27.464874  42.03
7  1.2    3        S  4.0  0.10396   0.3790200  5.5895112  40.897265  47.58
8  1.2    3        S  5.0  0.06907   0.4655350  6.8067516  49.803555  55.07
9  1.2    3        S  6.0  0.04574   0.5229400  7.6142434  55.711800  62.72
10 1.2    3        S  8.0  0.04443   0.6131100  8.9179626  65.250836  73.18
11 1.2    3        S 10.0  0.03608   0.6936200 10.0748327  73.715409  80.52
12 1.2    3        S 12.0  0.01893   0.7486300 10.8538417  79.415252  86.65
13 1.2    3        S 24.0  0.01353   0.9433900 13.6672005 100.000000 101.65

<< AUCobs(0~inf) is computed with trapezoidal method >>

[1] 0.9443248


****************************************************************************
* Next:                                                                    *
*      calculate AUCobs(0~t), AUCobs(0~inf), Fobs(t), FABobs               *
*--------------------------------------------------------------------------*
* AUCobs(0~t): area under the observed plasma concentration time curve     *
*              (time = 0 to t)                                             *
* AUCobs(0~inf): area under the observed plasma concentration time curve   *
*               (time = 0 to infinity)                                     *
* Fobs(t): observed absorption rate                                        *
* FABobs: observed cumulative absorption fraction(%)                       *
* FRD: cumulative released fraction(%)                                     *
****************************************************************************

<< Output >>
    pH subj formula. time conc.obs AUCobs(0~t)    Fobs(t)      FABobs   FRD
1  6.8    3        S  0.0  0.00000   0.0000000  0.0000000   0.0000000  0.00
2  6.8    3        S  0.5  0.05841   0.0146025  0.2697518   0.8775078 11.14
3  6.8    3        S  1.0  0.09937   0.0540475  0.8815987   2.8678579 17.32
4  6.8    3        S  1.5  0.18172   0.1243200  1.9810016   6.4442372 22.51
5  6.8    3        S  2.0  0.19667   0.2189175  3.3650600  10.9466061 28.10
6  6.8    3        S  3.0  0.10900   0.3717525  5.4893688  17.8570244 35.50
7  6.8    3        S  4.0  0.11729   0.4848975  7.1352048  23.2109613 39.09
8  6.8    3        S  5.0  0.13718   0.6121325  8.9965652  29.2660032 45.12
9  6.8    3        S  6.0  0.11617   0.7388075 10.8089208  35.1616313 52.33
10 6.8    3        S  8.0  0.08766   0.9426375 13.7304396  44.6653892 59.94
11 6.8    3        S 10.0  0.07792   1.1082175 16.1171366  52.4293616 67.63
12 6.8    3        S 12.0  0.07694   1.2630775 18.3574433  59.7171231 73.82
13 6.8    3        S 24.0  0.06579   2.1194575 30.7406692 100.0000000 91.71

<< AUCobs(0~inf) is computed with trapezoidal method >>

[1] 2.124003


****************************************************************************
* Step4: Develop an IVIVC Model: Model Dependent Method                    *
****************************************************************************

<< Output:IVIVC model (linear regression) >>

Call:
lm(formula = Y ~ X)

Coefficients:
(Intercept)            X  
     -5.674        1.068  

Analysis of Variance Table

Response: Y
           Df Sum Sq Mean Sq F value    Pr(>F)    
X           1 194017  194017  1113.8 < 2.2e-16 ***
Residuals 232  40412     174                      
---
Signif. codes:  0 .***・ 0.001 .**・ 0.01 .*・ 0.05 ..・ 0.1 . ・ 1

Call:
lm(formula = Y ~ X)

Residuals:
    Min      1Q  Median      3Q     Max 
-28.264 -10.138  -0.915   5.674  44.278 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   -5.674      1.632  -3.477 0.000605 ***
X              1.068      0.032  33.374  < 2e-16 ***
---
Signif. codes:  0 .***・ 0.001 .**・ 0.01 .*・ 0.05 ..・ 0.1 . ・ 1

Residual standard error: 13.2 on 232 degrees of freedom
Multiple R-squared:  0.8276,	Adjusted R-squared:  0.8269 
F-statistic:  1114 on 1 and 232 DF,  p-value: < 2.2e-16


****************************************************************************
* Next:                                                                    *
*      calculate AUCpred(0~t), AUCpred(0~inf), conc.pred, FABpred(%)       *
*--------------------------------------------------------------------------*
* AUCpred(0~t): area under the predicted plasma concentration time curve   *
*              (time = 0 to t)                                             *
* AUCpred(0~inf): area under the predicted plasma concentration time curve *
*                (time = 0 to infinity)                                    *
* conc.pred: predicted plasma concentration                                *
* FABpred: predicted cumulative absorption fraction(%)                     *
****************************************************************************

<< Predicted Output >>
    pH subj formula. time   FABpred     conc.pred    AUCpred
1  1.2    1        F  0.0  0.000000  0.0000000000 0.00000000
2  1.2    1        F  0.5  6.221854  0.1334734221 0.03336836
3  1.2    1        F  1.0  9.126392  0.0498364880 0.07919583
4  1.2    1        F  1.5 14.444258  0.1094236901 0.11901088
5  1.2    1        F  2.0 15.458710  0.0115370865 0.14925107
6  1.2    1        F  3.0 22.057990  0.0867539658 0.19839660
7  1.2    1        F  4.0 28.593200  0.0547339659 0.26914056
8  1.2    1        F  5.0 34.007172  0.0524356132 0.32272535
9  1.2    1        F  6.0 38.577547  0.0416865613 0.36978644
10 1.2    1        F  8.0 47.846439  0.0479404695 0.45941347
11 1.2    1        F 10.0 52.288673  0.0046155914 0.51196953
12 1.2    1        F 12.0 58.193854  0.0449510261 0.56153615
13 1.2    1        F 24.0 84.590973 -0.0002330158 0.82984421

<< AUCpred(0~inf) is computed with trapezoidal method >>

[1] 0.8297959



****************************************************************************
* Next:                                                                    *
*      calculate AUCpred(0~t), AUCpred(0~inf), conc.pred, FABpred(%)       *
*--------------------------------------------------------------------------*
* AUCpred(0~t): area under the predicted plasma concentration time curve   *
*              (time = 0 to t)                                             *
* AUCpred(0~inf): area under the predicted plasma concentration time curve *
*                (time = 0 to infinity)                                    *
* conc.pred: predicted plasma concentration                                *
* FABpred: predicted cumulative absorption fraction(%)                     *
****************************************************************************

<< Predicted Output >>
    pH subj formula. time   FABpred  conc.pred    AUCpred
1  6.8    1        F  0.0  0.000000 0.00000000 0.00000000
2  6.8    1        F  0.5  3.755133 0.08055644 0.02013911
3  6.8    1        F  1.0  9.371996 0.11296718 0.06852002
4  6.8    1        F  1.5 13.216237 0.07191158 0.11473971
5  6.8    1        F  2.0 16.526555 0.06429421 0.14879116
6  6.8    1        F  3.0 21.780351 0.04625716 0.20406684
7  6.8    1        F  4.0 27.792316 0.06423795 0.25931440
8  6.8    1        F  5.0 32.416084 0.03754224 0.31020450
9  6.8    1        F  6.0 37.253420 0.05155338 0.35475231
10 6.8    1        F  8.0 46.009746 0.03729683 0.44360252
11 6.8    1        F 10.0 53.826369 0.03902269 0.51992203
12 6.8    1        F 12.0 59.977154 0.02435389 0.58329861
13 6.8    1        F 24.0 80.906909 0.01034837 0.79151215

<< AUCpred(0~inf) is computed with trapezoidal method >>

[1] 0.7936571



****************************************************************************
* Next:                                                                    *
*      calculate AUCpred(0~t), AUCpred(0~inf), conc.pred, FABpred(%)       *
*--------------------------------------------------------------------------*
* AUCpred(0~t): area under the predicted plasma concentration time curve   *
*              (time = 0 to t)                                             *
* AUCpred(0~inf): area under the predicted plasma concentration time curve *
*                (time = 0 to infinity)                                    *
* conc.pred: predicted plasma concentration                                *
* FABpred: predicted cumulative absorption fraction(%)                     *
****************************************************************************

<< Predicted Output >>
    pH subj formula. time   FABpred   conc.pred    AUCpred
1  1.2    1        M  0.0   0.00000  0.00000000 0.00000000
2  1.2    1        M  0.5  12.15907  0.26084069 0.06521017
3  1.2    1        M  1.0  17.00709  0.07962657 0.15032699
4  1.2    1        M  1.5  23.26465  0.12679875 0.20193332
5  1.2    1        M  2.0  32.14912  0.17874380 0.27831896
6  1.2    1        M  3.0  38.67365  0.01651237 0.37594704
7  1.2    1        M  4.0  47.00284  0.10868780 0.43854712
8  1.2    1        M  5.0  54.18944  0.05469023 0.52023614
9  1.2    1        M  6.0  51.30626 -0.06262404 0.51626923
10 1.2    1        M  8.0  70.37796  0.19608550 0.64973069
11 1.2    1        M 10.0  79.78567 -0.05231467 0.79350151
12 1.2    1        M 12.0  84.53758  0.07296243 0.81414927
13 1.2    1        M 24.0 101.34546 -0.04152787 1.00275663

<< AUCpred(0~inf) is computed with trapezoidal method >>

[1] 0.9941492



****************************************************************************
* Next:                                                                    *
*      calculate AUCpred(0~t), AUCpred(0~inf), conc.pred, FABpred(%)       *
*--------------------------------------------------------------------------*
* AUCpred(0~t): area under the predicted plasma concentration time curve   *
*              (time = 0 to t)                                             *
* AUCpred(0~inf): area under the predicted plasma concentration time curve *
*                (time = 0 to infinity)                                    *
* conc.pred: predicted plasma concentration                                *
* FABpred: predicted cumulative absorption fraction(%)                     *
****************************************************************************

<< Predicted Output >>
    pH subj formula. time  FABpred   conc.pred    AUCpred
1  6.8    1        M  0.0  0.00000 0.000000000 0.00000000
2  6.8    1        M  0.5 12.41535 0.266338560 0.06658464
3  6.8    1        M  1.0 18.72632 0.110496476 0.16079340
4  6.8    1        M  1.5 23.26465 0.087032520 0.21017565
5  6.8    1        M  2.0 31.88216 0.176732883 0.27611700
6  6.8    1        M  3.0 38.13973 0.013642030 0.37130446
7  6.8    1        M  4.0 46.21264 0.106321276 0.43128611
8  6.8    1        M  5.0 54.18944 0.066629495 0.51776149
9  6.8    1        M  6.0 59.20831 0.042032302 0.57209239
10 6.8    1        M  8.0 68.30634 0.046325184 0.66044988
11 6.8    1        M 10.0 76.69960 0.037779770 0.74455483
12 6.8    1        M 12.0 82.99988 0.026384757 0.80871936
13 6.8    1        M 24.0 99.35927 0.001230445 0.97441057

<< AUCpred(0~inf) is computed with trapezoidal method >>

[1] 0.9746656



****************************************************************************
* Next:                                                                    *
*      calculate AUCpred(0~t), AUCpred(0~inf), conc.pred, FABpred(%)       *
*--------------------------------------------------------------------------*
* AUCpred(0~t): area under the predicted plasma concentration time curve   *
*              (time = 0 to t)                                             *
* AUCpred(0~inf): area under the predicted plasma concentration time curve *
*                (time = 0 to infinity)                                    *
* conc.pred: predicted plasma concentration                                *
* FABpred: predicted cumulative absorption fraction(%)                     *
****************************************************************************

<< Predicted Output >>
    pH subj formula. time  FABpred   conc.pred    AUCpred
1  1.2    1        S  0.0  0.00000 0.000000000 0.00000000
2  1.2    1        S  0.5 12.66096 0.271607350 0.06790184
3  1.2    1        S  1.0 15.28786 0.030972275 0.14354674
4  1.2    1        S  1.5 20.81929 0.115768049 0.18023182
5  1.2    1        S  2.0 26.76719 0.116778180 0.23836838
6  1.2    1        S  3.0 31.71131 0.020239623 0.30687728
7  1.2    1        S  4.0 37.68056 0.074413881 0.35420404
8  1.2    1        S  5.0 45.43311 0.076725375 0.42977366
9  1.2    1        S  6.0 52.06443 0.060217627 0.49824517
10 1.2    1        S  8.0 63.29815 0.051737400 0.61020019
11 1.2    1        S 10.0 71.73412 0.034573007 0.69651060
12 1.2    1        S 12.0 78.32273 0.030833106 0.76191671
13 1.2    1        S 24.0 99.02823 0.003947467 0.97060015

<< AUCpred(0~inf) is computed with trapezoidal method >>

[1] 0.9714183



****************************************************************************
* Next:                                                                    *
*      calculate AUCpred(0~t), AUCpred(0~inf), conc.pred, FABpred(%)       *
*--------------------------------------------------------------------------*
* AUCpred(0~t): area under the predicted plasma concentration time curve   *
*              (time = 0 to t)                                             *
* AUCpred(0~inf): area under the predicted plasma concentration time curve *
*                (time = 0 to infinity)                                    *
* conc.pred: predicted plasma concentration                                *
* FABpred: predicted cumulative absorption fraction(%)                     *
****************************************************************************

<< Predicted Output >>
    pH subj formula. time    FABpred  conc.pred    AUCpred
1  6.8    1        S  0.0   0.000000 0.00000000 0.00000000
2  6.8    1        S  0.5   8.699254 0.18661948 0.04665487
3  6.8    1        S  1.0  15.255820 0.12321477 0.12411343
4  6.8    1        S  1.5  20.808612 0.10760643 0.18181873
5  6.8    1        S  2.0  27.034146 0.12349688 0.23959456
6  6.8    1        S  3.0  33.313073 0.03597199 0.31932899
7  6.8    1        S  4.0  39.805569 0.07515960 0.37489478
8  6.8    1        S  5.0  47.024198 0.06901147 0.44698032
9  6.8    1        S  6.0  54.168079 0.07051937 0.51674574
10 6.8    1        S  8.0  65.134844 0.04280380 0.63006891
11 6.8    1        S 10.0  73.795064 0.04226118 0.71513389
12 6.8    1        S 12.0  80.885552 0.02986283 0.78725790
13 6.8    1        S 24.0 100.779498 0.00357041 0.98785736

<< AUCpred(0~inf) is computed with trapezoidal method >>

[1] 0.9885974



****************************************************************************
* Next:                                                                    *
*      calculate AUCpred(0~t), AUCpred(0~inf), conc.pred, FABpred(%)       *
*--------------------------------------------------------------------------*
* AUCpred(0~t): area under the predicted plasma concentration time curve   *
*              (time = 0 to t)                                             *
* AUCpred(0~inf): area under the predicted plasma concentration time curve *
*                (time = 0 to infinity)                                    *
* conc.pred: predicted plasma concentration                                *
* FABpred: predicted cumulative absorption fraction(%)                     *
****************************************************************************

<< Predicted Output >>
    pH subj formula. time   FABpred   conc.pred    AUCpred
1  1.2    2        F  0.0  0.000000 0.000000000 0.00000000
2  1.2    2        F  0.5  4.737550 0.088006320 0.02200158
3  1.2    2        F  1.0  8.880787 0.050016673 0.05650733
4  1.2    2        F  1.5 13.953049 0.078907826 0.08873845
5  1.2    2        F  2.0 19.484485 0.078590468 0.12811303
6  1.2    2        F  3.0 23.926719 0.004310640 0.16956358
7  1.2    2        F  4.0 31.519094 0.082815470 0.21312664
8  1.2    2        F  5.0 36.388466 0.006658620 0.25786368
9  1.2    2        F  6.0 40.948162 0.047374081 0.28488003
10 1.2    2        F  8.0 50.206376 0.021847846 0.35410196
11 1.2    2        F 10.0 55.652383 0.017459796 0.39340960
12 1.2    2        F 12.0 61.279925 0.021958647 0.43282804
13 1.2    2        F 24.0 85.658818 0.007258548 0.60813122

<< AUCpred(0~inf) is computed with trapezoidal method >>

[1] 0.609095



****************************************************************************
* Next:                                                                    *
*      calculate AUCpred(0~t), AUCpred(0~inf), conc.pred, FABpred(%)       *
*--------------------------------------------------------------------------*
* AUCpred(0~t): area under the predicted plasma concentration time curve   *
*              (time = 0 to t)                                             *
* AUCpred(0~inf): area under the predicted plasma concentration time curve *
*                (time = 0 to infinity)                                    *
* conc.pred: predicted plasma concentration                                *
* FABpred: predicted cumulative absorption fraction(%)                     *
****************************************************************************

<< Predicted Output >>
    pH subj formula. time   FABpred   conc.pred    AUCpred
1  6.8    2        F  0.0  0.000000 0.000000000 0.00000000
2  6.8    2        F  0.5  4.000737 0.074319038 0.01857976
3  6.8    2        F  1.0  9.617600 0.081582588 0.05755517
4  6.8    2        F  1.5 13.953049 0.055554358 0.09183940
5  6.8    2        F  2.0 17.338117 0.045870171 0.11719554
6  6.8    2        F  3.0 23.125835 0.038418354 0.15933980
7  6.8    2        F  4.0 29.917327 0.054022398 0.20556017
8  6.8    2        F  5.0 35.064338 0.026487705 0.24581522
9  6.8    2        F  6.0 40.681201 0.047746452 0.28293230
10 6.8    2        F  8.0 49.416170 0.018278265 0.34895702
11 6.8    2        F 10.0 56.164949 0.028370290 0.39560557
12 6.8    2        F 12.0 62.048773 0.015214718 0.43919058
13 6.8    2        F 24.0 82.433927 0.009079871 0.58495811

<< AUCpred(0~inf) is computed with trapezoidal method >>

[1] 0.5861638



****************************************************************************
* Next:                                                                    *
*      calculate AUCpred(0~t), AUCpred(0~inf), conc.pred, FABpred(%)       *
*--------------------------------------------------------------------------*
* AUCpred(0~t): area under the predicted plasma concentration time curve   *
*              (time = 0 to t)                                             *
* AUCpred(0~inf): area under the predicted plasma concentration time curve *
*                (time = 0 to infinity)                                    *
* conc.pred: predicted plasma concentration                                *
* FABpred: predicted cumulative absorption fraction(%)                     *
****************************************************************************

<< Predicted Output >>
    pH subj formula. time    FABpred   conc.pred    AUCpred
1  1.2    2        M  0.0   0.000000  0.00000000 0.00000000
2  1.2    2        M  0.5   9.446745  0.17548591 0.04387148
3  1.2    2        M  1.0  16.996407  0.08650736 0.10936979
4  1.2    2        M  1.5  23.264655  0.08995060 0.15348429
5  1.2    2        M  2.0  31.604522  0.12737929 0.20781676
6  1.2    2        M  3.0  39.741498  0.01751606 0.28026443
7  1.2    2        M  4.0  46.468919  0.06543244 0.32173869
8  1.2    2        M  5.0  53.922475  0.04578533 0.37734757
9  1.2    2        M  6.0  59.464589  0.03570769 0.41809407
10 1.2    2        M  8.0  70.644922  0.04284474 0.49664651
11 1.2    2        M 10.0  78.237298  0.01485854 0.55434979
12 1.2    2        M 12.0  84.291977  0.02663130 0.59583963
13 1.2    2        M 24.0 100.619322 -0.00654721 0.71634420

<< AUCpred(0~inf) is computed with trapezoidal method >>

[1] 0.7154748



****************************************************************************
* Next:                                                                    *
*      calculate AUCpred(0~t), AUCpred(0~inf), conc.pred, FABpred(%)       *
*--------------------------------------------------------------------------*
* AUCpred(0~t): area under the predicted plasma concentration time curve   *
*              (time = 0 to t)                                             *
* AUCpred(0~inf): area under the predicted plasma concentration time curve *
*                (time = 0 to infinity)                                    *
* conc.pred: predicted plasma concentration                                *
* FABpred: predicted cumulative absorption fraction(%)                     *
****************************************************************************

<< Predicted Output >>
    pH subj formula. time  FABpred    conc.pred    AUCpred
1  6.8    2        M  0.0  0.00000  0.000000000 0.00000000
2  6.8    2        M  0.5 10.93105  0.203058837 0.05076471
3  6.8    2        M  1.0 17.74390  0.064376636 0.11762358
4  6.8    2        M  1.5 17.63711 -0.021697222 0.12829343
5  6.8    2        M  2.0 32.95001  0.291101601 0.19564453
6  6.8    2        M  3.0 41.87719 -0.068615570 0.30688754
7  6.8    2        M  4.0 46.73588  0.094417078 0.31978830
8  6.8    2        M  5.0 53.39923  0.020085271 0.37703947
9  6.8    2        M  6.0 59.98783  0.062381531 0.41827287
10 6.8    2        M  8.0 68.56263  0.006068731 0.48672313
11 6.8    2        M 10.0 76.17636  0.043146947 0.53593881
12 6.8    2        M 12.0 82.99988  0.009800966 0.58888672
13 6.8    2        M 24.0 99.86115  0.010173389 0.70873286

<< AUCpred(0~inf) is computed with trapezoidal method >>

[1] 0.7100837



****************************************************************************
* Next:                                                                    *
*      calculate AUCpred(0~t), AUCpred(0~inf), conc.pred, FABpred(%)       *
*--------------------------------------------------------------------------*
* AUCpred(0~t): area under the predicted plasma concentration time curve   *
*              (time = 0 to t)                                             *
* AUCpred(0~inf): area under the predicted plasma concentration time curve *
*                (time = 0 to infinity)                                    *
* conc.pred: predicted plasma concentration                                *
* FABpred: predicted cumulative absorption fraction(%)                     *
****************************************************************************

<< Predicted Output >>
    pH subj formula. time    FABpred    conc.pred    AUCpred
1  1.2    2        S  0.0   0.000000  0.000000000 0.00000000
2  1.2    2        S  0.5   8.453649  0.157037830 0.03925946
3  1.2    2        S  1.0  15.768385  0.087792513 0.10046704
4  1.2    2        S  1.5  22.527842  0.098681916 0.14708565
5  1.2    2        S  2.0  29.725115  0.103480361 0.19762622
6  1.2    2        S  3.0  37.595130  0.028385194 0.26355900
7  1.2    2        S  4.0  43.532346  0.050245176 0.30287418
8  1.2    2        S  5.0  53.805012  0.086277691 0.37113562
9  1.2    2        S  6.0  57.382292 -0.009870069 0.40933943
10 1.2    2        S  8.0  68.797551  0.079212056 0.47868141
11 1.2    2        S 10.0  77.190810 -0.007955617 0.54993785
12 1.2    2        S 12.0  84.526903  0.052140666 0.59412290
13 1.2    2        S 24.0 102.584156 -0.028946188 0.73328977

<< AUCpred(0~inf) is computed with trapezoidal method >>

[1] 0.7294462



****************************************************************************
* Next:                                                                    *
*      calculate AUCpred(0~t), AUCpred(0~inf), conc.pred, FABpred(%)       *
*--------------------------------------------------------------------------*
* AUCpred(0~t): area under the predicted plasma concentration time curve   *
*              (time = 0 to t)                                             *
* AUCpred(0~inf): area under the predicted plasma concentration time curve *
*                (time = 0 to infinity)                                    *
* conc.pred: predicted plasma concentration                                *
* FABpred: predicted cumulative absorption fraction(%)                     *
****************************************************************************

<< Predicted Output >>
    pH subj formula. time    FABpred   conc.pred    AUCpred
1  6.8    2        S  0.0   0.000000  0.00000000 0.00000000
2  6.8    2        S  0.5   9.937954  0.18461076 0.04615269
3  6.8    2        S  1.0  17.498294  0.08391150 0.11328325
4  6.8    2        S  1.5  24.973206  0.11316092 0.16255136
5  6.8    2        S  2.0  32.149122  0.09864984 0.21550405
6  6.8    2        S  3.0  41.086982  0.04318803 0.28642298
7  6.8    2        S  4.0  45.678714  0.02653533 0.32128465
8  6.8    2        S  5.0  52.875987  0.06547820 0.36729141
9  6.8    2        S  6.0  59.464589  0.03603911 0.41805007
10 6.8    2        S  8.0  70.121678  0.03930651 0.49339569
11 6.8    2        S 10.0  78.504259  0.02252756 0.55522975
12 6.8    2        S 12.0  84.804542  0.02230190 0.60005921
13 6.8    2        S 24.0 102.082269 -0.00130335 0.72605049

<< AUCpred(0~inf) is computed with trapezoidal method >>

[1] 0.7258774



****************************************************************************
* Next:                                                                    *
*      calculate AUCpred(0~t), AUCpred(0~inf), conc.pred, FABpred(%)       *
*--------------------------------------------------------------------------*
* AUCpred(0~t): area under the predicted plasma concentration time curve   *
*              (time = 0 to t)                                             *
* AUCpred(0~inf): area under the predicted plasma concentration time curve *
*                (time = 0 to infinity)                                    *
* conc.pred: predicted plasma concentration                                *
* FABpred: predicted cumulative absorption fraction(%)                     *
****************************************************************************

<< Predicted Output >>
    pH subj formula. time   FABpred    conc.pred    AUCpred
1  1.2    3        F  0.0  0.000000  0.000000000 0.00000000
2  1.2    3        F  0.5  4.737550  0.095144820 0.02378621
3  1.2    3        F  1.0  9.126392  0.034200715 0.05612259
4  1.2    3        F  1.5 13.461841  0.067679791 0.08159272
5  1.2    3        F  2.0 17.338117  0.039477690 0.10838209
6  1.2    3        F  3.0 22.591913  0.029269870 0.14275586
7  1.2    3        F  4.0 29.127122  0.051428647 0.18310512
8  1.2    3        F  5.0 33.740211  0.013006046 0.21532247
9  1.2    3        F  6.0 38.043625  0.038611640 0.24113131
10 1.2    3        F  8.0 47.323195  0.022003200 0.30174615
11 1.2    3        F 10.0 50.996581  0.002860044 0.32660940
12 1.2    3        F 12.0 57.158044  0.034442946 0.36391239
13 1.2    3        F 24.0 81.387439 -0.008074675 0.52212201

<< AUCpred(0~inf) is computed with trapezoidal method >>

[1] 0.5215641



****************************************************************************
* Next:                                                                    *
*      calculate AUCpred(0~t), AUCpred(0~inf), conc.pred, FABpred(%)       *
*--------------------------------------------------------------------------*
* AUCpred(0~t): area under the predicted plasma concentration time curve   *
*              (time = 0 to t)                                             *
* AUCpred(0~inf): area under the predicted plasma concentration time curve *
*                (time = 0 to infinity)                                    *
* conc.pred: predicted plasma concentration                                *
* FABpred: predicted cumulative absorption fraction(%)                     *
****************************************************************************

<< Predicted Output >>
    pH subj formula. time   FABpred     conc.pred    AUCpred
1  6.8    3        F  0.0  0.000000  0.000000e+00 0.00000000
2  6.8    3        F  0.5  4.993833  1.002918e-01 0.02507294
3  6.8    3        F  1.0  8.635183  1.627076e-02 0.05421358
4  6.8    3        F  1.5 12.725028  7.291241e-02 0.07650937
5  6.8    3        F  2.0 14.380187 -8.095840e-03 0.09271352
6  6.8    3        F  3.0 20.445545  7.443028e-02 0.12588074
7  6.8    3        F  4.0 26.724472  1.434824e-02 0.17027000
8  6.8    3        F  5.0 31.615200  4.420894e-02 0.19954859
9  6.8    3        F  6.0 35.929292  1.510573e-02 0.22920593
10 6.8    3        F  8.0 44.963258  4.099858e-02 0.28531024
11 6.8    3        F 10.0 53.036164  1.269175e-02 0.33900057
12 6.8    3        F 12.0 58.941345  2.434584e-02 0.37603816
13 6.8    3        F 24.0 81.387439 -9.047601e-05 0.52157035

<< AUCpred(0~inf) is computed with trapezoidal method >>

[1] 0.5215641



****************************************************************************
* Next:                                                                    *
*      calculate AUCpred(0~t), AUCpred(0~inf), conc.pred, FABpred(%)       *
*--------------------------------------------------------------------------*
* AUCpred(0~t): area under the predicted plasma concentration time curve   *
*              (time = 0 to t)                                             *
* AUCpred(0~inf): area under the predicted plasma concentration time curve *
*                (time = 0 to infinity)                                    *
* conc.pred: predicted plasma concentration                                *
* FABpred: predicted cumulative absorption fraction(%)                     *
****************************************************************************

<< Predicted Output >>
    pH subj formula. time   FABpred   conc.pred    AUCpred
1  1.2    3        M  0.0  0.000000 0.000000000 0.00000000
2  1.2    3        M  0.5  8.944858 0.179640721 0.04491018
3  1.2    3        M  1.0 16.750802 0.054923126 0.10355114
4  1.2    3        M  1.5 22.527842 0.084883167 0.13850272
5  1.2    3        M  2.0 31.604522 0.134164855 0.19326472
6  1.2    3        M  3.0 40.809343 0.002066196 0.26138025
7  1.2    3        M  4.0 46.735880 0.065172598 0.29499964
8  1.2    3        M  5.0 53.132270 0.022680673 0.33892628
9  1.2    3        M  6.0 59.197628 0.051126976 0.37583010
10 1.2    3        M  8.0 68.039381 0.008481188 0.43543827
11 1.2    3        M 10.0 75.653114 0.038253629 0.48217308
12 1.2    3        M 12.0 81.718471 0.003048166 0.52347488
13 1.2    3        M 24.0 98.120565 0.014340354 0.62780600

<>

[1] 0.6287968



****************************************************************************
* Next:                                                                    *
*      calculate AUCpred(0~t), AUCpred(0~inf), conc.pred, FABpred(%)       *
*--------------------------------------------------------------------------*
* AUCpred(0~t): area under the predicted plasma concentration time curve   *
*              (time = 0 to t)                                             *
* AUCpred(0~inf): area under the predicted plasma concentration time curve *
*                (time = 0 to infinity)                                    *
* conc.pred: predicted plasma concentration                                *
* FABpred: predicted cumulative absorption fraction(%)                     *
****************************************************************************

<< Predicted Output >>
    pH subj formula. time   FABpred   conc.pred    AUCpred
1  6.8    3        M  0.0  0.000000 0.000000000 0.00000000
2  6.8    3        M  0.5  8.944858 0.179640721 0.04491018
3  6.8    3        M  1.0 16.013990 0.040125621 0.09985177
4  6.8    3        M  1.5 22.036633 0.098204896 0.13443439
5  6.8    3        M  2.0 30.259037 0.109455770 0.18634956
6  6.8    3        M  3.0 39.207576 0.017889449 0.25002217
7  6.8    3        M  4.0 44.333230 0.044173051 0.28105342
8  6.8    3        M  5.0 50.740298 0.038701318 0.32249061
9  6.8    3        M  6.0 56.560051 0.036230811 0.35995667
10 6.8    3        M  8.0 66.715254 0.029325042 0.42551252
11 6.8    3        M 10.0 76.155001 0.031049572 0.48588714
12 6.8    3        M 12.0 82.978528 0.013865697 0.53080241
13 6.8    3        M 24.0 99.102982 0.003475968 0.63485240

<>

[1] 0.6350926



****************************************************************************
* Next:                                                                    *
*      calculate AUCpred(0~t), AUCpred(0~inf), conc.pred, FABpred(%)       *
*--------------------------------------------------------------------------*
* AUCpred(0~t): area under the predicted plasma concentration time curve   *
*              (time = 0 to t)                                             *
* AUCpred(0~inf): area under the predicted plasma concentration time curve *
*                (time = 0 to infinity)                                    *
* conc.pred: predicted plasma concentration                                *
* FABpred: predicted cumulative absorption fraction(%)                     *
****************************************************************************

<< Predicted Output >>
    pH subj formula. time    FABpred   conc.pred    AUCpred
1  1.2    3        S  0.0   0.000000 0.000000000 0.00000000
2  1.2    3        S  0.5   8.699254 0.174708219 0.04367705
3  1.2    3        S  1.0  16.996407 0.067584538 0.10425024
4  1.2    3        S  1.5  23.990789 0.102153019 0.14668463
5  1.2    3        S  2.0  31.070599 0.084270583 0.19329053
6  1.2    3        S  3.0  39.207576 0.027820352 0.24933600
7  1.2    3        S  4.0  45.134113 0.045672111 0.28608223
8  1.2    3        S  5.0  53.132270 0.055483063 0.33665982
9  1.2    3        S  6.0  61.301282 0.049978376 0.38939054
10 1.2    3        S  8.0  72.470937 0.023435328 0.46280424
11 1.2    3        S 10.0  80.308916 0.026576617 0.51281619
12 1.2    3        S 12.0  86.854804 0.016096250 0.55548906
13 1.2    3        S 24.0 102.872474 0.001183448 0.65916724

<< AUCpred(0~inf) is computed with trapezoidal method >>

[1] 0.659249



****************************************************************************
* Next:                                                                    *
*      calculate AUCpred(0~t), AUCpred(0~inf), conc.pred, FABpred(%)       *
*--------------------------------------------------------------------------*
* AUCpred(0~t): area under the predicted plasma concentration time curve   *
*              (time = 0 to t)                                             *
* AUCpred(0~inf): area under the predicted plasma concentration time curve *
*                (time = 0 to infinity)                                    *
* conc.pred: predicted plasma concentration                                *
* FABpred: predicted cumulative absorption fraction(%)                     *
****************************************************************************

<< Predicted Output >>
    pH subj formula. time   FABpred   conc.pred    AUCpred
1  6.8    3        S  0.0  0.000000 0.000000000 0.00000000
2  6.8    3        S  0.5  6.221854 0.124954288 0.03123857
3  6.8    3        S  1.0 12.821134 0.061693194 0.07790044
4  6.8    3        S  1.5 18.363248 0.076326932 0.11240547
5  6.8    3        S  2.0 24.332500 0.076608815 0.15063941
6  6.8    3        S  3.0 32.234550 0.030976243 0.20443194
7  6.8    3        S  4.0 36.068112 0.019714131 0.22977713
8  6.8    3        S  5.0 42.507216 0.057581821 0.26842510
9  6.8    3        S  6.0 50.206376 0.043098375 0.31876520
10 6.8    3        S  8.0 58.332673 0.011183415 0.37304699
11 6.8    3        S 10.0 66.544399 0.039485200 0.42371561
12 6.8    3        S 12.0 73.154357 0.005240254 0.46844106
13 6.8    3        S 24.0 92.258098 0.015050872 0.59018781

<>

[1] 0.5912277


****************************************************************************
* Step5: Evaluate an IVIVC model: Prediction Error                         *
*--------------------------------------------------------------------------*
* PE_Cmax: average absolute prediction error of Cmax (%)                   *
* PE_AUC: average absolute prediction error of AUC (%)                     *
****************************************************************************

<>
   pH Formulation   PE_Cmax   PE_AUC
1 1.2           1  31.17526 29.57996
2 6.8           1  40.04350 36.02080
3 1.2           2  13.08336 55.63686
4 6.8           2  49.51321 47.41958
5 1.2           3  53.73785 31.75402
6 6.8           3  27.36152 62.86477

****************************************************************************
*<< Plots >>                                                                *
* - Fitting Plots                                                          *
* - In-vitro-in-vivo-correlation Model (linear regression)                 *
* - Fraction of in vitro Released(%) vs. time                              *
* - Observed plasma concentration vs. time                                 *
* - Fraction of Absorption(%) vs. time                                     *
* - Predicted plasma concentration vs. time                                *
****************************************************************************