~~~ This report is generated using bear v2.2.0 for R. ~~~ Authors: Hsin-ya Lee, Yung-jin Lee College of Pharmacy, Kaohsiung Medical University Kaohsiung, Taiwan 80708 E-mail: hsinyalee@gmail.com,pkpd.taiwan@gmail.com bear's website: http://pkpd.kmu.edu.tw/bear R website: http://www.r-project.org --------------------------------------------------- Statistical analysis (ANOVA(lm), 90%CI...) -------------------------------------------------------------------------- Dependent Variable: Cmax Type I SS Analysis of Variance Table Response: Cmax Df Sum Sq Mean Sq F value Pr(>F) seq 1 585 585 0.0160 0.9014 prd 1 63175 63175 1.7293 0.2131 drug 1 58149 58149 1.5917 0.2311 seq:subj 12 634325 52860 1.4469 0.2660 Residuals 12 438395 36533 Type III SS Single term deletions Model: Cmax ~ seq + subj:seq + prd + drug Df Sum of Sq RSS AIC F value Pr(F) 438395 302 prd 1 63175 501570 304 1.7293 0.2131 drug 1 58149 496544 304 1.5917 0.2311 seq:subj 12 634325 1072719 303 1.4469 0.2660 Tests of Hypothesis for SUBJECT(SEQUENCE) as an error term Error: subj Df Sum Sq Mean Sq F value Pr(>F) prd:drug 1 585 585 0.0111 0.918 Residuals 12 634325 52860 Error: Within Df Sum Sq Mean Sq F value Pr(>F) prd 1 63175 63175 1.7293 0.2131 drug 1 58149 58149 1.5917 0.2311 Residuals 12 438395 36533 Statistical analysis (ANOVA(lm), 90%CI...) -------------------------------------------------------------------------- Dependent Variable: AUC0t Type I SS Analysis of Variance Table Response: AUC0t Df Sum Sq Mean Sq F value Pr(>F) seq 1 1398283 1398283 0.2655 0.6158 prd 1 2101060 2101060 0.3989 0.5395 drug 1 4711024 4711024 0.8944 0.3629 seq:subj 12 35815052 2984588 0.5666 0.8308 Residuals 12 63208575 5267381 Type III SS Single term deletions Model: AUC0t ~ seq + subj:seq + prd + drug Df Sum of Sq RSS AIC F value Pr(F) 63208575 442 prd 1 2101060 65309635 441 0.3989 0.5395 drug 1 4711024 67919599 442 0.8944 0.3629 seq:subj 12 35815052 99023627 430 0.5666 0.8308 Tests of Hypothesis for SUBJECT(SEQUENCE) as an error term Error: subj Df Sum Sq Mean Sq F value Pr(>F) prd:drug 1 1398283 1398283 0.4685 0.5067 Residuals 12 35815052 2984588 Error: Within Df Sum Sq Mean Sq F value Pr(>F) prd 1 2101060 2101060 0.3989 0.5395 drug 1 4711024 4711024 0.8944 0.3629 Residuals 12 63208575 5267381 Statistical analysis (ANOVA(lm), 90%CI...) -------------------------------------------------------------------------- Dependent Variable: AUC0INF Type I SS Analysis of Variance Table Response: AUC0INF Df Sum Sq Mean Sq F value Pr(>F) seq 1 1776953 1776953 0.3137 0.5857 prd 1 2672250 2672250 0.4718 0.5052 drug 1 5438396 5438396 0.9602 0.3465 seq:subj 12 38852540 3237712 0.5717 0.8271 Residuals 12 67965050 5663754 Type III SS Single term deletions Model: AUC0INF ~ seq + subj:seq + prd + drug Df Sum of Sq RSS AIC F value Pr(F) 67965050 444 prd 1 2672250 70637300 443 0.4718 0.5052 drug 1 5438396 73403446 444 0.9602 0.3465 seq:subj 12 38852540 106817590 432 0.5717 0.8271 Tests of Hypothesis for SUBJECT(SEQUENCE) as an error term Error: subj Df Sum Sq Mean Sq F value Pr(>F) prd:drug 1 1776953 1776953 0.5488 0.473 Residuals 12 38852540 3237712 Error: Within Df Sum Sq Mean Sq F value Pr(>F) prd 1 2672250 2672250 0.4718 0.5052 drug 1 5438396 5438396 0.9602 0.3465 Residuals 12 67965050 5663754 Statistical analysis (ANOVA(lm), 90%CI...) -------------------------------------------------------------------------- Dependent Variable: lnCmax Type I SS Analysis of Variance Table Response: lnCmax Df Sum Sq Mean Sq F value Pr(>F) seq 1 0.000017 0.000017 0.0011 0.9743 prd 1 0.027294 0.027294 1.7187 0.2144 drug 1 0.025583 0.025583 1.6110 0.2284 seq:subj 12 0.255270 0.021273 1.3395 0.3103 Residuals 12 0.190565 0.015880 Type III SS Single term deletions Model: lnCmax ~ seq + subj:seq + prd + drug Df Sum of Sq RSS AIC F value Pr(F) 0.191 -107.719 prd 1 0.027 0.218 -105.971 1.7187 0.2144 drug 1 0.026 0.216 -106.192 1.6110 0.2284 seq:subj 12 0.255 0.446 -107.920 1.3395 0.3103 Tests of Hypothesis for SUBJECT(SEQUENCE) as an error term Error: subj Df Sum Sq Mean Sq F value Pr(>F) prd:drug 1 0.000017 0.000017 8e-04 0.9778 Residuals 12 0.255270 0.021273 Error: Within Df Sum Sq Mean Sq F value Pr(>F) prd 1 0.027294 0.027294 1.7187 0.2144 drug 1 0.025583 0.025583 1.6110 0.2284 Residuals 12 0.190565 0.015880 Intra_subj. CV=100*sqrt(exp(MSResidual)-1)= 12.65195 % Inter_subj. CV=100*sqrt(exp((MSSubject(seq)-MSResidual)/2)-1)= 5.195855 % Statistical analysis (ANOVA(lm), 90%CI...) -------------------------------------------------------------------------- Dependent Variable: lnAUC0t Type I SS Analysis of Variance Table Response: lnAUC0t Df Sum Sq Mean Sq F value Pr(>F) seq 1 0.00929 0.00929 0.2903 0.5999 prd 1 0.01675 0.01675 0.5231 0.4834 drug 1 0.02715 0.02715 0.8479 0.3753 seq:subj 12 0.20143 0.01679 0.5243 0.8613 Residuals 12 0.38421 0.03202 Type III SS Single term deletions Model: lnAUC0t ~ seq + subj:seq + prd + drug Df Sum of Sq RSS AIC F value Pr(F) 0.384 -88.086 prd 1 0.017 0.401 -88.891 0.5231 0.4834 drug 1 0.027 0.411 -88.174 0.8479 0.3753 seq:subj 12 0.201 0.586 -100.283 0.5243 0.8613 Tests of Hypothesis for SUBJECT(SEQUENCE) as an error term Error: subj Df Sum Sq Mean Sq F value Pr(>F) prd:drug 1 0.009295 0.009295 0.5537 0.4711 Residuals 12 0.201427 0.016786 Error: Within Df Sum Sq Mean Sq F value Pr(>F) prd 1 0.01675 0.01675 0.5231 0.4834 drug 1 0.02715 0.02715 0.8479 0.3753 Residuals 12 0.38421 0.03202 Intra_subj. CV=100*sqrt(exp(MSResidual)-1)= 18.03756 % Inter_subj. CV=100*sqrt(exp((MSSubject(seq)-MSResidual)/2)-1)= NaN % Statistical analysis (ANOVA(lm), 90%CI...) -------------------------------------------------------------------------- Dependent Variable: lnAUC0INF Type I SS Analysis of Variance Table Response: lnAUC0INF Df Sum Sq Mean Sq F value Pr(>F) seq 1 0.01031 0.01031 0.3307 0.5758 prd 1 0.01899 0.01899 0.6091 0.4503 drug 1 0.02822 0.02822 0.9050 0.3602 seq:subj 12 0.19499 0.01625 0.5212 0.8635 Residuals 12 0.37414 0.03118 Type III SS Single term deletions Model: lnAUC0INF ~ seq + subj:seq + prd + drug Df Sum of Sq RSS AIC F value Pr(F) 0.374 -88.829 prd 1 0.019 0.393 -89.443 0.6091 0.4503 drug 1 0.028 0.402 -88.793 0.9050 0.3602 seq:subj 12 0.195 0.569 -101.084 0.5212 0.8635 Tests of Hypothesis for SUBJECT(SEQUENCE) as an error term Error: subj Df Sum Sq Mean Sq F value Pr(>F) prd:drug 1 0.010312 0.010312 0.6346 0.4411 Residuals 12 0.194992 0.016249 Error: Within Df Sum Sq Mean Sq F value Pr(>F) prd 1 0.01899 0.01899 0.6091 0.4503 drug 1 0.02822 0.02822 0.9050 0.3602 Residuals 12 0.37414 0.03118 Intra_subj. CV=100*sqrt(exp(MSResidual)-1)= 17.79591 % Inter_subj. CV=100*sqrt(exp((MSSubject(seq)-MSResidual)/2)-1)= NaN % BE Summary Report -------------------------------------------------------------------------- Dependent Variable: lnCmax -------------------------------------------------------------------------- n1(R=>T) = 7 n2(T=>R) = 7 N(n1+n2) = 14 MEAN-ref = 7.32951 MEAN-test = 7.389964 MSE = 0.01588043 SE = 0.04763017 Diff. (test-ref) = 0.06045413 ************************90% C.I. for lnCmax******************************** Shortest Lower = 97.586 Upper = 115.644 -------------------------------------------------------------------------- Intra-subject and Inter-subject Residuals -------------------------------------------------------------------------- subj Obs Exp Intra Stud_Intra Inter Stud_Inter 8 1 7.398174 7.491068 -0.09289432 -1.1260208 0.13819986 0.7236963 1 2 7.300473 7.409175 -0.10870261 -1.3176414 0.09845413 0.5155641 9 3 7.636752 7.622009 0.01474313 0.1787092 0.40008101 2.0950610 2 4 7.225481 7.311596 -0.08611455 -1.0438396 -0.09670469 -0.5064030 10 5 7.233455 7.352792 -0.11933631 -1.4465380 -0.13835351 -0.7245009 3 6 7.470794 7.400282 0.07051214 0.8547147 0.08066654 0.4224178 11 7 7.404279 7.441728 -0.03744898 -0.4539388 0.03951924 0.2069462 4 8 7.569928 7.479503 0.09042423 1.0960796 0.23911012 1.2521222 12 9 7.472501 7.445906 0.02659513 0.3223736 0.04787426 0.2506980 5 10 7.235619 7.269715 -0.03409608 -0.4132965 -0.18046629 -0.9450283 13 11 7.427739 7.288975 0.13876356 1.6820259 -0.26598640 -1.3928622 6 12 7.340836 7.235660 0.10517533 1.2748853 -0.24857627 -1.3016925 14 13 7.380879 7.311301 0.06957779 0.8433889 -0.22133447 -1.1590383 7 14 7.376508 7.413707 -0.03719847 -0.4509021 0.10751646 0.5630198 ------------------------------------------------ Obs: Observed lnCmax Exp: Expected lnCmax Intra: Intra-subject residuals Stud_Intra: Studentized intra-subject residuals Inter: Inter-subject residuals Stud_Inter: Studentized inter-subject residuals ------------------------------------------------------------------------- BE Summary Report -------------------------------------------------------------------------- Dependent Variable: lnAUC0t -------------------------------------------------------------------------- n1(R=>T) = 7 n2(T=>R) = 7 N(n1+n2) = 14 MEAN-ref = 9.474286 MEAN-test = 9.536562 MSE = 0.03201728 SE = 0.06763059 Diff. (test-ref) = 0.06227613 ************************90% C.I. for lnAUC0t******************************* Shortest Lower = 94.340 Upper = 120.059 -------------------------------------------------------------------------- Intra-subject and Inter-subject Residuals -------------------------------------------------------------------------- subj Obs Exp Intra Stud_Intra Inter Stud_Inter 8 1 9.416858 9.553085 -0.13622640 -1.1629404 0.02057198 0.1212735 1 2 9.434774 9.528465 -0.09369108 -0.7998240 0.02300575 0.1356208 9 3 9.627998 9.689725 -0.06172751 -0.5269568 0.29385229 1.7322830 2 4 9.311371 9.421754 -0.11038344 -0.9423237 -0.19041665 -1.1225216 10 5 9.380220 9.518090 -0.13786980 -1.1769699 -0.04941765 -0.2913210 3 6 9.640586 9.581188 0.05939784 0.5070688 0.12845152 0.7572321 11 7 9.422326 9.519810 -0.09748433 -0.8322063 -0.04597732 -0.2710400 4 8 9.504630 9.531269 -0.02663909 -0.2274132 0.02861348 0.1686788 12 9 9.668044 9.602746 0.06529757 0.5574337 0.11989440 0.7067872 5 10 9.496267 9.425610 0.07065745 0.6031901 -0.18270518 -1.0770619 13 11 9.640233 9.447437 0.19279598 1.6458649 -0.19072371 -1.1243317 6 12 9.616827 9.436437 0.18038970 1.5399547 -0.16105074 -0.9494072 14 13 9.643913 9.468699 0.17521449 1.4957749 -0.14819999 -0.8736509 7 14 9.614282 9.694013 -0.07973139 -0.6806526 0.35410183 2.0874590 ------------------------------------------------ Obs: Observed lnAUC0t Exp: Expected lnAUC0t Intra: Intra-subject residuals Stud_Intra: Studentized intra-subject residuals Inter: Inter-subject residuals Stud_Inter: Studentized inter-subject residuals ------------------------------------------------------------------------- BE Summary Report -------------------------------------------------------------------------- Dependent Variable: lnAUC0INF -------------------------------------------------------------------------- n1(R=>T) = 7 n2(T=>R) = 7 N(n1+n2) = 14 LSMEAN-ref = 9.519987 LSMEAN-test = 9.583477 MSE = 0.03117832 SE = 0.06673864 Diff. (test-ref) = 0.06349039 ************************90% C.I. for lnAUC0INF***************************** Shortest Lower = 94.605 Upper = 120.014 -------------------------------------------------------------------------- Intra-subject and Inter-subject Residuals -------------------------------------------------------------------------- subj Obs Exp Intra Stud_Intra Inter Stud_Inter 8 1 9.470745 9.598578 -0.12783370 -1.1058785 0.016498958 0.09885474 1 2 9.483002 9.580807 -0.09780531 -0.8461054 0.031174302 0.18678317 9 3 9.659970 9.727936 -0.06796666 -0.5879738 0.275215317 1.64897323 2 4 9.362824 9.470759 -0.10793492 -0.9337358 -0.188920802 -1.13193316 10 5 9.432655 9.567027 -0.13437245 -1.1624446 -0.046602824 -0.27922432 3 6 9.677251 9.618427 0.05882400 0.5088814 0.106414706 0.63759170 11 7 9.471115 9.568584 -0.09746931 -0.8431987 -0.043488964 -0.26056739 4 8 9.544559 9.563916 -0.01935705 -0.1674562 -0.002608321 -0.01562795 12 9 9.715071 9.648438 0.06663307 0.5764370 0.116218091 0.69632942 5 10 9.550123 9.484902 0.06522058 0.5642177 -0.160634649 -0.96245456 13 11 9.683597 9.492831 0.19076589 1.6502995 -0.194994515 -1.16832427 6 12 9.665094 9.483556 0.18153803 1.5704701 -0.163328029 -0.97859214 14 13 9.699149 9.528906 0.17024315 1.4727590 -0.122846063 -0.73604141 7 14 9.673686 9.754171 -0.08048533 -0.6962718 0.377902792 2.26423294 ------------------------------------------------ Obs: Observed lnAUC0INF Exp: Expected lnAUC0INF Intra: Intra-subject residuals Stud_Intra: Studentized intra-subject residuals Inter: Inter-subject residuals Stud_Inter: Studentized inter-subject residuals ------------------------------------------------------------------------- **************************************************************************** Analysis of Outlier Detection **************************************************************************** Test for Normality Assumption (Shapiro-Wilk) -------------------------------------------------------------------------- Parameter Test P_value 1 lnCmax_Stud_Intra 0.93758 0.3882 2 lnCmax_Stud_Inter 0.94438 0.4773 3 lnAUC0t_Stud_Intra 0.87462 0.0488 4 lnAUC0t_Stud_Inter 0.90178 0.1197 5 lnAUC0INF_Stud_Intra 0.86775 0.0390 6 lnAUC0INF_Stud_Inter 0.91205 0.1687 ------------------------------------------------- Stud_Intra: studentized intra-subject residuals Stud_Inter: studentized intra-subject residuals Shapiro-Wilk: the normality of the studentized intra-subject residuals and the studentized inter-residuals was examined using the test of Shapiro-Wilk. ------------------------------------------------------------------------- Test for Normality Assumption (Pearson) -------------------------------------------------------------------------- Parameter Test P_value 1 lnCmax -0.19043 0.5143 2 lnAUC0t -0.39188 0.1658 3 lnAUC0INF -0.39827 0.1584 ------------------------------------------------- Pearson: Pearson's correlation coefficient ------------------------------------------------------------------------- Test for Normality Assumption (Spearman) -------------------------------------------------------------------------- Parameter Test P_value 1 lnCmax -0.28352 0.3253 2 lnAUC0t -0.23956 0.4086 3 lnAUC0INF -0.26154 0.3656 ------------------------------------------------- Spearman: Spearman's rank correlation coefficient ------------------------------------------------------------------------- Hotelling T^2 -------------------------------------------------------------------------- subj HT_Cmax HT_lnCmax HT_AUC0t HT_lnAUC0t HT_AUC0INF HT_lnAUC0INF 1 1 0.88638 0.85650 0.97444 0.90466 0.82225 0.76937 2 2 1.37871 1.25816 0.46862 0.48286 0.54162 0.56592 3 3 10.76389 8.19027 2.55956 2.47460 2.15554 2.13130 4 4 0.59829 0.53345 1.36768 1.19256 1.32453 1.15615 5 5 1.82827 1.97183 1.27839 1.29252 1.17989 1.20035 6 6 1.59714 1.41680 1.45271 1.28884 1.27021 1.13141 7 7 0.01658 0.04381 0.71059 0.65357 0.68229 0.63622 8 8 4.67137 3.47390 0.06496 0.13465 0.00974 0.04163 9 9 0.58431 0.55860 0.90283 0.87754 0.91402 0.88872 10 10 0.99704 0.92403 1.53365 1.57887 1.21948 1.24508 11 11 5.41157 7.05871 5.44089 6.42777 5.76052 6.93837 12 12 5.58454 7.54222 4.16338 4.89954 4.29064 5.12118 13 13 2.26730 2.47522 4.16519 4.53151 3.94232 4.17831 14 14 0.24448 0.31984 11.39161 9.03305 15.08591 11.63398 ------------------------------------------------- HT_Cmax: Hotelling T^2 for Cmax HT_lnCmax: Hotelling T^2 for lnCmax HT_AUC0t: Hotelling T^2 for AUC0t HT_lnAUC0t: Hotelling T^2 for lnAUC0t HT_AUC0INF: Hotelling T^2 for AUC0INF HT_lnAUC0INF: Hotelling T^2 for lnAUC0INF ------------------------------------------------------------------------- Test for Equality of Intra-subject variabilities between formulations -------------------------------------------------------------------------- Method Test P_value 1 lnCmax_Pearson -0.18320 0.5307 2 lnCmax_Pitman_Morgan 0.41674 0.5307 3 lnCmax_Spearman -0.20879 0.4731 4 lnAUC0t_Pearson -0.11204 0.7029 5 lnAUC0t_Pitman_Morgan 0.15256 0.7029 6 lnAUC0t_Spearman -0.16044 0.5838 7 lnAUC0INF_Pearson -0.09780 0.7394 8 lnAUC0INF_Pitman_Morgan 0.11589 0.7394 9 lnAUC0INF_Spearman -0.13846 0.6375 Point and Interval Estimation of Inter- and Intra-subject Variability -------------------------------------------------------------------------- Parameter Point_Estimate CI95_lower CI95_upper 1 lnCmax_intra 0.016 0.008 0.043 2 lnCmax_inter 0.003 -0.008 0.022 3 lnCmax_intraclass 0.145 -0.420 0.629 4 lnCmax_prob 0.31029 - - 5 lnAUC0t_intra 0.032 0.016 0.087 6 lnAUC0t_inter -0.008 -0.023 0.010 7 lnAUC0t_intraclass -0.312 -0.724 0.264 8 lnAUC0t_prob 0.86134 - - 9 lnAUC0INF_intra 0.031 0.016 0.085 10 lnAUC0INF_inter -0.007 -0.022 0.009 11 lnAUC0INF_intraclass -0.315 -0.726 0.261 12 lnAUC0INF_prob 0.86349 - - ------------------------------------------------- intra: intra-subject variability inter: inter-subject variability intraclass: intraclass correlation prob: the probability for obtaining a negative estimate of inter-subject variability CI95: 95% confidence interval ------------------------------------------------------------------------- Quantiles for Boxplots (intrasubj) -------------------------------------------------------------------------- Quantile lnCmax_Estimate lnAUC0t_Estimate lnAUC0INF_Estimate 100% Max 100% 1.6820259 1.6458649 1.6502995 99% 99% 1.6820259 1.6458649 1.6502995 95% 95% 1.6820259 1.6458649 1.6502995 90% 90% 1.2748853 1.5399547 1.5704701 75% Q3 75% 0.8547147 0.6031901 0.5764370 50% Median 50% -0.1172936 -0.3771850 -0.3777150 25% Q1 25% -1.0438396 -0.8322063 -0.8461054 10% 10% -1.3176414 -1.1629404 -1.1058785 5% 5% -1.4465380 -1.1769699 -1.1624446 1% 1% -1.4465380 -1.1769699 -1.1624446 0% Min 0% -1.4465380 -1.1769699 -1.1624446 ------------------------------------------------------------------------- Quantiles for Boxplots (intersubj) -------------------------------------------------------------------------- Quantile lnCmax_Estimate lnAUC0t_Estimate lnAUC0INF_Estimate 100% Max 100% 2.0950610 2.0874590 2.2642329 99% 99% 2.0950610 2.0874590 2.2642329 95% 95% 2.0950610 2.0874590 2.2642329 90% 90% 1.2521222 1.7322830 1.6489732 75% Q3 75% 0.5630198 0.7067872 0.6375917 50% Median 50% 0.2288221 -0.2710400 -0.1380977 25% Q1 25% -0.9450283 -0.9494072 -0.9624546 10% 10% -1.3016925 -1.1225216 -1.1319332 5% 5% -1.3928622 -1.1243317 -1.1683243 1% 1% -1.3928622 -1.1243317 -1.1683243 0% Min 0% -1.3928622 -1.1243317 -1.1683243 -------------------------------------------------------------------------