Estimation of Bioavailability of Environmental Estrogens in Population Models Dr. Silvia Selinski Department of Statistics University of Dortmund Germany
Contents I. Introduction Xenoestrogens Risk Assessment Enterohepatic Circulation II. Data Daidzein, bisphenol A, p-tert-octylphenol III. Models Bioavailability Population Models EM Algorithm IV. Results V. Discussion TIES 2002 2
Introduction Endocrine Active Compounds Alter signaling processes of the endocrine system by hormone mimetic effects Environmental Estrogens/ Xenoestrogens Synthetic compounds (DDT, bisphenol A, alkylphenols, e.g. p-tert-octylphenol) Phytoestrogens (isoflavones, e.g. daidzein) TIES 2002 3
Risk Assessment Exposure to synthetic and natural estrogens Estrogenic and anti-estrogenic effects of the same compound Endocrine effects are not necessarily adverse effects Background level of endogenous estrogens TIES 2002 4
Biological Endpoints Proposed to be associated with Endocrine Active Compounds Cancers (ovarian, breast, testicular) Transplacental carcinogenesis Decreased sperm count and motility Malformations of female reproductive tract and male urogenital tract Increased ectopic pregnancies Decreased reproductive success Decreased weights of uterus or testes Altered estrous or mentrual cycling Steroid receptor binding or inhibition Altered hormone levels Altered cell proliferation and cell differentiation Altered behaviour Hyperactivity Degraded immune function Imposex/ hermaphroditism TIES 2002 5
Investigated Compounds Daidzein Phytoestrogen Bisphenol A Industrial chemical p-tert-octylphenol Industrial chemical TIES 2002 6
Enterohepatic Circulation parent compound blood intestines liver elimination bile conjugate TIES 2002 7
Data Institute of Occupational Physiology at the University of Dortmund (IfADo): Animal experiments with female DA/Han rats 3-7 blood samples per animal Daidzein, bisphenol A, p-tert-octylphenol Application: intravenously (low dose) orally (low dose, high dose) TIES 2002 8
Models Oral Bioavailability F oral = AUC AUC oral dose intravenous intravenous dose oral F oral : oral bioavailability AUC: area under the concentration-time curve Oral: after oral application Intravenous (short: i.v.): after intravenous application TIES 2002 9
Models Three-exponential function (intravenous application) C p = A e αt + B e βt + C e γt TIES 2002 0
Population Model ln(auc), σ² ln(auc i ) ~ (ln(auc), σ²g(ln(auc i ) ) i =,..., ln(auc a priori ), τ² ln(auc) ~ (ln(auc a priori ), τ²) r, λ / σ² ~ Ga(r, λ) AUC a priori prior information, g(x) = x² E(/ σ²) = r/ λ / τ² τˆ 2 = ( ln( ) ln( )) 2 AUCi AUCa priori i= TIES 2002
Bayes Estimate b In case of fixed σ² the posterior distribution of ln(auc) is given by ln(auc) ~ (Bb, B), where ( 2 ) σ + ( 2 g(ln( AUC τ ) i )) ln( AUCi ) = i= B = i= ( 2 ) (ln( )) ( 2 ) σ g AUC + τ and i ln( AUC apriori ) TIES 2002 2
EM Algorithm E-step: ln( AUC) ( l ) = + i= i= ( ) 2 ( l ) (ln( )) ( 2 σ g AUC + τˆ ) ( ) 2 ( l ) σ g(ln( AUC )) ( ) ] 2 τˆ ln( AUC ) i apriori i ln( AUC i ) TIES 2002 3
EM Algorithm M-step: 2 ( l) i= σ = Starting value: σ 2 (0) = ln( AUC i= ( ( l) ) 2 ln( AUC ) ln( AUC ) / g( ln( AUC )) i + 2 ( r + 2 ( r ( AUC AUC ) 2 ln( i) ln( ) ( ) ) = ln( AUCi i= ) ) TIES 2002 4 2) + 2 λ with i + 2λ
Results Difficulties with estimation of AUC i Fast convergence of the EM algorithm: -3 iterations Impact of the choice of g(.) TIES 2002 5
Daidzein Estimates of oral bioavailability F 0 apriori = 9.7 % g(x) = F 00 apriori = 2.2 % x x² Dose in mg/kg σ -2 ~ F-AUC i.v. apriori F pop. mean F-AUC i.v. apriori F i.v. pop. mean F-AUC i.v. apriori F i.v. pop. mean 0 (i.v.) Ga(8;2) 0 (oral) Ga(2;,85) 8.69 % 8.37 % 9.07 % 8.38 % 8.28 % 9.06 % 00 (oral) Ga(,2;3,9).22 %.26 %.79 %.8 %.25 %.79 % TIES 2002 6
Daidzein Estimates of AUC, B, and σ² for group B (0 mg/kg oral) AUC apriori = 48623 g(x) = Estimate of x x² AUC 43565 4954 45442 B 36.24 5.08.50 σ² 0.34 0.29 0.28 TIES 2002 7
Bisphenol A F 0 apriori = 6.4 % g(x)=x² F 00 apriori = 5.6 % Dose σ -2 ~ F-AUC i.v. apriori F population mean in mg/kg 0 (i.v.) Ga(;2) 0 (oral) Ga(;7) 5.4 % 20.27 % 00 (oral) Ga(;4) 3.8 % 5.0 % TIES 2002 8
p-tert-octylphenol F 50 apriori = 2.3 % g(x)=x² F 200 apriori = 8.4 % Dose σ -2 ~ F-AUC i.v. apriori F population mean in mg/kg 5 (i.v.) Ga(2;2) 50 (oral) Ga(3;2).75 % 2.4 % 200 (oral) Ga(3;2) 8.3 % 8.58 % TIES 2002 9
Estimation of AUC i : Spline functions Discussion Linear approximation t) = y exp y& ( y ( t t ) { } EM algorithm: -3 iterations 4-stage model, 4 4 matrices: 7-5 minutes Impact of prior density Comparison with pregnant rats for daidzein y TIES 2002 20