Estimation of Bioavailability of Environmental Estrogens in Population Models

Transcription

1 Estimation of Bioavailability of Environmental Estrogens in Population Models Dr. Silvia Selinski Department of Statistics University of Dortmund Germany

2 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

3 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

4 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

5 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

6 Investigated Compounds Daidzein Phytoestrogen Bisphenol A Industrial chemical p-tert-octylphenol Industrial chemical TIES

7 Enterohepatic Circulation parent compound blood intestines liver elimination bile conjugate TIES

8 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

9 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

10 Models Three-exponential function (intravenous application) C p = A e αt + B e βt + C e γt TIES

11 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

12 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

13 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

14 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 ) + 2 λ with i + 2λ

15 Results Difficulties with estimation of AUC i Fast convergence of the EM algorithm: -3 iterations Impact of the choice of g(.) TIES

16 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

17 Daidzein Estimates of AUC, B, and σ² for group B (0 mg/kg oral) AUC apriori = g(x) = Estimate of x x² AUC B σ² TIES

18 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 % % 00 (oral) Ga(;4) 3.8 % 5.0 % TIES

19 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

20 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