DECURION : Descartes-Curie Model for Cancer Risks Assessment based on Family History

Transcription

1 DECURION : Descartes-Curie Model for Cancer Risks Assessment based on Family History F. Alarcon(1), N. Belaribi(1), N. Andrieu(2), D. Stoppa-LyonnetG(3), Nuel(1). (1) MAP5 UMR CNRS 8145, (2) Inserm U900-Institut Curie-Mines ParisTech, (3)Service de Génétique, Institut Curie - Inserm U830 - Univ Paris Descartes GDR Statistique et Santé (DECURION Project) GDR Statistique et Santé 25 Juin / 26

2 Introduction Mutations in BRCA1 and BRCA2 genes are responsible for monogenic form of breast and ovarian cancer. For patients with severe family history (FH), genetic testing for BRCA1 and BRCA2 is now a standard procedure in every oncological facility. However, mutations in BRCA genes don t explain all familial cases. Statistical model (ex: BRCAPRO, IBIS, etc.) taking into account patient s FH are therefore needed to assess their cancer risks from which prevention strategies are proposed. In 2002, Antoniou et al. presente a genetic model for familial breast cancer, which takes into account the simultaneous effect of mutations in BRCA1, BRCA2 genes and other genes of small effect (the polygenic component). However, it has been shown from Institute Curie s family cancer data that the BOADICEA model have a poor predictive power (de Paw, 2011) (DECURION Project) GDR Statistique et Santé 25 Juin / 26

3 DECURION project To built a new model called DECURION for cancer risk assessment based on Family History to achieve the best possible predictive reliability. Inspired from the BOADICEA model. Addition tools for DECURION Provide a local implementation of an improved BOADICEA model. Exploit Institute Curie s databases to updates the parameters. Improve parameters estimation and prediction taking into account the Ascertainment bias. Use message propagation in Bayesian network to handle likelihood computations in pedigrees. Consideration of environnemental and genetics covariates (DECURION Project) GDR Statistique et Santé 25 Juin / 26

4 DECURION Project 1- The BOADICEA Model 2- The problem of ascertainment bias. 3- Simulations study (DECURION Project) GDR Statistique et Santé 25 Juin / 26

5 DECURION Project 1- The BOADICEA Model (DECURION Project) GDR Statistique et Santé 25 Juin / 26

6 Variables Y i is the individual history of i (ex : Y 4 = BC 40, Y 8 = U 67 ) X i is the genotype for individual i (X i = 0 if i is non carrier ; X i = 1 if i is BRCA1 carrier ; X i = 2 if i is BRCA2 carrier) Z is the familial polygenic effect assumed N(0, σ 2 ) θ = (q, λ 0, λ 1, σ) In practice, all these variables are only partially observed. Likelihood for a family f L f (θ) = P(Y, X, Z ; θ) = P(Y X, Z ; θ)p(x Z ; θ)p(z ) = P(Z )P(X; θ)p(y X, Z ; θ) = P(Z ) P(X i pa(x i ); θ)p(y i X i, Z ; θ) i (DECURION Project) GDR Statistique et Santé 25 Juin / 26

7 individual history : survival analysis The distribution P(Y i X i, Z i ) is modeled by a survival approach with an hazard rate depending on the genotype : λ x(t) = λ x,0 (t)exp(z ) with Z N(0, σ 2 ) Cumulative risk at 60 years X=0 X=1 Risk= z (DECURION Project) GDR Statistique et Santé 25 Juin / 26

8 Prediction The probability that a women unaffected at age a will develop breast cancer by age a + n given the known FH and the vector of parameters θ is given by : P(Y = BC a+n U a, FH; θ) = P(Y = BC a+n X i, U a, FH, Z ; θ)p(z, X i U a, FH; θ)dz X i {0,1,2} Z R (1) As (Y = BC a+n ) does not depend on FH given Z and (Z, X i ) does not depend on U a, equation (1) becomes : P(Y = BC a+n X i, U a, Z ; θ)p(z, X i FH; θ)dz (2) X i in{0,1,2} Z R That can be approximate by : P(Y = BC a+n X i, U a,, Z = z, θ)p(x i Z = z, FH, θ)dz (3) X i in{0,1,2} Where z = argmaxp(z FH) and P(Z FH) = P θ(y Z )P(Z ) Z R P θ(y, Z )dz P θ(y Z )P(Z ) (DECURION Project) GDR Statistique et Santé 25 Juin / 26

9 Density à posteriori of Z GREEN : x = (0, 0, 0, 0, 0) and Y = (BC 25, BC 34, BC 41, BC 29, BC 21 ) RED: x = (1, 1, 1, 1, 1) and Y = (U 68, U 65, U 43, U 37, U 29 ) BLUE : x = (0, 0, 0, 0, 0) and Y = (BC 44, U 65, U 43, U 37, U 29 ) Density of Z a posteriori All Non carrier All affected All carrier None affected All non carrier One affected z (DECURION Project) GDR Statistique et Santé 25 Juin / 26

10 DECURION model How to improve the BOADICEA model (to become the DECURION model)? (DECURION Project) GDR Statistique et Santé 25 Juin / 26

11 DECURION model How to improve the BOADICEA model (to become the DECURION model)? Bayesian network (loops) instead of MENDEL Estimate model parameter on Curie s databas Add covariates (ex: breast density, HRT, parity, etc.) Add latent genetic mutation (DECURION Project) GDR Statistique et Santé 25 Juin / 26

12 DECURION model How to improve the BOADICEA model (to become the DECURION model)? Bayesian network (loops) instead of MENDEL Estimate model parameter on Curie s databas Add covariates (ex: breast density, HRT, parity, etc.) Add latent genetic mutation Major Issue: Taking into account ascertainment to avoid bias. (DECURION Project) GDR Statistique et Santé 25 Juin / 26

13 DECURION Project 2- The problem of ascertainment bias. (DECURION Project) GDR Statistique et Santé 25 Juin / 26

14 Ascertainment bias Ascertainment bias occurs when data are not selected randomly in the population but through several criteria in order to have carriers. Institute Curie s data are obtained from pedigrees ascertained through affected individuals. If the ascertainment bias is not taking into account, the estimation of the cumulative risk for carriers can be significantly overestimated. (DECURION Project) GDR Statistique et Santé 25 Juin / 26

15 Correction of ascertainment bias When the ascertainment process is known, the likelihood can be conditioned by the ascertainment scheme in order to correct the estimation bias (called the Prospective correction). ˆθ MLE = argmax θ L(θ) ˆθ Asc = argmax θ L(θ Asc) If ˆθ is not corrected for ascertainment bias, this implies a false prediction : P(Y = BC x+n U x, FH, ˆθ Asc ) = Risk(ˆθ Asc ) = P(Y = BC x+n X i, U x, FH, Z, ˆθ Asc ) X i in{0,1,2} Z R P(Y = BC x+n X i, U x, FH, Z, ˆθ MLE ) Z R X i in{0,1,2} P(Z, X i U x, FH, ˆθ Asc )dz P(Z, X i U x, FH, ˆθ MLE )dz (DECURION Project) GDR Statistique et Santé 25 Juin / 26

16 The Prospective correction The Prospective correction consists in mathematically modeling the selection process : L prosp (θ Asc) = P(Y, X, Z ; θ Asc) = P(Y, X, Z ; θ) P(Asc) If families with at least one affected are ascertained, the correction can be written as : P(Asc) = 1 P(Asc) = 1 i P(Y i = U X i ) (DECURION Project) GDR Statistique et Santé 25 Juin / 26

17 Ascertainment in BOADICEA (1) Families ascertained through index phenotype. ABC families : Families were ascertained through women with breast cancer diagnosed before the age 55 years. UK families : Some families were ascertained through patients diagnosed under the âge 36 years and registered between 1982 and Other were ascertained patients diagnosed between the ages 36 to 45 years and registered between 1988 and Manchester families : Families were ascertained through women with breast cancer diagnosed before the age 30 years and registered between 1980 and British families : Families were ascertained through at least 2 breast cancer cases, one or more diagnosed before the age of 50 years. Adjusment for ascertainment Conditionning the likelihood on the disease status and age at diagnosis of the index case (denoted k) : L f (θ Asc) = L f (θ) P(Y k ) (DECURION Project) GDR Statistique et Santé 25 Juin / 26

18 DECURION Project 3- Simulations study (DECURION Project) GDR Statistique et Santé 25 Juin / 26

19 Simulation study Simulation of pedigrees with fixed size and structure : 2 parents and 3 offsprings Genotypes X i {0, 1, NA} Polygenic effect Z N (0, σ 2 ) with σ = 1.67 Waiting time W before the first breast cancer λ X (t, x, z; θ) = λ 0,X (t; θ) e z Ascertainment process : Only families with at least on affected before 55 years are ascertained. MLE No correction for ascertainment ˆθ MLE BOA Correction for ascertainment like in BOADICEA model ˆθ BOA Prosp Prospective correction for ascertainment ˆθ Prosp (DECURION Project) GDR Statistique et Santé 25 Juin / 26

20 Estimation of θ according to the ascertainment correction NO correction BOADICEA correction Loglikelihood Loglikelihood Sigma Sigma Prospective correction Boadicea VS Prospective Loglikelihood Boadicea Prospective Sigma Sigma (DECURION Project) GDR Statistique et Santé 25 Juin / 26

21 Empirique distribution of ˆθ for 600 samples of a data set of 50 families according to the ascertainment correction Distribution of estimated sigma Density MLE Boadicea Prospective Sigma= (DECURION Project) GDR Statistique et Santé 25 Juin / 26

22 Empirique distribution of predictive risk for 600 samples of a data set of 50 families according to the ascertainment correction FH : x = (NA, NA, 0, 0, NA) and Y = (BC 36, BC 23, BC 40, U 37, BC 28 ) Risk( ˆθ Asc ) = P(Y 4 = BC 60 U 37, FH, ˆθ Asc ) with Asc = (MLE, BOA, Prosp) ; Risk(θ Real ) = Distribution of risks Density Risk MLE Risk Boadicea Risk Prospective Risk(Sigma=1.67) (DECURION Project) GDR Statistique et Santé 25 Juin / 26

23 Prediction comparison for 2 FH FH1 : x = (NA, NA, 0, 0, NA) and Y = (BC 36, BC 23, BC 40, U 37, BC 28 ) FH2 : x = (NA, NA, NA, 0, NA) and Y = (U 70, U 67, BC 40, U 37, U 40 ) Risk( ˆθ Asc ) = P(Y 4 = BC 60 U 37, FH, ˆθ Asc ) with Asc = (MLE, BOA, Prosp) ; Risks for family N 1 Risks for family N 2 X=(NA,NA,1,1,NA), W=(36, 23, 40, 37, 28) X=(NA,NA,NA,1,NA), W=( 70, 67,40, 37, 40) Risks MLE Boadicea Prospective Sigma= Risks MLE Boadicea Prospective Sigma= Sigma Sigma (DECURION Project) GDR Statistique et Santé 25 Juin / 26

24 Ascertainment in BOADICEA (2) Families ascertained through index phénotype and genotype BRCA1 and BRCA2 positive families : Meta-analysis families : Families were ascertained through affected carrier and who are unselected for family history of cancer. Adjusment for ascertainment Conditionning the likelihood on the disease status, age at diagnosis and carrier genotype of the index case (denoted k) : L f (θ Asc) = L f (θ) P(Y k, X k ) (DECURION Project) GDR Statistique et Santé 25 Juin / 26

25 Ascertainment in BOADICEA (3) Families ascertained through index s family history British (B) families : Families were ascertained through at least two breast cancer cases, one or more diagnosed before the age of 50 years. Adjusment for ascertainment Conditionning the likelihood on all the phenotypic information for the family. L f (θ Asc) = L f (θ) P(Y, X) = P(Y obs ) P(Y obs ) = P(X Y ) Retrospective likelihood When ascertainment depend only on phenotypes, P(X Y ) = P(X Y, Asc) biased if ascertainment process depend on genotype of index case (Carayol, 2004). (DECURION Project) GDR Statistique et Santé 25 Juin / 26

26 Ascertainment in BOADICEA (3) The Genotype Restricted Likelihood (GRL) Families ascertained through FH dependent of the index genotype : the GRL GRL f (θ) = P(X Y, Asc) = P(Asc X, Y )P(Y X)P(X) Ω C P(Asc X, Y )P(Y X)P(X) Where Ω C = set of all possible genotypic configuration for a family f compatible with the selection criteria (i.e. the index carrier status). GRL : advantages and disadvantages Correct for ascertainment bias whatever ascertainment criteria. lack of efficiency when there are unknown genotypes. If only the index case is genotyped the family is not informative (DECURION Project) GDR Statistique et Santé 25 Juin / 26

27 Conclusion DECURION has the ambition to become a valid alternative to BOADICEA (and other models) for clinicians and researchers with several advantages: to achieve better tumor risk predictive reliability for French patients thanks to the data used for its parameter estimation (up to date, none of the existing model have been developed from French families); to improve the medical management of patients in terms of surveillance and prevention strategies to provide a better understanding of the etiology of cancers through research. The DECURION model might also help to convince clinicians to collect additional data on their patients (covariates, level of uncertainty, details on the ascertainment process) that will help to further improve the model. (DECURION Project) GDR Statistique et Santé 25 Juin / 26

28 Bibliography A. de Pauw and D. Stoppa-Lyonnet. Genetic consultation: hereditary cancer risk?. La Revue du praticien, 61(4):538, G. Parmigiani, D.A. Berry, and O. Aguilar. Determining carrier probabilities for breast cancer-susceptibility genes BRCA1 and BRCA2. The American Journal of Human Genetics, 62 (1) : 145 à 158, AC Antoniou et al. The BOADICEA model of genetic susceptibility to breast and ovarian cancer. British journal of cancer, 91(8): 1580 à 1590, J. Tyrer, S.W. Duffy and J. Cuzick. A breast cancer prediction model incorporating familial and personal risk factors. Statistics in medicine, 23(7):1111 à 1130, J. Carayol, M. Khlat, J. Maccario, and C. Bonaiti-Pellie. Hereditary non-polyposis colorectal cancer: current risks of colorectal cancer largely overestimated. Journal of medical genetics, 39(5): 335 à 339, F. Alarcon et al. Estimating cancer risk in HNPCC by the GRL method. European Journal of Human Genetics, 15(8):831 à 836, J. Carayol, and C. Bonaïti. Estimating penetrance from family data using a retrospective likelihood when ascertainment depends on genotype and age of onset. Genetic epidemiology, 27(2):109 à 117, (DECURION Project) GDR Statistique et Santé 25 Juin / 26