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Approaches to modeling precursor lesions in cancer etiology:
applications to testicular and colorectal cancers
Duncan C. ThomasVictoria Cortessis
University of Southern California
Cancer Epidemiol Biomark Prev 2013:22(4): 521-7
Statistics Sweden maintains a ‘Multigeneration Register’ in which offspring, born in Sweden in 1932 and later, are registered with their parents (as declared at birth) and they are organized as families (Hemminki et al, 2001a).
The Family-Cancer Database, which covered years 1961-2000 from the Swedish Cancer Registry, included 4082 testicular cancers in sons of ages 0–68 years and 3878 fathers with testicular cancer (Table 1). Seminoma accounted for 49.8% and teratoma 48.4% in sons, while in fathers the proportions were 59.1 and 38.2%,
J Clin Edocrin Metab 2012;92:E393-9
Dependent Data!
• Between two phenotypes• Within families• Between two organs
COl
COr
TCl
TCr
G1 G2G3
Conceptual DAG for Genetic Etiology of Cryptorchidism and Testicular Germ Cell Tumors
Schemes for Defining Testicular Phenotype
Scheme Defined Phenotypes Parameters Examples of Use
TC2 TC- TC+ marginal G2 basis of GWAS scans of TGCT
TC3 TC- TCu TCb marginal G2, marginal F2
post scan stratified analyses of TGCT
TC2CO2 TC- CO-TC- CO+
TC+ CO-TC+ CO+
marginal G1, marginal G2
post scan stratified analyses of TGCT
TC3CO3 TC- CO-TC- COuTC- COb
TCu CO-TCu COuTCu COb
TCb CO-TCb COuTCb COb
marginal G1, marginal F1,marginal G2, marginal F2
equivalent to model for precursor and disease of unpaired organ
TC4CO4 TC- CO-TC- COlTC- COrTC- COb
TCl CO-TCl COlTCl COrTCl COb
TCr CO-TCr COlTCr COrTCr COb
TCb CO-TCb COlTCb COrTCb COb
G1, F1, G2, F2, G3
present analysis
Families Individuals N/family (max)
Phase 0 17,844 17,844 1 (1)
Phase 1* 5,702 32,949 4.8 (29)
Phase 2** 697 23,867 33 (118)
Phase 2 w SNPs 527 1,639 3.1 (16)
Total 17,514 64,315
4,994 69711,824 4,994 69635,482 23,143
* Consenting consenting probands who returned a family history questionnaire and their first-degree relatives
** Probands with bilateral TC or unilateral TC plus either a personal history of CO or a family history of CO or TC
Families Individuals
COil
COir
TCil
TCir
Gi1 Gi2Gi3Xi1 Xi2
COjl
COjr
TCjl
TCjr
Gj1 Gj2Gj3Xj1 Xj2
Model Form and Fitting
• Penetrance modelslogit Pr(COil=1) = α0 + α1Gi1 + α2Xi1
logit Pr(TCil=1) = β0 + β1Gi2 + β2Xi2 + γ1COil + γ2COil× Gi3
• MCMC fitting:– Update Gi and Xi given COi, TCi, G(-i), X(-i), e.g.
Pr(Gi1 | COi1,G(−i)1, α) propto Pr(COi1 | Gi1, α) Pr(Gi1 | G(−i)1)
= N [ μ(Gi1) + α (COi* − 2pi) V(Gi1), V(Gi1) ]
– Update α,β,γ conditional on G,X,CO,TC
Ascertainment Correction
• Prospective ascertainment-corrected likelihood
• Implemented by random sampling yr=(CO,TC) vectors meeting ascertainment criteria and applying importance sampling to compute AR(θ’:θ)
• Works for estimating penetrance parameters, not MAFs or LD (would require
sampling (y,g|Asc))
-150 -100 -50 0 50 100 150 200 250
-10
-9
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-1
0
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0
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-4
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-1
0
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0.5
1
1.5
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-6.4
-6.2
-6
-5.8
-5.6
-5.4
-5.2
-5
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-0.1
0
0.1
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-1
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-1
-0.5
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1.5
Full model estimates by subset of data
GWAS hits from literature
Available on 1639 individuals from 527
phase 2 families
Updating the MGs
• Linked MGs are updated conditional on subject’s and immediate relative’s measured genotypes (if any), subject’s own phenotype, all other covariates, and model parameters– Assuming no recombination– Assuming LD between GWAS and causal SNPs– So far unable to jointly estimate LD, MAFs, and RRs.
Linked MG Univariate Effects
CO model TC baseline CO->TC transition
Estimates of linked gene effects by whether PG, FR, residual MG included
Estimates of PG, FR, residual MG effects across alternative models
Gene SNP lnRR (S.E.)CO model
UCK2 rs3790672 – 0.44 (0.41)
TERT/CLPT1 rs4635969 – 1.74 (0.44)
CNPE rs4699052 + 1.04 (0.41)
Frailty + 3.28 (0.20)
TC baseline risk model
SPRY4 rs4624820 – 0.39 (0.22)
KITLG rs995030 – 0.51 (0.24)
UCK2 rs6703280 + 0.46 (0.21)
Frailty +0.41 (0.19)
CO to TC transition model
CO status + 1.17 (0.29)
BAK1 rs210138
+ 0.93 (0.70)
TERT/CLPT1 rs4635969 +1.26 (0.71)
Frailty +1.27 ((0.45)
Wish list for TC-CO paper
• Linkage between 3 major genes and correlation between 3 polygenes
• Age-dependent frailty model for TC• Additional genotype data at GWAS hits• Covariates: birth order, left/right side,
histology, race/ethnicity• Better treatment of missing data and selection
bias
… And now for something completely different!Colorectal Polyps and Cancer
• Similar model structure, but set in a time-to-event framework
• Combining 3 (simulated) datasets– Case-control data on prevalent polyps– Short-term longitudinal study of subsequent
polyps– Cohort study of cancer incidence
• Secondary aim to model folate metabolism combining ODEs with statistical model
Y10
u21
u20
U,Y2
X1
X3
X2
Y1l
First discovered adenoma
Recurrent adenomas
Carcinoma from adenoma
Carcinoma without prior adenoma
Observable carcinoma and
adenoma history
X = Generic vector of risk factors: exposures, genes, interactions, predicted metabolite concentrations and reaction rates, etc.
denotes a deterministic link function
Z2Experimental animal data
t1n
Complete adenoma history
T0
Tl
λ(α,k) μ(γ,m1)
ν(δ,m0)
Time at screening
Follow-up times
Model Details
• Polyps prevalenceλi(t) = tk exp(α0 + α1Xi1 + ai)
• Polyps recurrence
Y1l = Σj I(Til < tij ≤ Ti,l+1) , l = 1,…,Nfu
• Cancer incidence
μi(u1) = exp(γ0 + γXi2) Σj|tij < u1 (u1 - tij)m1
νi(u0) = exp(δ0 + δXi3) um0
Conclusions
• Joint modeling of precursors and cancer is feasible and avoids some potential nasty biases:– E.g., polyps & cancer in
family studies (under review)
• Can be informative about genetic co-determinants of two traits
Mechanistic Modeling of Folate Pathway
• System of ODEs for metabolism– Duncan, Reed & Nijhout, Nutrients 2013
– Ulrich et al, CEPB 2008
• Combined with stochastic models for disease and inter-individual variation in metabolism given genotypes
– Thomas et al, Hum Genom 2012
• Simulation of “virtual population” of 10K individuals with genotypes, exposures, enzyme activity rates, intermediate metabolites, and disease
• Fitting by Approximate Bayesian Computation– Jung & Marjoram, Stat Appl Genet Mol Biol 2011
X
G V
C
p,e
Y
B
μ,σ
α,ω
φ
β
exposures
genotypes
enzyme reaction
rates
metabolites
biomarkers
disease phenotypes
precursor & enzyme input indicators
Cms
Cpmrs
Vemrs
αmrs
ωmsr = 1,…,Pm , s = 0,2
Cm1
Xm
αm01
αm0s
Definitely a work in progress !
ß SNP Crude Adjusted for PG and FR
Also adjusted for unlinked
MG
Unlinked residual MG
estimateGenes for CO
SPRY4 rs4624820 –0.37 (0.38) –0.01 (0.41) +0.06 (0.36) +1.90 (0.64)BAK1 rs210138 –1.31 (0.44) –0.72 (0.39) –0.87 (0.40) +2.25 (0.34)
KITLG rs1508595 –0.29 (0.65) –0.16 (0.44) –0.15 (0.56) +1.48 (0.39)rs995030 –0.54 (0.43) –0.15 (0.44) –0.23 (0.39) +2.17 (0.31)
UCK2rs4657482 –1.01 (0.31) –0.59 (0.40) –0.54 (0.37) +2.87 (0.30)rs3790672 –1.14 (0.38) –0.69 (0.45) –0.82 (0.41) +2.45 (0.43)rs6703280 +0.81 (0.35) +0.38 (0.44) +0.14 (0.44) +2.27 (0.43)
TERT rs4635969 –2.01 (0.41) –1.23 (0.34) –1.72 (0.49) –1.31 (1.03)CNPE rs4699052 +1.83 (0.49) +0.82 (0.37) +0.55 (0.47) +2.15 (0.31)BNC2 rs3814113 –0.78 (0.33) –0.31 (0.39) –0.35 (0.47) +1.56 (0.69)
Genes for TC baseline riskSPRY4 rs4624820 –0.35 (0.21) –0.28 (0.27) –0.27 (0.27) +0.00 (0.23)BAK1 rs210138 +0.27 (0.20) +0.15 (0.33) +0.21 (0.31) +0.05 (0.23)KITLG
rs1508595 –0.27 (0.25) –0.31 (0.32) –0.24 (0.32) +0.02 (0.21)rs995030 –0.46 (0.25) –0.48 (0.32) –0.48 (0.30) –0.01 (0.23)
UCK2
rs4657482 +0.08 (0.22) +0.05 (0.25) +0.05 (0.26) –0.05 (0.23)rs3790672 +0.01 (0.21) +0.15 (0.27) +0.06 (0.27) +0.07 (0.22)rs6703280 +0.13 (0.48) –0.04 (0.59) +0.01 (0.33) +1.34 (0.24)
TERT rs4635969 +0.10 (0.25) +0.09 (0.23) +0.12 (0.25) –0.05 (0.23)CNPE rs4699052 –0.13 (0.23) –0.24 (0.28) –0.20 (0.28) +0.06 (0.24)BNC2 rs3814113 –0.07 (0.20) –0.05 (0.24) +0.01 (0.25) +0.00 (0.26)
Genes for CO to TC transitionSPRY4 rs4624820 –0.04 (0.65) +0.08 (0.62) +0.76 (0.85) +1.23 (1.03)BAK1 rs210138 +0.29 (0.59) +0.31 (0.62) +0.05 (0.85) –0.43 (0.86)KITLG
rs1508595 +0.19 (0.61) +0.05 (0.59) +0.09 (0.98) –0.23 (1.36)rs995030 +0.07 (0.64) +0.06 (0.59) +0.48 (0.65) +0.63 (0.64)
UCK2
rs4657482 +0.07 (0.63) +0.15 (0.63) +0.70 (0.77) +0.88 (0.91)rs3790672 –0.10 (0.59) +0.20 (0.64) –0.42 (0.78) –0.76 (0.79)rs6703280 +0.17 (0.58) +0.29 (0.63) +0.77 (0.66) +0.78 (0.62)
TERT rs4635969 +0.49 (0.53) +0.43 (0.61) +1.73 (0.77) –1.91 (0.77)CNPE rs4699052 +0.04 (0.56) +0.06 (0.59) –0.33 (0.93) –0.51 (1.10)BNC2 rs3814113 +0.18 (0.59) +0.18 (0.60) –0.93 (1.29) –1.79 (1.66)