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))

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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)