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Approaches to modeling precursor lesions in cancer etiology: applications to testicular and colorectal cancers. Duncan C. Thomas Victoria Cortessis University of Southern California. Cancer Epidemiol Biomark Prev 2013:22(4): 521-7.

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slide1

Approaches to modeling precursor lesions in cancer etiology: applications to testicular and colorectal cancers

Duncan C. Thomas

Victoria Cortessis

University of Southern California

slide3

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%,

dependent data
Dependent Data!
  • Between two phenotypes
  • Within families
  • Between two organs
conceptual dag for genetic etiology of cryptorchidism and testicular germ cell tumors
Conceptual DAG for Genetic Etiology of Cryptorchidism and Testicular Germ Cell Tumors

COl

TCl

G1

G3

G2

COr

TCr

slide11

* 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

11,824

696

23,143

35,482

697

4,994

4,994

Individuals

Families

slide13

COil

TCil

Gi2

Gi1

Xi1

Gi3

Xi2

COir

TCir

COjl

TCjl

Gj2

Gj1

Xj1

Gj3

Xj2

COjr

TCjr

model form and fitting
Model Form and Fitting
  • Penetrance models

logitPr(COil=1) = α0+ α1Gi1+ α2Xi1

logitPr(TCil=1) = β0+ β1Gi2+ β2Xi2+ γ1COil + γ2COil×Gi3

  • MCMC fitting:
    • Update Gi andXigiven COi, TCi, G(-i), X(-i), e.g.

Pr(Gi1 | COi1,G(−i)1, α) proptoPr(COi1 | Gi1, α) Pr(Gi1 | G(−i)1)

= N [ μ(Gi1) + α(COi*−2pi) V(Gi1), V(Gi1) ]

    • Update α,β,γconditional on G,X,CO,TC
ascertainment correction
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))
updating the mgs
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
Linked MG Univariate Effects

CO model TC baseline CO->TC transition

wish list for tc co paper
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
… 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
slide27

First discovered adenoma

T0

X2

Time at screening

Y10

Z2

Experimental animal data

u21

t1n

Carcinoma from adenoma

X1

μ(γ,m1)

λ(α,k)

Complete adenoma history

Y1l

Recurrent adenomas

Observable carcinoma and adenoma history

U,Y2

Tl

Follow-up times

X = Generic vector of risk factors: exposures, genes, interactions, predicted metabolite concentrations and reaction rates, etc.

u20

X3

ν(δ,m0)

denotes a deterministic link function

Carcinoma without prior adenoma

model details
Model Details
  • Polyps prevalence

λi(t) = tkexp(α0+ α1Xi1+ ai)

  • Polyps recurrence

Y1l = ΣjI(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
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
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 MolBiol 2011
slide33

β

precursor & enzyme

input indicators

p,e

Y

disease

phenotypes

metabolites

C

X

biomarkers

exposures

B

enzyme

reaction

rates

α,ω

V

G

genotypes

φ

μ,σ

slide34

Xm

αm01

Cm1

αmrs

αm0s

Cpmrs

Cms

Vemrs

ωms

r = 1,…,Pm , s = 0,2