Duncan C. Thomas Victoria Cortessis University of Southern California

1. Approaches to modeling precursor lesions in cancer etiology: applications to testicular and colorectal cancers Duncan C. Thomas Victoria Cortessis University of Southern California

2. Cancer EpidemiolBiomarkPrev 2013:22(4): 521-7

3. 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%,

7. J ClinEdocrinMetab2012;92:E393-9

8. Dependent Data! • Between two phenotypes • Within families • Between two organs

9. Conceptual DAG for Genetic Etiology of Cryptorchidism and Testicular Germ Cell Tumors COl TCl G1 G3 G2 COr TCr

10. Schemes for Defining Testicular Phenotype

11. * 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

13. COil TCil Gi2 Gi1 Xi1 Gi3 Xi2 COir TCir COjl TCjl Gj2 Gj1 Xj1 Gj3 Xj2 COjr TCjr

14. 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

15. 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))

18. Full model estimates by subset of data

19. GWAS hits from literatureAvailable on 1639 individuals from 527 phase 2 families

20. 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.

21. Linked MG Univariate Effects CO model TC baseline CO->TC transition

22. Estimates of linked gene effects by whether PG, FR, residual MG included

23. Estimates of PG, FR, residual MG effects across alternative models

25. 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

26. … 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

27. 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

28. 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

30. 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

31. 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

33. 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

34. Xm αm01 Cm1 αmrs αm0s Cpmrs Cms Vemrs ωms r = 1,…,Pm , s = 0,2

35. Definitely a work in progress !