We used modified segregation analysis to fit a range of genetic models to the
observed colorectal cancer family histories for the proband and their first-degree
relatives. Individuals were assumed to be at risk of colorectal cancer from birth until
the earliest of the following: diagnosis of colorectal cancer or any other cancer (except
skin cancer); first polypectomy; death; and the earlier of last known age at baseline
interview or age 80 years.
The colorectal cancer incidence
λi(
t,
k) for
individual
i at age
t in sex group
k(
k = 1 for males or 2 for females) was assumed to depend on
genotype according to a parametric survival analysis model
λi(
t,
k)=
λ0(
t,
k)
exp(
Gi+
Pi(t)), where
λ0(
t,
k) is the
sex-specific baseline incidence at age
t.
Giis the natural logarithm of the relative risk associated with the major genotype and
Pi(
t) is the polygenic component for age
t.
The major genotype was defined by six components representing each of the genes
MLH1, MSH2, MSH6, PMS2, MUTYH and one representing the hypothetical
unidentified major genes. We fitted models in which the unidentified major genes were
autosomal with a normal and a mutant allele unlinked to mutations in the MMR genes or
MUTYH. We also fitted models in which the average relative risk for the
unidentified major genes was assumed to be age dependent. We used the published age-, sex-
and country-specific incidences for
MLH1 and
MSH2mutation carriers (32 (
link)), and published age- and
sex-specific incidences for
MSH6, PMS2 and
MUTYHmutation carriers (26 (
link), 33 (
link), 34 (
link)).
The polygenic component for age
t,
Pi(
t), was assumed to be normally
distributed with zero mean and variance
σ
2p(
t).
P was approximated by the hypergeometric polygenic model (35 (
link), 36 ). We also
fitted models where the variance of the polygenic ‘modifying’ component
was allowed to take a different value σ
2mfor MMR gene and
MUTYH carriers.
To compute the baseline colorectal cancer incidence
λ0(
t), we constrained the overall
incidence of colorectal cancer to agree with the national age- and sex-specific incidences
(1998–2002) separately for Australia, Canada and USA (37 ). Other cancers were ignored in this model.
We assumed that the sensitivity of the mutation testing of probands for MMR
genes and
MUTYH was 80%,(38 (
link)) and we examined the effect of varying this sensitivity. For relatives, we
assumed the mutation screening for the proband’s mutation (i.e. predictive
testing) was 100% sensitive and specific.
The genetic models were specified in terms of colorectal cancer incidence for
MMR gene and
MUTYH mutation carriers, the frequency
(
qA) of the putative high risk allele “A” of
the unidentified major genes component, the average relative risk of colorectal cancer for
carriers of mutations in the unidentified major genes, and the variances of the polygenic
and modifying components (σ
2p and
σ
2m). Maximum likelihood estimation was
used to estimate parameters. The estimates we present are the values that were the most
likely (i.e. most consistent) with the data. Maximum likelihood is the optimal method for
making such estimates, and provides confidence intervals (CIs). We adjusted for
ascertainment by maximizing the likelihood of each pedigree conditioned on the colorectal
cancer status of the proband and his or her age of diagnosis (but not the mutation carrier
status as this information was not known at the time of recruitment).
The relative goodness of fit for nested models was tested by the likelihood
ratio test. The Akaike’s Information Criterion(39 ) [AIC=−2×log-likelihood +
2×(no. of parameters)] was used to assess goodness of fit between non-
nested models (40 ).
The expected versus observed number of affected relatives under each fitted
model was assessed using the Pearson χ
2 goodness of fit statistic. The
expected number of probands with MMR and
MUTYH mutation carriers for
families that had undergone mutation testing based on their cancer family history was
computed using Bayes theorem (41 (
link)). Statistical
methods are described further in the
Appendix.
Win A.K., Jenkins M.A., Dowty J.G., Antoniou A.C., Lee A., Giles G.G., Buchanan D.D., Clendenning M., Rosty C., Ahnen D.J., Thibodeau S.N., Casey G., Gallinger S., Le Marchand L., Haile R.W., Potter J.D., Zheng Y., Lindor N.M., Newcomb P.A., Hopper J.L, & MacInnis R.J. (2016). Prevalence and Penetrance of Major Genes and Polygenes for Colorectal Cancer. Cancer epidemiology, biomarkers & prevention : a publication of the American Association for Cancer Research, cosponsored by the American Society of Preventive Oncology, 26(3), 404-412.