# Family age-at-onset data simulation and penetrance estimation

### Description

Family-based studies are used to characterize the disease risk associated
with being a carrier of a major gene. When the disease risk can vary with
age of onset, penetrance or disease risk functions need to provide age-dependent
estimates of this disease risk over lifetime.
This FamEvent package can generate age-at-onset data in the context of familial studies,
with correction for ascertainment (selection) bias arising from a specified
study design based on proband's mutation and disease statuses.
Possible study designs are: `"pop"`

for population-based design where
families are ascertained through affected probands, `"pop+"`

are similar to
`"pop"`

but probands are also known mutation carriers, `"cli"`

for
clinic-based design that includes affected probands with at least one
parent and one sib affected, `"cli+"`

are similar to `"cli"`

but probands are
also known mutation carrriers. And `"twostage"`

for two-stage design that randomly samples families from
the population in the first stage and oversamples high risk families that includes at least two
affected members in the family at the second stage.

Ages at disease onset are generated specific to family members' gender and mutation status according to the specified study design with residual familial correlations induced by either a shared frailty or a second gene. For estimating age at onset risks with family data, an ascertainment corrected prospective likelihood approach is used to account for the population or clinic-based study designs while a composite likelihood approach is used for the two-stage sampling design. The Expectation and Maximization (EM) algorithm has been implemented for inferring missing genotypes conditional on observed genotypes and phenotypes in the families. For family members who have missing genotypes, their carrier probabilities are obtained either from the fitted model or from Mendelian transmission probabilities. This package also provides functions to plot the age-dependent penetrance curves estimated parametrically from the fitted model or non-parametrically from the data, pedigree plots of simulated families and penetrance function curves for carriers and non-carriers of a major and second gene based on specified parameter values.

### Author(s)

Yun-Hee Choi, Karen Kopciuk, Laurent Briollais, Wenqing He

Maintainer: Yun-Hee Choi < yun-hee.choi@schulich.uwo.ca >

### References

Choi, Y.-H., Kopciuk, K. and Briollais, L. (2008) Estimating Disease Risk Associated Mutated Genes in Family-Based Designs, Human Heredity 66, 238-251

Choi, Y.-H. and Briollais (2011) An EM Composite Likelihood Approach for Multistage Sampling of Family Data with Missing Genetic Covariates, Statistica Sinica 21, 231-253

### See Also

`simfam, summary.simfam, plot.simfam, penplot,`

`penmodel, summary.penmodel, plot.penmodel`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 | ```
# Simulate family data
fam <- simfam(N.fam=100, design="pop+", variation="none", base.dist="Weibull",
base.parms=c(0.01, 3), vbeta=c(-1.13, 2.35), allelefreq=0.02)
# summary of simulated family data
summary(fam)
# Pedigree plots for family 1 and 2
plot(fam, famid=c(1,2))
# penetrance function plots given model parameter values for Weibull baseline
penplot(base.parms=c(0.01,3), vbeta=c(-1.3, 2.35), base.dist="Weibull",
variation="none", agemin=20)
# model fit of family data
fit <- penmodel(parms=c(0.01, 3), vbeta=c(-1.13, 2.35), data=fam,
design="pop+", base.dist="Weibull")
# summary of estimated model parameters and penetrance estimates
summary(fit)
# penetrance curves useful for model checking
plot(fit)
``` |