probFamilial: Probability that a pedigree is segregating familial disease

In DudbridgeLab/familialdisease: Probability calculations for pedigrees segregating a familial form of disease

Description

Given k relatives of the proband, among which m are affected, probFamilial calculates the probability that the pedigree is segregating familial disease as opposed to simply having m sporadic cases.

Usage

probFamilial(m, k, pf, pr, priorF, r = 0)

Arguments

m	Number of affected relatives of the proband.
k	Number of relatives of the proband with known affection status.
pf	Probability of relative being affected with familial disease.
pr	Probability of relative being affected with sporadic disease.
priorF	Prior probability that a pedigree is segregating familial disease.
r	Number of sporadic cases allowed when calculating probability that all cases are familial.

Details

pf can be understood as a combination of penetrance and relatedness. For example, considering 1st degree relatives and a fully penetrant dominant mutation, pf=0.5 since a full sibling of the proband has 0.5 prob of inheriting the same mutation, a child of the proband has 0.5 prob of receiving the mutation, and a parent of the proband has 0.5 prob of being the one who transmitted the mutation. For general pedigrees containing a mix of relationships, pf can be understood as the average over all observed relatives to the proband.

For a rare disease, pr is approximately the population lifetime risk.

If parameter r equals 0, the returned value allFamilial is the probability that all m cases have the familial form of disease. Otherwise allFamilial is the probability that at least (m-r) of the m cases have the familial form.

Value

mprob Probability of m affected relatives in a pedigree segregating familial disease (equation 2 in Dudbridge et al).

rprob Probability of m affected relatives in a pedigree with only sporadic disease (calculated as a binomial probability).

probFamilial Posterior probability that the pedigree is segregating familial disease.

allFamilial Posterior probability that all the cases in a pedigree are familial, except for up to r sporadic cases.

References

Dudbridge F, Brown SJ, Ward L, Wilson SG, Walsh JP. How many cases of disease in a pedigree imply familial disease? Submitted.

Examples

# Familial nonmedullary thyroid cancer, figure 1 in Dudbridge et al.
pf <- 0.0981
pr <- 0.0031
priorF <- 0.013
for(k in 2:8)
  print(probFamilial(1,k,pf,pr,priorF)$probFamilial)
for(k in 2:8)
  print(probFamilial(2,k,pf,pr,priorF)$probFamilial)

# Colorectal cancer, probabilities that all cases are familial
pf <- 0.2
pr <- 0.05
priorF <- 0.0865
probFamilial(2,8,pf,pr,priorF)$allFamilial
# [1] 0.6944444
probFamilial(8,8,pf,pr,priorF)$allFamilial
# [1] 0.232568
# Allowing up to one sporadic case in the pedigree
probFamilial(2,8,pf,pr,priorF,r=1)$allFamilial
# [1] 0.9722222
probFamilial(8,8,pf,pr,priorF,r=1)$allFamilial
# [1] 0.6046769

DudbridgeLab/familialdisease documentation built on May 8, 2019, 3:42 p.m.