| Title: | Calculating Likelihoods by Pedigree Paring |
|---|---|
| Description: | A fast and general implementation of the Elston-Stewart algorithm that can calculate the likelihoods of large and complex pedigrees. References for the Elston-Stewart algorithm are Elston & Stewart (1971) <doi:10.1159/000152448>, Lange & Elston (1975) <doi:10.1159/000152714> and Cannings et al. (1978) <doi:10.2307/1426718>. |
| Authors: | James Dowty [aut, cre], Kevin Wong [aut] |
| Maintainer: | James Dowty <[email protected]> |
| License: | GPL-3 |
| Version: | 1.1.1 |
| Built: | 2024-11-08 04:12:17 UTC |
| Source: | https://github.com/cran/clipp |
clipp provides a fast and general implementation of the Elston-Stewart
algorithm, and can calculate the log-likelihoods of large and complex pedigrees,
including those with loops. General references for the Elston-Stewart algorithm are
(Elston & Stewart, 1971), (Lange & Elston, 1975) and (Cannings et al., 1978).
The main function is pedigree_loglikelihood, which calculates
the pedigree likelihood on page 117 of (Lange, 2002) for almost any choice of
genotype frequencies, transmission matrix and penetrance matrix. Helper
functions are provided to calculate the genotype frequencies and transmission
matrices for genetic models that often arise in applications. The function
genotype_probabilities calculates genotype probabilities
for a target person within a family, given the family's phenotypes.
The clipp package can handle pedigree loops, such as those
caused by inbreeding or by two sisters having children with two brothers
from an unrelated family (see (Totir et al., 2009) for a precise definition).
However, pedigrees with more than a few loops could greatly reduce the speed
of the calculation.
It is feasible to apply clipp to very large families. For instance,
in the examples for pedigree_loglikelihood,
the log-likelihood of one family with approximately 10,000 members is calculated
in less than one minute on a standard desktop computer.
Numerical issues will eventually limit the family size,
though clipp takes care to avoid arithmetic underflow and other issues.
Maintainer: James Dowty [email protected]
Authors:
Kevin Wong [email protected]
Cannings C, Thompson E, Skolnick M. Probability functions on complex pedigrees. Advances in Applied Probability, 1978;10(1):26-61.
Elston RC, Stewart J. A general model for the genetic analysis of pedigree data. Hum Hered. 1971;21(6):523-542.
Lange K. Mathematical and Statistical Methods for Genetic Analysis (second edition). Springer, New York. 2002.
Lange K, Elston RC. Extensions to pedigree analysis I. Likehood calculations for simple and complex pedigrees. Hum Hered. 1975;25(2):95-105.
Totir LR, Fernando RL, Abraham J. An efficient algorithm to compute marginal posterior genotype probabilities for every member of a pedigree with loops. Genet Sel Evol. 2009;41(1):52.
A function to calculate the genotype frequencies and the transition matrices
for the joint genotypes of two unlinked genetic loci in linkage
equilibrium, given the corresponding objects for the separate loci.
The results from this function can be used as inputs to
pedigree_loglikelihood or
genotype_probabilities
to model the combined effect of the two loci on phenotypes.
combine_loci(geno_freq1, geno_freq2, trans1, trans2, annotate = FALSE)combine_loci(geno_freq1, geno_freq2, trans1, trans2, annotate = FALSE)
geno_freq1 |
A vector of strictly positive numbers that sum to |
geno_freq2 |
Similar to |
trans1 |
An |
trans2 |
Similar to |
annotate |
A logical flag. When |
This function combines the genotype frequencies and transition
probabilities of two unlinked genetic loci that are in linkage equilibrium
in a given population. Because
the loci are unlinked, any person's genotypes at the two loci are
conditionally independent given his or her parental genotypes,
and because the loci are in linkage equilibrium, the genotypes at the two
loci for a random person from the population are independent.
This function uses these assumptions to calculate the population frequencies
and transition probabilities for the joint genotypes of the two loci, where a
joint genotype is just a pair consisting of a genotype at locus 1
and a genotype at locus 2. If the annotate option is set to FALSE then
these frequencies and probabilities can be used in
pedigree_loglikelihood to model the combined effect of the two
loci on the phenotypes. By a repeated application of this function, more
than two genetic loci can be included in the genetic model.
A list with the following components:
geno_freq |
A vector of strictly positive numbers (the joint genotype
frequencies) that sum to |
trans |
Either a matrix of genetic transmission probabilities suitable to be
used as the |
genotype_decoder |
A data frame giving the locus 1 and locus 2 genotypes
that correspond to each joint genotype. In some cases, this could aid the user's
calculation of the |
pa1 <- c(0.9, 0.1); names(pa1) <- c("-","+") pa2 <- c(0.5, 0.5); names(pa2) <- c("A","a") (geno_freq1 <- geno_freq_monogenic(pa1, TRUE)) (geno_freq2 <- geno_freq_monogenic(pa2, TRUE)) (trans1 <- trans_monogenic(2, TRUE)) (trans2 <- trans_monogenic(2)) (cl <- combine_loci(geno_freq1, geno_freq2, trans1, trans2, TRUE)) sum(cl$geno_freq) apply(cl$trans[,-(1:2)], 1, sum)pa1 <- c(0.9, 0.1); names(pa1) <- c("-","+") pa2 <- c(0.5, 0.5); names(pa2) <- c("A","a") (geno_freq1 <- geno_freq_monogenic(pa1, TRUE)) (geno_freq2 <- geno_freq_monogenic(pa2, TRUE)) (trans1 <- trans_monogenic(2, TRUE)) (trans2 <- trans_monogenic(2)) (cl <- combine_loci(geno_freq1, geno_freq2, trans1, trans2, TRUE)) sum(cl$geno_freq) apply(cl$trans[,-(1:2)], 1, sum)
A dataset giving the relationship structure of one large family and phenotypic data on the family members
dat_largedat_large
A data frame with 10,002 rows (corresponding to persons) and the following 6 variables:
indivan individual identifier for each person
motherthe individual identifier of the person's mother
fatherthe individual identifier of the person's father
sexthe person's sex (1 = male, 2 = female)
affthe person's disease status (1 = case, 0 = control)
agethe person's last known age in years (for controls) or age at diagnosis in years (for cases)
Simulated
A dataset giving the relationship structure of 10 families and phenotypic data on the family members
dat_smalldat_small
A data frame with 1018 rows (corresponding to persons) and the following 7 variables:
familyan identifier for each person's family
indivan individual identifier for each person
motherthe individual identifier of the person's mother
fatherthe individual identifier of the person's father
sexthe person's sex (1 = male, 2 = female)
affthe person's disease status (1 = case, 0 = control)
agethe person's last known age in years (for controls) or age at diagnosis in years (for cases)
genothe person's genotype, or blank ("") if not known
Simulated
A function to calculate the unphased genotype frequencies for a single autosomal genetic locus that has given allele frequencies and is at Hardy-Weinberg equilibrium (HWE).
geno_freq_monogenic(p_alleles, annotate = FALSE)geno_freq_monogenic(p_alleles, annotate = FALSE)
p_alleles |
A vector of strictly positive numbers that sum to |
annotate |
A logical flag. When |
For a genetic locus at Hardy-Weinberg equilibrium, the population
allele frequencies at the locus determine the population genotype frequencies;
see Sections 1.2 and 1.3 of (Lange, 2002).
Given a vector p_alleles containing the allele
frequencies, this function returns the frequencies of the possible unphased
genotypes, in a particular order that can be viewed by setting annotate to
TRUE. If the alleles are named 1:length(p_alleles), so that p_alleles[i]
is the frequency of allele i, then the unphased genotypes are named
1/1, 1/2, .... Note that if the output of this function is to be used
as the geno_freq argument of pedigree_loglikelihood
then the annotate option must be set to FALSE.
A vector of strictly positive numbers (the genotype frequencies)
that sum to 1, named with the genotype names if annotate is TRUE.
Lange K. Mathematical and Statistical Methods for Genetic Analysis (second edition). Springer, New York. 2002.
# Genotype frequencies for a biallelic locus at HWE and with a minor allele frequency of 10% p_alleles <- c(0.9, 0.1) geno_freq_monogenic(p_alleles, annotate = TRUE) # Genotype frequencies for a triallelic locus at Hardy-Weinberg equilibrium p_alleles <- c(0.85, 0.1, 0.05) geno_freq_monogenic(p_alleles, annotate = TRUE) sum(geno_freq_monogenic(p_alleles))# Genotype frequencies for a biallelic locus at HWE and with a minor allele frequency of 10% p_alleles <- c(0.9, 0.1) geno_freq_monogenic(p_alleles, annotate = TRUE) # Genotype frequencies for a triallelic locus at Hardy-Weinberg equilibrium p_alleles <- c(0.85, 0.1, 0.05) geno_freq_monogenic(p_alleles, annotate = TRUE) sum(geno_freq_monogenic(p_alleles))
A function to calculate the population frequencies of the phased genotypes at a single autosomal genetic locus that has given allele frequencies and is at Hardy-Weinberg equilibrium. Phased genotypes can be used to investigate parent-of-origin effects, e.g. see (van Vliet et al., 2011).
geno_freq_phased(p_alleles, annotate = FALSE)geno_freq_phased(p_alleles, annotate = FALSE)
p_alleles |
A vector of strictly positive numbers that sum to |
annotate |
A logical flag. When |
For a genetic locus that is at Hardy-Weinberg equilibrium in a particular population, the population allele frequencies at the locus determine the population genotype frequencies; see Sections 1.2 and 1.3 of (Lange, 2002) for the unphased version of this law. When a genetic locus is at Hardy-Weinberg equilibrium, the maternal and paternal alleles of a random person from the population are independent. A phased genotype at a genetic locus is an ordered pair consisting of a maternal and paternal allele at the locus. So to any heterozygous unphased genotype, there are two corresponding phased genotypes, and these two phased genotypes have equal frequencies under Hardy-Weinberg equilibrium.
Given a vector p_alleles containing the allele frequencies,
this function returns the frequencies of the possible phased genotypes,
in a particular order that can be viewed by setting annotate to TRUE.
If the alleles are named 1:length(p_alleles), so that p_alleles[i] is
the frequency of allele i, then the phased genotypes are of the form
1|1, 1|2, ..., where a|b means the maternal allele is a and the
paternal allele is b. Note that if the output of this function is to be
used as the geno_freq argument of pedigree_loglikelihood
then the annotate option must be set to FALSE.
A vector of strictly positive numbers (the genotype frequencies)
that sum to 1, named with the genotype names if annotate is TRUE.
Lange K. Mathematical and Statistical Methods for Genetic Analysis (second edition). Springer, New York. 2002.
van Vliet CM, Dowty JG, van Vliet JL, et al. Dependence of colorectal cancer risk on the parent-of-origin of mutations in DNA mismatch repair genes. Hum Mutat. 2011;32(2):207-212.
# Genotype frequencies for a biallelic locus at Hardy-Weinberg equilibrium # and with a minor allele frequency of 10% p_alleles <- c(0.9, 0.1) geno_freq_phased(p_alleles, annotate = TRUE) # Genotype frequencies for a triallelic locus at Hardy-Weinberg equilibrium p_alleles <- c(0.85, 0.1, 0.05) geno_freq_phased(p_alleles, annotate = TRUE) sum(geno_freq_phased(p_alleles))# Genotype frequencies for a biallelic locus at Hardy-Weinberg equilibrium # and with a minor allele frequency of 10% p_alleles <- c(0.9, 0.1) geno_freq_phased(p_alleles, annotate = TRUE) # Genotype frequencies for a triallelic locus at Hardy-Weinberg equilibrium p_alleles <- c(0.85, 0.1, 0.05) geno_freq_phased(p_alleles, annotate = TRUE) sum(geno_freq_phased(p_alleles))
A function to calculate the genotype frequencies for the hypergeometric polygenic model of (Cannings et al., 1978), see Section 8.9 of (Lange, 2002) for a nice description of this model.
geno_freq_polygenic(n_loci, annotate = FALSE)geno_freq_polygenic(n_loci, annotate = FALSE)
n_loci |
A positive integer, interpreted as the number of biallelic
genetic loci that contribute to the polygene. The polygene will have
|
annotate |
A logical flag. When |
The hypergeometric polygenic model
(Cannings et al., 1978; Lange, 2002) is a computationally feasible
genetic model that approximates the combined effect of a given number
(n_loci) of unlinked biallelic genetic loci. This model is often used to model
the effect of such loci on a trait when the alleles at these loci either
increase the trait by a certain, locus-independent amount (if a 'positive'
allele) or decrease
the trait by the same amount (if a 'negative' allele), with 'positive' and
'negative' alleles equally likely at each locus. In this case, the only
relevant aspect of the 3 ^ n_loci possible joint genotypes is the total number
of 'positive' alleles, so the possible genotypes of
the hypergeometric polygenic model are taken to be 0:(2*n_loci).
The transmission probabilities and genotype frequencies of the hypergeometric
polygenic model approximate these quantities for the combination of the n_loci
biallelic genetic loci described above. Under this model, the polygenic
genotype for each person is approximately normally distributed, and these
genotypes are correlated within families with correlation coefficients
(in non-inbred families) equal to the kinship coefficients (Lange, 2002).
Setting annotate to TRUE names each element of the output vector with
the corresponding genotype. The annotate option must be set to FALSE
if the output of this function is to be used as the geno_freq argument of
pedigree_loglikelihood.
A vector of strictly positive numbers (the genotype frequencies)
that sum to 1, named with the genotype names if annotate is TRUE.
Cannings C, Thompson E, Skolnick M. Probability functions on complex pedigrees. Advances in Applied Probability, 1978;10(1):26-61.
Lange K. Mathematical and Statistical Methods for Genetic Analysis (second edition). Springer, New York. 2002.
geno_freq_polygenic(4, annotate = TRUE) sum(geno_freq_polygenic(4))geno_freq_polygenic(4, annotate = TRUE) sum(geno_freq_polygenic(4))
For a chosen individual within a specified family, calculate the person's conditional genotype probabilities, given the family's phenotypes and relationship structure
genotype_probabilities(target, fam, geno_freq, trans, penet, monozyg = NULL)genotype_probabilities(target, fam, geno_freq, trans, penet, monozyg = NULL)
target |
The individual identifier (an element of |
fam |
A data frame specifying the family's relationship structure,
with rows corresponding to people and columns
corresponding to the following variables (other variables can be included
but will be ignored), which will be coerced to
|
geno_freq |
A vector of strictly positive numbers that sum to |
trans |
An |
penet |
An |
monozyg |
An optional list that can be used to specify genetically
identical persons, such as monozygotic twins, monozygotic triplets,
a monozygotic pair within a set of dizygotic triplets, etc.
Each element of the list should be a vector containing the individual
identifiers of a group of genetically identical persons, e.g. if |
The genotype probabilities are calculated by essentially the same algorithm
as pedigree_loglikelihood;
see there for details. The genotype probabilities only depend on the
connected component of the pedigree that contains target, so the
function first restricts fam and penet to the rows corresponding to this
connected component. For example, if fam is the union of two
unrelated families then this function will restrict to the subfamily
containing target before performing the calculation.
A vector of length length(geno_freq), whose jth element is
the conditional probability that the target person has genotype j,
given the family's relationship structure and phenotypes. A vector of NAs
will be returned if a row of penet consists entirely of zeroes or if
the pedigree is impossible for any other reason
(after restricting fam and penet to the connected component of
the pedigree containing target).
# Read in some sample data data("dat_small", "penet_small") str(dat_small) str(penet_small) # Calculate the genotype probabilities for individual "ora008" in the family "ora" w <- which(dat_small$family == "ora") fam <- dat_small[w, -1] penet <- penet_small[w, ] monozyg <- list(c("ora024", "ora027")) # ora024 and ora027 are identical twins trans <- trans_monogenic(2) geno_freq <- geno_freq_monogenic(p_alleles = c(0.9, 0.1)) genotype_probabilities(target = "ora008", fam, geno_freq, trans, penet, monozyg)# Read in some sample data data("dat_small", "penet_small") str(dat_small) str(penet_small) # Calculate the genotype probabilities for individual "ora008" in the family "ora" w <- which(dat_small$family == "ora") fam <- dat_small[w, -1] penet <- penet_small[w, ] monozyg <- list(c("ora024", "ora027")) # ora024 and ora027 are identical twins trans <- trans_monogenic(2) geno_freq <- geno_freq_monogenic(p_alleles = c(0.9, 0.1)) genotype_probabilities(target = "ora008", fam, geno_freq, trans, penet, monozyg)
For one or more pedigrees, this function calculates the natural logarithm of the pedigree likelihood that is on page 117 of (Lange, 2002), given inputs that correspond to the terms in this formula.
pedigree_loglikelihood( dat, geno_freq, trans, penet, monozyg = NULL, sum_loglik = TRUE, ncores = 1, load_balancing = TRUE )pedigree_loglikelihood( dat, geno_freq, trans, penet, monozyg = NULL, sum_loglik = TRUE, ncores = 1, load_balancing = TRUE )
dat |
A data frame with rows corresponding to people and columns
corresponding to the following variables (other variables can be included
but will be ignored), which will be coerced to
|
geno_freq |
A vector of strictly positive numbers that sum to |
trans |
An |
penet |
An |
monozyg |
An optional list that can be used to specify genetically
identical persons, such as monozygotic twins, monozygotic triplets,
a monozygotic pair within a set of dizygotic triplets, etc.
Each element of the list should be a vector containing the individual
identifiers of a group of genetically identical persons, e.g. if |
sum_loglik |
A logical flag. Return a named vector giving the
log-likelihood of each family if |
ncores |
The number of cores to be used, with |
load_balancing |
A logical flag. When |
This function provides a fast and general implementation of the Elston-Stewart algorithm to calculate the log-likelihoods of potentially large and complex pedigrees. General references for the Elston-Stewart algorithm are (Elston & Stewart, 1971), (Lange & Elston, 1975) and (Cannings et al., 1978).
Each family within dat should be a complete pedigree, meaning that each
person should either have both parental identifiers missing (if a founder)
or both non-missing (if a non-founder), and each (non-missing) mother or
father should have a corresponding row of dat.
Observed genotypes should be incorporated into penet, as described above.
The function can handle pedigree loops, such as those caused by inbreeding or by two sisters having children with two brothers from an unrelated family (see (Totir et al., 2009) for a precise definition), though pedigrees with more than a few loops could greatly reduce the speed of the calculation.
In geno_freq, trans and penet, the order of the possible genotypes
must match, in the sense that the genotype that corresponds to element j
of geno_freq must also correspond to column j of trans and penet,
for each j in 1:length(geno_freq).
Sex-specific genetics, such as X-linked genes or genetic loci with sex-specific
recombination fractions, can be modelled by letting genotypes 1:nm be
the possible male genotypes and letting (nm+1):(nm+nf) be the possible
female genotypes, where nm and nf are the number of possible genotypes
for males and females, respectively. Then, for example, penet[i,j] will
be 0 if j %in% 1:nm and row i of dat corresponds to a female, and
penet[i,j] will be 0 if j %in% (nm+1):(nm+nf) and row i of
dat corresponds to a male.
Either a named vector giving the log-likelihood of each family
or the sum of these log-likelihoods, depending on sum_loglik (see above).
Cannings C, Thompson E, Skolnick M. Probability functions on complex pedigrees. Advances in Applied Probability, 1978;10(1):26-61.
Elston RC, Stewart J. A general model for the genetic analysis of pedigree data. Hum Hered. 1971;21(6):523-542.
Lange K. Mathematical and Statistical Methods for Genetic Analysis (second edition). Springer, New York. 2002.
Lange K, Elston RC. Extensions to pedigree analysis I. Likehood calculations for simple and complex pedigrees. Hum Hered. 1975;25(2):95-105.
Totir LR, Fernando RL, Abraham J. An efficient algorithm to compute marginal posterior genotype probabilities for every member of a pedigree with loops. Genet Sel Evol. 2009;41(1):52.
# Load pedigree files and penetrance matrices data("dat_small", "penet_small", "dat_large", "penet_large") # Settings for a single biallelic locus in Hardy-Weinberg equilibrium # and with a minor allele frequency of 10% geno_freq <- geno_freq_monogenic(c(0.9, 0.1)) trans <- trans_monogenic(2) # In dat_small, ora024 and ora027 are identical twins, and so are aey063 and aey064 monozyg_small <- list(c("ora024", "ora027"), c("aey063", "aey064")) # Calculate the log-likelihoods for 10 families, each with approximately # 100 family members pedigree_loglikelihood( dat_small, geno_freq, trans, penet_small, monozyg_small, sum_loglik = FALSE, ncores = 2 ) # Calculate the log-likelihood for one family with approximately 10,000 family members # Note: this calculation should take less than a minute on a standard desktop computer # Note: parallelization would achieve nothing here because there is only one family str(dat_large) system.time( ll <- pedigree_loglikelihood(dat_large, geno_freq, trans, penet_large) ) ll# Load pedigree files and penetrance matrices data("dat_small", "penet_small", "dat_large", "penet_large") # Settings for a single biallelic locus in Hardy-Weinberg equilibrium # and with a minor allele frequency of 10% geno_freq <- geno_freq_monogenic(c(0.9, 0.1)) trans <- trans_monogenic(2) # In dat_small, ora024 and ora027 are identical twins, and so are aey063 and aey064 monozyg_small <- list(c("ora024", "ora027"), c("aey063", "aey064")) # Calculate the log-likelihoods for 10 families, each with approximately # 100 family members pedigree_loglikelihood( dat_small, geno_freq, trans, penet_small, monozyg_small, sum_loglik = FALSE, ncores = 2 ) # Calculate the log-likelihood for one family with approximately 10,000 family members # Note: this calculation should take less than a minute on a standard desktop computer # Note: parallelization would achieve nothing here because there is only one family str(dat_large) system.time( ll <- pedigree_loglikelihood(dat_large, geno_freq, trans, penet_large) ) ll
dat_large to three genotypesA matrix relating the phenotypes of dat_large to the three unphased
genotypes of a single biallelic, autosomal genetic locus.
The element penet_large[i,j] is the conditional probability of
the phenotypes (i.e. sex, aff and age) of the person
in row i of dat_large, given that
his or her genotype is j (here labelling the genotypes as 1, 2, 3,
where genotype 2 is the heterozygous genotype).
penet_largepenet_large
A matrix with 10,002 rows (corresponding to persons) and 3 columns (corresponding to genotypes).
Simulated
dat_small to three genotypesA matrix relating the phenotypes of dat_small to the three unphased
genotypes of a single biallelic, autosomal genetic locus.
The element penet_small[i,j] is the conditional probability of
the phenotypes (i.e. sex, aff and age) of the person
in row i of dat_small, given that
his or her genotype is j (here labelling the genotypes as 1, 2, 3,
where genotype 2 is the heterozygous genotype).
penet_smallpenet_small
A matrix with 1018 rows (corresponding to persons) and 3 columns (corresponding to genotypes).
Simulated
A function to calculate the transmission matrix for a single autosomal genetic locus with an arbitrary number of alleles and unphased genotypes, based on Mendel's laws of inheritance.
trans_monogenic(n_alleles, annotate = FALSE)trans_monogenic(n_alleles, annotate = FALSE)
n_alleles |
A positive integer, interpreted as the number of possible alleles at the genetic locus. |
annotate |
A logical flag. When |
When annotate is FALSE, this function returns a matrix of
genetic transmission probabilities, whose rows corresponding to the possible
joint parental genotypes and whose columns corresponding to the possible
offspring genotypes. There are ngeno = n_alleles * (n_alleles + 1) / 2 possible
unphased genotypes, and by choosing an order on these genotypes (which can be
viewed by setting annotate to TRUE, see below)
we can label the set of possible genotypes as 1:ngeno.
Then the (ngeno * gm + gf - ngeno, go)th element of the outputted matrix is
the conditional probability that a person has genotype go, given that his
or her biological mother and father have genotypes gm and gf,
respectively.
When annotate is TRUE, the function converts this matrix to a data frame,
adds column names giving the offspring genotype corresponding to each
column, and adds columns gm and gf describing the parental genotypes
corresponding to each row. In this data frame, genotypes are written
in the usual form 1/1, 1/2, ... for the alleles 1:n_alleles.
Note that if the output of this function is to be used as the trans
argument of pedigree_loglikelihood then the annotate option
must be set to FALSE.
Either a matrix of genetic transmission probabilities suitable to be
used as the trans argument of pedigree_loglikelihood
(if annotate is FALSE), or a data frame that is an annotated version of
this matrix (if annotate is TRUE).
# The transition matrix for a biallelic, autosomal locus with unphased genotypes trans_monogenic(2) trans_monogenic(2, annotate = TRUE)# The transition matrix for a biallelic, autosomal locus with unphased genotypes trans_monogenic(2) trans_monogenic(2, annotate = TRUE)
A function to calculate the transmission matrix for a single autosomal genetic locus with an arbitrary number of alleles and phased genotypes, based on Mendel's laws of inheritance. Phased genotypes can be used to investigate parent-of-origin effects, e.g. see (van Vliet et al., 2011).
trans_phased(n_alleles, annotate = FALSE)trans_phased(n_alleles, annotate = FALSE)
n_alleles |
A positive integer, interpreted as the number of possible alleles at the genetic locus. |
annotate |
A logical flag. When |
When annotate is FALSE, a matrix of genetic transmission
probabilities is returned, with rows corresponding to the possible joint
parental genotypes and columns corresponding to the possible offspring
genotypes.
There are ngeno = n_alleles^2 possible phased genotypes,
and by choosing an order on these genotypes (which can be
viewed by setting annotate to TRUE, see below)
we can label the set of possible phased genotypes as 1:ngeno.
Then the (ngeno * gm + gf - ngeno, go)th element of the outputted matrix is
the conditional probability that a person has genotype go, given that his
or her biological mother and father have genotypes gm and gf,
respectively.
When annotate is TRUE, the function converts this matrix to a data frame,
adds column names giving the offspring genotype corresponding to each
column, and adds columns gm and gf describing the parental genotypes
corresponding to each row.
In this data frame, phased genotypes are written in the usual form
1|1, 1|2, ... for the alleles 1:n_alleles, where a|b means the
maternal allele is a and the paternal allele is b.
Note that if the output of this function is to be used as the trans
argument of pedigree_loglikelihood then the annotate option
must be set to FALSE.
Either a matrix of genetic transmission probabilities suitable to be
used as the trans argument of pedigree_loglikelihood
(if annotate is FALSE), or a data frame that is an annotated version of
this matrix (if annotate is TRUE).
van Vliet CM, Dowty JG, van Vliet JL, et al. Dependence of colorectal cancer risk on the parent-of-origin of mutations in DNA mismatch repair genes. Hum Mutat. 2011;32(2):207-212.
# The transition matrix for a biallelic, autosomal locus with phased genotypes trans_phased(2) trans_phased(2, annotate = TRUE)# The transition matrix for a biallelic, autosomal locus with phased genotypes trans_phased(2) trans_phased(2, annotate = TRUE)
A function to calculate the transmission matrix for the hypergeometric polygenic model of (Cannings et al., 1978), see also Section 8.9 of (Lange, 2002) for a nice description of this model.
trans_polygenic(n_loci, annotate = FALSE)trans_polygenic(n_loci, annotate = FALSE)
n_loci |
A positive integer, interpreted as the number of biallelic
genetic loci that contribute to the polygene. The polygene will have
|
annotate |
A logical flag. When |
This function calculates the genetic transmission probabilities
(i.e. the conditional probability of a person's genotype, given his
or her biological parents' genotypes) for the hypergeometric polygenic model,
which is described in geno_freq_polygenic.
When annotate is FALSE,
a matrix of transmission probabilities is returned, with rows
corresponding to the possible joint parental genotypes and columns
corresponding to the possible offspring genotypes.
Setting annotate to TRUE shows which rows and columns correspond to
which genotypes, by adding offspring genotypes as column names and adding
columns gm and gf containing (respectively) the mother's and father's
genotypes. Note that if the output of this function is to be used as the trans
argument of pedigree_loglikelihood then the annotate option
must be set to FALSE.
Either a matrix of genetic transmission probabilities suitable to be
used as the trans argument of pedigree_loglikelihood
(if annotate is FALSE), or a data frame that is an annotated version of
this matrix (if annotate is TRUE).
Cannings C, Thompson E, Skolnick M. Probability functions on complex pedigrees. Advances in Applied Probability, 1978;10(1):26-61.
Lange K. Mathematical and Statistical Methods for Genetic Analysis (second edition). Springer, New York. 2002.
trans_polygenic(4, annotate = TRUE) apply(trans_polygenic(4), 1, sum)trans_polygenic(4, annotate = TRUE) apply(trans_polygenic(4), 1, sum)