Pedigree Analysis and Familial Aggregation
27 April 2020
## Loading required package: kinship2## Loading required package: Matrix## Loading required package: quadprog## Loading required package: igraph##
## Attaching package: 'igraph'## The following objects are masked from 'package:stats':
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## Attaching package: 'FamAgg'## The following object is masked from 'package:igraph':
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## pedigreePackage: FamAgg
Authors: J. Rainer, D. Taliun, C.X. Weichenberger
Modified: 2020-04-27 16:44:25
Compiled: Mon Apr 27 22:04:56 2020
1 Introduction
This package provides basic pedigree analysis and plotting utilities as well as a variety of methods to evaluate familial clustering of cases from a given trait. Identification of families or groups of individuals within families with significant aggregation of cases can aid also in the selection of interesting and promising individuals for whole genome or exome sequencing projects.
For kinship coefficient calculations and pedigree plotting the package relies
and extends the functionality of the kinship2 package [1].
If you use this package please cite Rainer et al. [2].
2 Basic pedigree operations
In the examples below we perform some simple pedigree operations, such as
plotting the pedigree for an individual or family, finding the closest common
ancestor for a set of individuals in a pedigree or retrieving the identifiers
(IDs) of all ancestors for an individual. Basic pedigree information is stored
in FAData objects, thus we first generate such an object from a subset of the
Minnesota Breast Cancer Study provided by the kinship2 package. In the example
below, we generate the FAData providing a data.frame with the pedigree data,
alternatively, the pedigree information could be imported from a file (see
Section 3). Upon data set creation the kinship matrix (i.e. a
matrix containing the kinship coefficient between each pair of individuals in
the whole pedigree) is internally calculated using the functionality from the
kinship2 package [1].
library(FamAgg)
data(minnbreast)
## Subsetting to only few families of the whole data set.
mbsub <- minnbreast[minnbreast$famid %in% 4:14, ]
mbped <- mbsub[, c("famid", "id", "fatherid", "motherid", "sex")]
## Renaming column names.
colnames(mbped) <- c("family", "id", "father", "mother", "sex")
## Defining the optional argument age.
endage <- mbsub$endage
names(endage) <- mbsub$id
## Create the object.
fad <- FAData(pedigree = mbped, age = endage) We can access all the pedigree information stored in this object using the
pedigree method, but also using $. The row names of the pedigree
data.frame as well as the names of the vectors returned by $ are the IDs of
the individuals in the pedigree.
## Use the pedigree method to access the full pedigree
## data.frame,
head(pedigree(fad))## family id father mother sex
## 1 4 1 NA NA M
## 2 4 2 NA NA F
## 3 4 3 25 4 F
## 4 4 4 1 2 F
## 5 4 5 1 2 M
## 6 4 6 1 2 M## or access individual columns using $.
## The ID of the father (0 representing "founders"):
head(fad$father)## 1 2 3 4 5 6
## NA NA 25 1 1 1## Mother:
head(fad$mother)## 1 2 3 4 5 6
## NA NA 4 2 2 2## Sex:
head(fad$sex)## 1 2 3 4 5 6
## M F F F M M
## Levels: M F## We can also access the age of each individual, if
## provided.
head(age(fad)) ## 1 2 3 4 5 6
## NA 78.05886 55.50000 48.00000 75.00342 53.63997To extract the pedigree for a single family we can use the family method,
specifying either the ID of the family or the ID of an individual in the family.
## Extract the pedigree information from family "4"...
nrow(family(fad, family = 4))## [1] 43head(family(fad, family = 4))## family id father mother sex
## 1 4 1 NA NA M
## 2 4 2 NA NA F
## 3 4 3 25 4 F
## 4 4 4 1 2 F
## 5 4 5 1 2 M
## 6 4 6 1 2 M## ...which is the same as extracting the family pedigree
## for an individual of this family.
head(family(fad, id = 3))## family id father mother sex
## 1 4 1 NA NA M
## 2 4 2 NA NA F
## 3 4 3 25 4 F
## 4 4 4 1 2 F
## 5 4 5 1 2 M
## 6 4 6 1 2 M## Note that IDs are internally always converted to character,
## thus, using id=3 and id="3" return the same information.
head(family(fad, id = "3")) ## family id father mother sex
## 1 4 1 NA NA M
## 2 4 2 NA NA F
## 3 4 3 25 4 F
## 4 4 4 1 2 F
## 5 4 5 1 2 M
## 6 4 6 1 2 MAlternatively, we could subset the FAData to individuals of a single family.
## Subset the object to a single family.
fam4 <- fad[fad$family == "4", ]
table(fam4$family) ##
## 4
## 43To explore this family we can plot its pedigree. By default, the plotting
capabilities of the kinship2 package are used to plot pedigrees, but
alternatively, if all required dependencies are available, the HaploPainter
[3] perl script (http://haplopainter.sourceforge.net/) can be
used instead. The switchPlotfun function can be used to switch the plotting
back-end. Available arguments are ks2paint and haplopaint for kinship2 and
HaploPainter plotting, respectively. Note however, that HaploPainter only
allows to export plots to a file, while kinship2 plotting allows, in addition
to export the plot, also to show it as a standard R plot.
Below we use the switchPlotfun to ensure the use of kinship2 plotting
(usually not required) and plot the full available pedigree of individual 3.
If the age of individuals is available, it will be plotted below the
individual’s ID.
switchPlotfun("ks2paint")
## By supplying device="plot", we specify that we wish to visualize the
## pedigree in an R plot. This is the default for "ks2paint", anyway.
plotPed(fad, id = 3, device = "plot") 
The pedigree for an individual or a list of individuals can be extracted using
the buildPed method. By default the method first tries to identify all parents
up to 3 generations in the pedigree, and subsequently all children of the
individuals and all identified parents.
## Build the pedigree for individual 3.
fullPed <- buildPed(fad, id = "3")
nrow(fullPed) ## [1] 29Alternatively, we can extract the smallest possible pedigree for a list of
individuals by specifying prune=TRUE. Internally, the function transforms the
pedigree into a graph, tries to find all paths between the individuals and
returns the sub-graph of all individuals along with individuals along the paths
between them.
## Find the subpedigree for individuals 21, 22 and 17.
buildPed(fad, id = c(21, 22, 17), prune = TRUE) ## family id father mother sex
## 3 4 3 25 4 F
## 4 4 4 1 2 F
## 1 4 1 NA NA M
## 8 4 8 1 2 F
## 17 4 17 28 8 M
## 21 4 21 24 3 M
## 22 4 22 24 3 F
## 2 4 2 NA NA F
## 25 4 25 NA NA M
## 28 4 28 NA NA M
## 24 4 24 NA NA MAnd the pedigree plot for that subset of the whole family:
plotPed(fad, id = c(21, 22, 17), prune = TRUE) 
Note that the pedigree returned by the buildPed method for an individual might
be different than the pedigree of a whole family. The pedigree returned by
buildPed contains only individuals that share kinship with the specified
individual. To exemplify this, we plot the pedigree for the family 14 in the
Minnesota Breast Cancer data set. Note that the individuals in the pedigree plot
depicted as diamonds are individuals with unknown gender. (The message “Did not
plot…” is issued by the kinship2 plotting function and indicates singletons
that are assigned to the family but do neither have parents nor children.)
plotPed(fad, family = "14", cex = 0.4) 
## Did not plot the following people: 457 463 470 471 26067 26068 26098 26099In this family, founder 441 is the founder of two family branches. Building
the pedigree for individual 440 will not include any of the individuals of the
second branch, as he does not share kinship with any of them. The pedigree built
for 447 on the other hand contains also individuals from the second branch as
she shares kinship with them (via her mother 441).
## Check if we have individual 26064 from the second branch in the pedigree
## of individual 440.
any(buildPed(fad, id = "440")$id == "26064")## [1] FALSE## What for the pedigree of 447?
any(buildPed(fad, id = "447")$id == "26064") ## [1] TRUEA family pedigree may consist of many founder couples (i.e. individuals for
which neither father nor mother is defined in the pedigree). To identify the
pedigree’s founder couple (being the couple with the largest number of offspring
generations in the pedigree) the findFounders method can be used. Note that
the function returns always only one couple, even if there might be two founder
couples in the family pedigree with the same number of offspring generations.
## Find founders for family 4.
findFounders(fad, "4") ## [1] "1" "2"Alternatively, it might be of interest to determine the closest common ancestor
between individuals in a pedigree. Below we use the getCommonAncestor method
to identify the common ancestor for individuals 21, 22 and 17 (which we
know from the pedigree a bit above are 1 and 2).
## Find the closest common ancestor.
getCommonAncestor(fad, id = c(21, 22, 17)) ## [1] "1" "2"Other useful methods are getChildren, getAncestors and getSiblings, that
return the children (or all offspring generations up to a specified level), the
parents (or all ancestors) or the siblings for the specified individuals,
respectively.
## Get the children of ID 4.
getChildren(fad, id = "4", max.generations = 1)## [1] "3"## Get the offsprings.
getChildren(fad, id = "4")## [1] "3" "21" "22" "23"## Get all ancestors.
getAncestors(fad, id = "4")## [1] "1" "2"## Get the siblings.
getSiblings(fad, id = c("4")) ## [1] "4" "5" "6" "7" "8" "9" "10"In the whole Minnesota Breast Cancer data set there are 426 families corresponding to 426 founders that had cancer during the screening phase between 1944 and 1952. In the code block below we identify the affected founders per family.
## Add the trait information to the FAData object.
cancer <- mbsub$cancer
names(cancer) <- as.character(mbsub$id)
trait(fad) <- cancer
## Identify the affected founders.
## First all affected individuals.
affIds <- affectedIndividuals(fad)
## Identify founders for each family.
founders <- lapply(unique(fad$family), function(z){
return(findFounders(fad, family = z))
})
names(founders) <- unique(fad$family)
## Track the affected founder.
affFounders <- lapply(founders, function(z){
return(z[z %in% affIds])
})
## Interestingly, not all founders are affected! It seems in some cases
## parents of the affected participants in the screening phase have also
## been included.
affFounders <- affFounders[unlist(lapply(affFounders, length)) > 0]
## The number of families analyzed.
length(founders)## [1] 10## The number of families with affected founder.
length(affFounders)## [1] 2Unexpectedly, only in few families one of the founders is affected. For the other families additional (unaffected) ancestors might have been added at a later time point.
Next we get the number of affected individuals that are related to these affected founders.
kin2affFounders <- shareKinship(fad, unlist(affFounders))
## How many of these are affected?
sum(kin2affFounders %in% affIds)## [1] 7## How many affected are not related to an affected founder?
sum(!(affIds %in% kin2affFounders))## [1] 212.1 Pedigree analysis methods
In this section we perform some more advanced pedigree operations. First, we
identify all individuals in the pedigree that share kinship with individual 4.
## Get all individuals sharing kinship with individual 4.
shareKinship(fad, id = "4") ## [1] "1" "2" "3" "4" "5" "6" "7" "8" "9" "10" "11" "12" "13" "14" "15"
## [16] "16" "17" "18" "19" "20" "21" "22" "23"Next, we determine generations within the pedigree. Generations can only be
estimated for a single family, since in most instances e.g. the year of birth is
not available. Thus, generations are estimated considering the relation between
individuals, starting from the founder couple, i.e. generation 0, assigning
generation 1 to their children and all the mates of their children and so
on. The estimateGenerations method calculates such generation numbers for each
family defined in the object (or for a single family, if the family ID is
provided). The result is returned as a list with the list names corresponding to
the family ID and the list elements being the estimated generation numbers (with
names corresponding to the ID of the respective individual).
## Estimate generation levels for all families.
estimateGenerations(fad)[1:3] ## $`4`
## 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
## 0 0 2 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3 2 1 1
## 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43
## 1 1 1 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
##
## $`5`
## 44 45 46 47 48 49 50 51 52 53 54 55 56
## 0 0 2 2 2 2 2 2 2 2 1 3 3
## 57 58 59 60 61 62 63 64 65 66 67 68 69
## 3 3 3 3 3 3 3 3 2 2 2 NA 2
## 70 71 72 73 74 75 76 77 78 79 26050 26051
## 1 NA NA NA NA NA NA NA NA 2 NA NA
##
## $`6`
## 80 81 82 83 84 85 86 87 88 89 90 91 92
## 0 0 2 2 1 1 1 1 1 1 1 1 1
## 93 94 95 96 97 98 99 100 101 102 103 104 105
## 1 2 2 2 2 2 2 2 3 3 3 3 2
## 106 107 108 109 110 111 112 113 114 115 116 117 118
## 2 1 1 1 NA NA NA NA 2 NA NA NA NA
## 26052 26053
## 3 3Individuals without generation level (i.e. with an NA) are not connected to
any other individual in the pedigree (and thus most likely represent errors in
the pedigree).
In addition, it is also possible to calculate generation levels relative to a (single) specified individual:
gens <- generationsFrom(fad, id = "4") We can render these generation numbers into the pedigree:
plotPed(fad, family = 4, label2 = gens) 
## Did not plot the following people: 30 31 32 33 34 35 36 37 38 39 40 41 42 432.2 Additional plotting options
If a trait information is available it might be of interest to highlight
affected individuals in the pedigree. Trait information should always be coded
as 0 (or FALSE) for unaffected and 1 (or TRUE) for affected. In the
example below, we use the cancer information from the Minnesota Breast Cancer
Study.
## Extract the cancer trait information.
tcancer <- mbsub$cancer
names(tcancer) <- mbsub$id
## Set the trait.
trait(fad) <- tcancerWe can now extract the trait information from the object or identify directly the phenotyped or affected individuals.
## Extract the trait information.
head(trait(fad))## 1 2 3 4 5 6
## 0 0 0 1 0 0## We can also extract the IDs of the affected individuals.
head(affectedIndividuals(fad))## [1] "4" "11" "37" "54" "84" "122"## Or the IDs of the phenotyped individuals.
head(phenotypedIndividuals(fad)) ## [1] "1" "2" "3" "4" "5" "6"Plotting a FAData object with trait information results in a pedigree plot
with highlighted affected individuals (for kinship2 pedigree plotting:
affected, unaffected and not phenotyped are represented as filled symbols, open
symbols and symbols with a question mark inside, respectively).
## Plotting the pedigree for family "9".
plotPed(fad, family = "9") 
## Did not plot the following people: 200 204 206 210 212 214 215 216 217 219In addition, we can manually highlight individuals using the highlight.ids
argument. For kinship2 pedigree plotting, a list of length 2 is supported as
argument highlight.ids, with the first element being plotted on the top left
corner of the symbol and the second element on the top right corner.
## Plotting the pedigree for family "9".
plotPed(fad, family = "9", highlight.ids = list(a = c("185", "201", "198"),
b = c("193"))) 
## Did not plot the following people: 200 204 206 210 212 214 215 216 217 219An alternative way to highlight individuals or add text to the plot is to use
the arguments label1, label2 and label3 or the plotPed method.
2.3 Graph utilities
Pedigrees can also be transformed to graphs using the ped2graph function. That
way all graph theory methods implemented in e.g. the igraph package can be
applied to pedigrees.
## Transform the full pedigree to a graph.
fullGraph <- ped2graph(pedigree(fad))
## In addition, build the graph for a single family.
singleFam <- ped2graph(family(fad, family=4)) We can plot these pedigrees also as graph and could use any of the layout
methods provided in the igraph package.
## Build the layout.
plot(fullGraph)
Figure 1: Pedigrees represented as graphs
lay <- layout_(singleFam, on_grid())
plot(singleFam, layout = lay) 
Figure 2: Pedigrees represented as graphs
The connectedSubgraph function implemented in the FamAgg package provides
additional functionality to find the smallest connected subgraph of a list of
submitted nodes (i.e. individuals).
In the code below we want to extract the smallest possible connected subgraph of
the pedigree-graph of family 4 containing individuals 7, 8, 27 and 17.
subgr <- connectedSubgraph(singleFam, nodes = c("7", "8", "27", "17")) This is in principle what the buildPed method with the option prune=TRUE
does to find the smallest pedigree for a set of individuals, only that
buildPed ensures that also eventually missing parents are added.
## Plot the graph.
plot(subgr)
## Similar to buildPed/plotPed with prune=TRUE.
plotPed(fad, id=c("7", "8", "17", "27"), prune=TRUE) ## Removing singletons... none present.
3 Importing and exporting pedigree data
Besides providing the pedigree data as a data.frame, the FAData constructor
can also read pedigree data from various file formats, such as plink
[4] ped or fam files
(http://pngu.mgh.harvard.edu/~purcell/plink/data.shtml) or generic text files.
## Import a "ped" file.
pedFile <- system.file("txt/minnbreastsub.ped.gz", package = "FamAgg")
## Quick glance at the file.
readLines(pedFile, n = 1)## [1] "4\t1\t0\t0\t1\t1"fad <- FAData(pedFile)
head(pedigree(fad))## family id father mother sex
## 1 4 1 <NA> <NA> M
## 2 4 2 <NA> <NA> F
## 3 4 3 25 4 F
## 4 4 4 1 2 F
## 5 4 5 1 2 M
## 6 4 6 1 2 MAlternatively, we can import pedigree data from generic input files.
## Create the FAData by reading data from a txt file.
pedFile <- system.file("txt/minnbreastsub.txt", package = "FamAgg")
fad <- FAData(pedigree = pedFile, header = TRUE, id.col = "id",
family.col = "famid", father.col = "fatherid",
mother.col = "motherid")And we can export pedigree data again using the export method. In the example
below, we subset the whole pedigree to the pedigree of family 4 and export this
as a ped file.
tmpF <- tempfile()
## Subset the pedigree to family 4
fam4 <- fad[fad$family == 4, ]
## Export data in ped format.
export(fam4, tmpF, format = "ped") 4 Testing for familial aggregation
Familial aggregation aims to identify families within large ancestral pedigrees that show a non-random aggregation of traits.
As an example, we analyze here data from the Minnesota Breast Cancer Record,
which is provided by the kinship2 package. In brief, this data set consists of
genealogical information from 426 unrelated founders diagnosed with breast
cancer whose families entered a longitudinal study on cancer in the state of
Minnesota (USA) in 1944. Cancer cases are encoded with a 1 in column cancer
in the minnbreast data.frame. Note however that, besides breast cancer, also
prostate cancer cases are reported. This unfortunately causes a systematic bias
in the data set as families were only included if a founder was diagnosed with
breast cancer, but all occurrences of both breast and prostate cancer are
reported. Based on this bias many of the results below should be taken with
caution. Another important information is provided in column endage, which
represents either the age of cancer onset, the age at the end of the study or
the age at death of the participant.
Note that, to reduce computation time, we perform the analysis only on a subset
of families from the Minnesota Breast Cancer record and reduce the number of
simulation runs. We specifically selected some families with a high percentage
of cancer cases, thus, the analysis presented here is biased. Also, in a real
analysis you should increase the nsim argument.
library(FamAgg)
set.seed(18011977)
data(minnbreast)
## Subset the dataset to reduce processing time.
mbsub <- minnbreast[minnbreast$famid %in% c(4:100, 173, 432), ]
## Uncomment the line below to use the whole dataset instead.
## mbsub <- minnbreast
## Define the number of simulations we perform.
## nsim <- 10000
nsim <- 1000
mbped <- mbsub[, c("famid", "id", "fatherid", "motherid", "sex")]
## Renaming column names.
colnames(mbped) <- c("family", "id", "father", "mother", "sex")
## Create the FAData object.
fad <- FAData(pedigree = mbped)
## Define the trait.
tcancer <- mbsub$cancer
names(tcancer) <- as.character(mbsub$id) In the following section we analyze the data set first using the genealogical index method [5] (Section 4.1), then we estimate the per-individual risk of disease using the familial incidence rate (FIR, also abbreviated as FR in the original work) [6] (Section 4.2) and apply our kinship sum test to identify affected individuals exhibiting a higher relationship to other affected individuals than what would be expected by chance (Section 4.3). Subsequently, we apply our kinship group test (Section 4.4) that allows to identify highly clustered affected individuals within families.
The genealogical index of familiality and the familial incidence rate test are well established methods while the kinship sum test and the kinship group test are novel approaches presented here for the first time.
4.1 Genealogical index of familiality
We next calculate the genealogical index of familiality (GIF) [5] (referred to as the genealogical index in the original work) for cancer occurrence in a subset of the Minnesota Breast Cancer Record data set. For a given trait (e.g. whether or not an individual was diagnosed with a certain type of cancer), the method computes the mean kinship between affected individuals (cases) in the whole pedigree along with mean kinship values of randomly drawn sets of individuals. The distribution of average kinship values among the control sets is then used to estimate the probability that the observed level of kinship among the cases is due to chance.
Below, we perform the analysis using the genealogicalIndexTest method on the
cancer trait. In its default setting, the genealogicalIndexTest function uses
all phenotyped individuals in the pedigree as control population from which sets
of random samples equal in size to the number of affected are drawn.
Note that by default the function excludes all singletons (i.e. unconnected
individuals in the pedigree) from the analysis. Changing the argument
rm.singletons to FALSE will estimate the GIF on the full data set.
## Calculate the genealogical index of familiality.
gi <- genealogicalIndexTest(fad, trait = tcancer,
traitName = "cancer", nsim = nsim)
## Display the result.
result(gi) ## trait_name total_phenotyped total_affected entity_id entity_ctrls
## 1 cancer 3508 248 1 2804
## entity_affected genealogical_index pvalue padj
## 1 214 192.5102 0.001 0.001The column genealogical index of the result data.frame shown above represents
the mean kinship between all pairs of affected individuals in the pedigree
multiplied by 100000 for easier interpretation. Thus, according to the GIF
test, a clustering of cancer cases is present in the analyzed pedigree. The
output messages from the method call indicate that some individuals have been
excluded from the test since they were either not phenotyped in the trait
(i.e. have a missing value in trait), or are not connected in the family
pedigree (do not share kinship with any other individual in the pedigree after
removing non-phenotyped individuals).
The genealogical index of familiality implementation in this package adds some
more flexibility to the original approach. The definition of the appropriate set
of control individuals from which random samples are drawn can be specified with
the controlSetMethod argument. Also, it is possible to perform a stratified
sampling, e.g. if the group of affected cases in a pedigree consists of 5 female
and 3 male individuals, submitting the sex of each individual in the pedigree
with the argument strata (i.e. strata=fad$sex, with fad being the FAData object
on which the analysis is performed) allows the function to define random control
sets with the same proportion of male/female individuals.
In the next example, we use the getSexMatched function to define the set of
control individuals and also the getExternalMatched submitting the gender
information of each individual. The results from both approaches are essentially
identical, and in the present data set not that useful, as the Minnesota Breast
Cancer data set lists both, breast cancer and prostate cancer in column cancer,
thus, the set of control individuals will contain all individuals with known
sex.
## Calculate the genealogical index of familiality using random sampling from
## a sex matched control set.
giSexMatch <- genealogicalIndexTest(fad, trait = tcancer,
traitName = "cancer", nsim = nsim,
controlSetMethod = "getSexMatched")
## Use an external vector to perform the matching.
## The results are essentially identical.
giExtMatch <- genealogicalIndexTest(fad, trait = tcancer,
traitName = "cancer", nsim = nsim,
controlSetMethod = "getExternalMatched",
match.using = fad$sex) Note that any matching or stratified sampling can lead to the exclusion of individuals with missing values in either the matching criteria or the strata.
In the Minnesota Breast Cancer data set, the number of prostate cancer cases is much lower than the number of breast cancer cases, thus, simple random sampling might result in an biased genealogical index of familiality estimate since about the same proportion of male and female individuals will be sampled. To account for such cases a stratified sampling, as performed below, can be used instead.
## Evaluate the proportion of male and femal cases.
table(gi$sex[affectedIndividuals(gi)])##
## M F
## 39 206## We can use the gender information to perform stratified sampling, i.e.
## in each permutation a random set of 3 male and 15 females will be selected.
giStrata <- genealogicalIndexTest(fad, trait = tcancer,
traitName = "cancer", nsim = nsim,
strata = fad$sex)
result(giStrata) ## trait_name total_phenotyped total_affected entity_id entity_ctrls
## 1 cancer 3508 248 1 2801
## entity_affected genealogical_index pvalue padj
## 1 214 192.5102 0.001 0.001Finally, we plot the result from the simulation. The blue vertical line in the plot below represents the mean kinship value between all affected individuals in the pedigree. The distribution of mean kinship values from the 1000 randomly drawn sets are shown in grey color.
## Plot the result.
plotRes(giStrata) 
The genealogical index of familiality can also be estimated by the gif
function from the gap R-package. Below we calculate the estimate using both
methods and compare the resulting estimate. Note that the gif method reports
only the genealogical index of familiality estimate but does not estimate
significance.
library(gap)
## Adding the trait information, so the extracted pedigree data.frame will
## also contain a column "affected" with that information.
trait(fad) <- tcancer
## Extract the pedigree and re-format it for the gif function.
pedi <- pedigree(fad)
## Remove singletons.
pedi <- removeSingletons(pedi)
pedi[is.na(pedi$father), "father"] <- 0
pedi[is.na(pedi$mother), "mother"] <- 0
## Identify the affected individuals.
affIds <- as.numeric(pedi$id[which(pedi$affected == 1)])
## Execute the gif method contained in the gap package.
gifRes <- gif(pedi[, c("id", "father", "mother")], affIds)
## Calculate the GIF using FamAgg's genealogicalIndexTest.
gifT <- genealogicalIndexTest(fad, trait = tcancer, nsim = 100)
## Comparing the results:
gifRes[[1]] == result(gifT)$genealogical_index ## [1] FALSEThus, the GIF estimate from the gap package is identical to the one from the
FamAgg package.
In the examples above, we tested for an enrichment of cancer cases in the full
data set, i.e. across all families. In addition, we can perform the test
individually for each family, by setting the perFamilyTest parameter of the
genealogicalIndexTest to TRUE, and thus test for a clustering of cancer
cases within each family.
## Perform the analysis (no strata etc) separately for each family.
giFam <- genealogicalIndexTest(fad, trait = tcancer, nsim = nsim,
perFamilyTest = TRUE,
traitName = "Cancer")
## Display the result from the analysis.
head(result(giFam)) ## trait_name total_phenotyped total_affected entity_id entity_ctrls
## 13 Cancer 3508 248 13 29
## 432 Cancer 3508 248 432 106
## 14 Cancer 3508 248 14 31
## 89 Cancer 3508 248 89 78
## 30 Cancer 3508 248 30 25
## 40 Cancer 3508 248 40 39
## entity_affected genealogical_index pvalue padj
## 13 5 21250.000 0.001 0.0510
## 432 15 9940.476 0.002 0.0510
## 14 5 21250.000 0.003 0.0510
## 89 5 15625.000 0.028 0.3315
## 30 3 25000.000 0.037 0.3315
## 40 3 20833.333 0.039 0.33154.2 Familial incidence rate (FIR)
A per-individual risk of e.g. disease can be calculated using the familial incidence rate (FIR, abbreviated as FR in the original work) [6]. This measure considers the kinship of each individual with any affected in a given trait in the pedigree and the time at risk for each individual. Thus, the FIR is an estimate for the risk per gene-time for each individual given the disease-experience in the cohort.
As time at risk for each individual we use the endage column in the
Minnesota Breast Cancer data set, which represents the participant’s age at the
last follow-up or at cancer incidence. This estimate of time at risk is rather
crude and in a real life situation a better, more accurate, estimate that is
based e.g. on the birth dates and dates of last follow up or incidence might be
used instead. See the help of functions estimateTimeAtRisk and sliceAge for
details and options related to time at risk.
## Estimate the risk for each individual using the familial incidence
## rate method. We use the "endage" provided in the Minnesota Breast Cancer
## Record as a measure for time at risk.
fr <- familialIncidenceRate(fad, trait = tcancer, timeAtRisk = mbsub$endage)A note on singletons: for all per-individual measures unconnected individuals
within the pedigree are automatically excluded from the calculations as no
kinship-based statistics can be estimated for them (they do, by definition, not
share kinship with any other individual in the pedigree, thus their kinship
coefficient with any other individual in the pedigree will be 0). Note also
that the removal of e.g. not phenotyped individuals prior to the calculation can
also generate singletons, that additionally become removed. This removal
results in an estimate with the value NA for all singletons as well as not
phenotyped individuals.
Next, we calculate the mean FIR within each family and plot this information.
## Split the FIR by family and average the values within each.
frFam <- split(fr, f = fad$family)
frFamAvg <- lapply(frFam, mean, na.rm = TRUE)
## Sort and plot the averages.
frFamAvg <- sort(unlist(frFamAvg), decreasing = TRUE)
plot(frFamAvg, type = "h", xaxt = "n", xlab = "", ylab = "mean FIR",
main = "Per family averaged familial incidence rate")
axis(side = 1, las = 2, at = 1:length(frFamAvg), label = names(frFamAvg))
Not unexpectedly, individuals in some families have on average a higher familial incidence rate, and thus a higher risk of cancer than others.
In the next example, we calculate the familial incidence rate assessing in addition the significance of each estimate using Monte Carlo simulations. This extension to the original approach from Kerber [6] does also allow stratified sampling.
## Estimate the risk for each individual using the familial incidence
## rate method. We use the endage provided in the Minnesota Breast Cancer
## Record as a measure for time at risk.
frTest <- familialIncidenceRateTest(fad, trait = tcancer,
traitName = "cancer",
timeAtRisk = mbsub$endage,
nsim = nsim)The familial incidence rate can be extracted easily from the result object using
the familialIncidenceRate method or using $fir. Also, the empirical p-value
from the simulation analysis and the time at risk can be accessed using the $
operator (i.e. using $pvalue, $tar or $timeAtRisk, respectively).
head(familialIncidenceRate(frTest))## 1 2 3 4 5 6
## NA 0.002278208 0.002365165 0.000670492 0.002709228 0.002098398head(frTest$fir)## 1 2 3 4 5 6
## NA 0.002278208 0.002365165 0.000670492 0.002709228 0.002098398Finally, we inspect the results from the analysis.
head(result(frTest))## trait_name total_phenotyped total_affected total_tested id family
## 3185 cancer 3508 248 1778 3185 77
## 7122 cancer 3508 248 1778 7122 173
## 7125 cancer 3508 248 1778 7125 173
## 7123 cancer 3508 248 1778 7123 173
## 7124 cancer 3508 248 1778 7124 173
## 7121 cancer 3508 248 1778 7121 173
## fir pvalue padj
## 3185 0.015789474 0 0
## 7122 0.010449918 0 0
## 7125 0.008874950 0 0
## 7123 0.008848773 0 0
## 7124 0.008587047 0 0
## 7121 0.008249860 0 0We can also identify the families containing individuals with a significant FIR.
frRes <- result(frTest)
frSig <- frRes[which(frRes$padj < 0.05), ]
## Split by family.
frFam <- split(frSig, frSig$family)
frRes <- data.frame(family = names(frFam),
no_sign_fir = unlist(lapply(frFam, nrow)))
## Determine the number of phenotyped and affected individuals per family.
noPheNAff <- sapply(names(frFam), function(z){
fam <- family(frTest, family = z)
return(c(no_pheno = sum(!is.na(fam$affected)),
no_aff = length(which(fam$affected == 1))
))
})
frRes <- cbind(frRes, t(noPheNAff))
## Display the number of phenotyped and affected individuals as well as
## the number of individuals within the families with a significant FIR.
frRes[order(frRes[, "no_sign_fir"], decreasing = TRUE), ] ## family no_sign_fir no_pheno no_aff
## 432 432 12 123 15
## 173 173 8 35 10
## 77 77 1 68 5We have an enrichment of affected cases in families 173, 13 and 432.
4.3 Kinship sum test
Next, we use the kinship sum test that evaluates familial aggregation based on
the sum of kinship values between affected cases. The test identifies affected
individuals exhibiting a higher relationship to other affected individuals than
would be expected by chance. By specifying the strata we perform
sex-stratified random sampling, i.e. ensure that the proportion of male and
female individuals in each randomly sampled group matches the corresponding
proportions in the real, observed, affected.
## Perform the kinship sum test.
kinSum <- kinshipSumTest(fad, trait = tcancer, traitName = "cancer",
nsim = nsim, strata = fad$sex)
head(result(kinSum))## trait_name total_phenotyped total_affected affected_id family affected
## 17528 cancer 3508 248 17528 432 245
## 17517 cancer 3508 248 17517 432 245
## 17529 cancer 3508 248 17529 432 245
## 17547 cancer 3508 248 17547 432 245
## 17548 cancer 3508 248 17548 432 245
## 17549 cancer 3508 248 17549 432 245
## kinship_sum freq pvalue padj
## 17528 2.00 0.0004081633 5.714286e-05 0.004714286
## 17517 1.75 0.0040816327 1.346939e-04 0.004714286
## 17529 1.75 0.0040816327 1.346939e-04 0.004714286
## 17547 1.75 0.0040816327 1.346939e-04 0.004714286
## 17548 1.75 0.0040816327 1.346939e-04 0.004714286
## 17549 1.75 0.0040816327 1.346939e-04 0.004714286Next, we identify those individuals that have a significant kinship sum accepting a 10% false discovery rate (FDR).
## Extract the IDs of the individuals with significant kinship. By default,
## the raw p-values are adjusted for multiple hypothesis testing using the
## method from Benjamini and Hochberg.
kinSumRes <- result(kinSum)
kinSumIds <- as.character(kinSumRes[kinSumRes$padj < 0.1, "affected_id"])
## From which families are these?
table(kinSumRes[kinSumIds, "family"]) ##
## 173 432
## 6 12Thus, most of the identified significant individuals are from two families. Next, we compare the FIR scores of affected or unaffected (but phenotyped) individuals in this family to the FIR scores of affected or unaffected individuals of all other families.
## Get the familial ratio of the significant in this family, of all in
## this family, and of all others.
famId <- kinSumRes[1, "family"]
## Extract the family.
fam <- family(kinSum, family = famId)
## Stratify individuals in affected/unaffected.
strat <- rep("All, unaff.", length(kinSum$id))
strat[which(kinSum$affected > 0)] <- "All, aff."
strat[kinSum$id %in% fam$id] <- paste0("Fam ", famId, ", unaff.")
strat[kinSum$id %in% fam$id[which(fam$affected > 0)]] <-
paste0("Fam ",famId,", aff.")
famData <- data.frame(fr = fr, group = strat)
boxplot(fr~group, data = famData, na.rm = TRUE, ylab = "FIR",
col = rep(c("#FBB4AE", "#B3CDE3"), 2))
As expected, the familial incidence rate (i.e., in the present data set, the risk of individuals to get cancer, given their kinship to other cancer cases) for individuals (whether affected or yet unaffected) in this family is higher than in the data set analyzed here.
Next, we plot the pedigree of this family.
## Plot the pedigree for the family of the selected individual removing
## all individuals that were not phenotypes.
plotPed(kinSum, id = kinSumIds[1], cex = 0.3, only.phenotyped = TRUE)
And finally, also plot the kinship sum for the individuals with the largest kinship sum in relation to the expected kinship sums from the Monte Carlo simulations.
plotRes(kinSum, id = kinSumIds[1]) 
4.4 Kinship group test
Here we apply the kinship group test to the data set. This test first defines for each affected individual a group of individuals considering only individuals that are as closely related as the most distant affected individual. For each of these kinship groups two tests are then performed, one by comparing the mean kinship among affected in the group with the mean kinship from Monte Carlo simulations (ratio test) and one evaluating the largest observed kinship value between affected individuals with those of random samples from the simulation (kinship group test).
In the example below we specify again the strata argument and thus perform
sex-stratified random sampling.
## Calculate the kinship test.
kinGroup <- kinshipGroupTest(fad, trait = tcancer,
traitName = "cancer",
nsim = nsim, strata = fad$sex)
head(result(kinGroup))## trait_name total_phenotyped total_affected phenotyped affected group_id
## 410 cancer 3508 248 1147 174 410
## 2984 cancer 3508 248 1147 174 2984
## 17609 cancer 3508 248 1147 174 17609
## 7117 cancer 3508 248 1147 174 7117
## 17517 cancer 3508 248 1147 174 17517
## 17547 cancer 3508 248 1147 174 17547
## family group_phenotyped group_affected ratio_pvalue ratio_padj
## 410 13 8 5 0 0
## 2984 72 1 2 0 0
## 17609 432 6 5 0 0
## 7117 173 19 8 0 0
## 17517 432 53 13 0 0
## 17547 432 55 14 0 0
## mean_kinship kinship_pvalue kinship_padj
## 410 0.2500000 0 0
## 2984 0.2500000 0 0
## 17609 0.2500000 0 0
## 7117 0.1607143 0 0
## 17517 0.1458333 0 0
## 17547 0.1346154 0 0The kinship group test finds a significant aggregation of cases in families 13, 72, 173 and 432. In fact, as we see further below, the test identified a subgroup in the latter which shows with an exceptional high proportion of cases.
Below, we summarize the results further by listing the total number of families in the pedigree and the number of families in which kinship groups with significant kinship p-value and significant ratio p-value (both at a 5% FDR).
kinGroupRes <- result(kinGroup)
## Create a data.frame with the summarized results.
resTab <- data.frame(total_families = length(unique(kinGroup$family)),
ratio_sign = length(unique(
kinGroupRes[kinGroupRes$ratio_padj < 0.05, "family"]
)),
kinship_sign = length(unique(
kinGroupRes[kinGroupRes$kinship_padj < 0.05, "family"]
))
)
resTab ## total_families ratio_sign kinship_sign
## 1 69 6 9The most significant kinship group identified by the kinship group test is shown
in the figure below. The mother (individual 17609) of the nuclear family
representing this group and all her daughters have cancer (see figure
below). This mother is however not directly related to the affected founder of
this family, individual 17517, but did marry her son (id 17530; see figure above
for the full pedigree of this family 432).
We are also submitting the familial incidence rate values calculated above with
argument label1 which are then displayed below the ID of each individual in the
plot.
plotPed(kinGroup, id = kinGroupRes[kinGroupRes$family == "432",
"group_id"][1],
prune = TRUE, label1 = fr) 
4.5 Binomial test
The binomial test evaluates whether the number of affected in a family (or the
whole pedigree) is significantly higher than what would be expected by chance
(given a probability of being affected in a trait). In contrast to most other
methods this test does not take the degree of kinship between individuals into
account and is hence independent of the family structure in the pedigree. We can
perform this type of test using the binomialTest function on any FAData object
or any object extending it. Below we use the binomial test to evaluate a
significant enrichment of affected individuals in any family in the pedigree.
binRes <- binomialTest(fad, trait = tcancer, traitName = "Cancer")
binResTab <- result(binRes)
head(binResTab) ## trait_name total_phenotyped total_affected family phenotyped affected
## 173 Cancer 3508 248 173 35 10
## 19 Cancer 3508 248 19 24 5
## 432 Cancer 3508 248 432 123 15
## 94 Cancer 3508 248 94 36 6
## 8 Cancer 3508 248 8 37 6
## 14 Cancer 3508 248 14 32 5
## pvalue prob padj
## 173 0.0001101636 0.07069555 0.007601286
## 19 0.0241694261 0.07069555 0.603487360
## 432 0.0273283250 0.07069555 0.603487360
## 94 0.0388827384 0.07069555 0.603487360
## 8 0.0437309681 0.07069555 0.603487360
## 14 0.0720884731 0.07069555 0.766407020The probability used on the binomial test is shown in column "prob" and is in
essence the ratio between the affected and phenotyped in the pedigree
(i.e. 154/2202). This might be an overestimation, especially if the provided
pedigree is not representative of the population. A population-based probability
can however be provided with argument prob. Below we test specifically whether
we have families in which the number of individuals with breast cancer is
significantly higher than expected. To this end we set the trait status of all
male individuals to NA and repeat the test providing the probability of
developing breast cancer during in women, which, according to the U.S. Breast
Cancer Statistics (from breastcancer.org) is 1 out of 8 in their life time.
## Set the trait status to NA for all male individuals.
tcancer[fad$sex == "M" | is.na(fad$sex)] <- NA
## Perform the test providing also the population probability
binRes <- binomialTest(fad, trait = tcancer, prob = 1/8)
binResTab <- result(binRes)
head(binResTab) ## trait_name total_phenotyped total_affected family phenotyped affected
## 14 NA 1990 206 14 15 5
## 19 NA 1990 206 19 12 4
## 13 NA 1990 206 13 18 5
## 94 NA 1990 206 94 18 5
## 8 NA 1990 206 8 19 5
## 173 NA 1990 206 173 19 5
## pvalue prob padj
## 14 0.03107294 0.125 0.9090792
## 19 0.05281048 0.125 0.9090792
## 13 0.06464965 0.125 0.9090792
## 94 0.06464965 0.125 0.9090792
## 8 0.07905037 0.125 0.9090792
## 173 0.07905037 0.125 0.9090792Below we plot the pedigree for the family with the strongest enrichment with affected individuals.
plotPed(binRes, family = 173) ## Warning in kinship2::pedigree(id = individual, dadid = father, momid = mother, :
## More than 25% of the gender values are 'unknown'
## Did not plot the following people: 7135 7141 7143 7144 7145 7146 7148 7149 26800 26811 26812 26813References
1. Sinnwell JP, Therneau TM, Schaid DJ: The kinship2 R package for pedigree data. Human heredity 2014, 78:91–93.
2. Rainer J, Taliun D, D’Elia Y, Pattaro C, Domingues FS, Weichenberger CX: FamAgg: an R Package to Evaluate Familial Aggregation of Traits in Large Pedigrees. Bioinformatics 2016:btw019.
3. Thiele H, Nuernberg P: HaploPainter: A tool for drawing pedigrees with complex haplotypes. Bioinformatics 2005, 21:1730–1732.
4. Purcell S, Neale B, Todd-Brown K, Thomas L, Ferreira MAR, Bender D, Maller J, Sklar P, Bakker PIW de, Daly MJ, Sham PC: PLINK: a tool set for whole-genome association and population-based linkage analyses. American journal of human genetics 2007, 81:559–575.
5. Hill JR: A kinship survey of cancer in the Utah Mormon population. In Cancer incidence in defined populations. Banbury report 4. Edited by Cairns MJ, Lyon JL, Skolnic M. Cold Spring Harbor, NY; 1980:299–318.
6. Kerber RA: Method for calculating risk associated with family history of a disease. Genetic epidemiology 1995, 12:291–301.