BIOSTAT516 Statistical Methods in Genetic Epidemiology
Prepared by Stephanie Monks and Kathleen Kerr
Autumn 2005
Handout 4
Aggregation and Segregation Studies I
Aggregation and segregation studies are generally the first step when studying the
genetics of a human trait. Aggregation studies evaluate the evidence for whether
there is a genetic component to a study. They do this by examining whether there is
familial aggregation of the trait. For instance,


Are relatives of diseased individuals more likely to be diseased than the general
population?
Is the clustering of disease in families different from what you’d expect based on the
prevalence in the general population?
Exercise: Twin studies – Consider the following four types of twin pairs. What
comparisons could you make to address whether there is familial aggregation? What
are some of the problems inherent in these comparisons?
Exercise: Suppose we also had data on full sibling who are not twins. (Note: dizygotic
twins are just like regular full siblings from a genetic point of view.) How might this be
useful?
1
BIOSTAT516 Statistical Methods in Genetic Epidemiology
Prepared by Stephanie Monks and Kathleen Kerr
Autumn 2005
Handout 4
Example: Alzheimer’s Disease1 - Studies based on twins have found differences in
concordance rates between monozygotic and dizygotic twins. In particular, 80% of
monozygotic twin pairs were concordant whereas only 35% of dizygotic twins were
concordant. In a separate study, first-degree relatives of individuals (parents,
offspring, siblings) with Alzheimer’s disease were studied. First degree relatives of
patients had a 3.5 fold increase in risk for developing Alzheimer’s disease as compared
to the general population. This was age-dependent with the risk decreasing with ageof-onset.
Segregation analysis moves beyond aggregation of disease and seeks to more
precisely identify the factors responsible for familial aggregation. For instance,




Is the aggregation due to environmental, cultural or genetic factors?
What proportion of the trait is due to genetic factors?
What mode of inheritance best represents the genetic factors?
Does there appear to be genetic heterogeneity?
Definitions
Mode of inheritance – “The manner in which a particular genetic trait or disorder is
passed from one generation to the next. Autosomal dominant, autosomal recessive, Xlinked dominant, X-linked recessive, multifactorial, and mitochondrial inheritance are
examples.”2
Genetic heterogeneity – “The presence of apparently similar characters for which the
genetic evidence indicates that different genes or different genetic mechanisms are
involved in different pedigrees. In clinical settings genetic heterogeneity refers to the
presence of a variety of genetic defects (that) cause the same disease, often due to
mutations at different loci on the same gene, a finding common to many human
diseases including alzheimer's disease, cystic fibrosis, lipoprotein lipase and polycystic
kidney disease.”3
Pedigree – “A diagram of the genetic relationships and medical history of a family using
standardized symbols and terminology.”2
Founder – Individuals in a pedigree whose parents are not part of the pedigree.
1
Bishop T, Sham P (2000) Analysis of multifactorial disease. Academic Press, San Diego.
Genetic Home Reference Glossary, http://ghr.nlm.nih.gov/ghr/glossary
3 Medical Dictionary Search Engine, http://www.books.md/
2
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BIOSTAT516 Statistical Methods in Genetic Epidemiology
Prepared by Stephanie Monks and Kathleen Kerr
Autumn 2005
Handout 4
Mode of Inheritance
Inheritance of a trait can be broken into two classes. A simple Mendelian trait can be
modeled precisely using Mendel’s laws. Generally, these traits are close to completely
penetrant and are a function of a small number of factors. Complex traits are everything
else: traits with all other modes of inheritance and generally involving more than a
single genetic factor, reduced penetrance, and variation due to environmental factors.
On top of all that, there might be interactions between genetic and environmental
factors.
Many statistical methods in genetic epidemiology explicitly model the inheritance for a
trait. A model seeks to mathematically explain the inheritance of a trait. Based on some
assumptions, the model defines the relationship between the train and genetic and/or
environmental factors.
What are an advantage and a disadvantage of using an explicit model?
One distinguishing feature among methods is whether they explicitly model the mode of
inheritance. For methods that explicitly model the mode of inheritance, it is clearly
important to understand the underlying model. However, the performance of all
methods depends on the true underlying mode of inheritance. Therefore, even for
methods that do not explicitly model the mode of inheritance, It is important to have a
good understanding of how factors can come together to affect a trait. This will allow for
a better understanding of how all methods perform.
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BIOSTAT516 Statistical Methods in Genetic Epidemiology
Prepared by Stephanie Monks and Kathleen Kerr
Autumn 2005
Handout 4
Exercise: Characterize the pattern of inheritance one would expect to see in a pedigree
for autosomal dominant and recessive genes. Do the same for x-linked inheritance.
Assume full penetrance.
Dominant autosomal
Recessive autosomal
Dominant X-linked
Recessive X-linked
4
BIOSTAT516 Statistical Methods in Genetic Epidemiology
Prepared by Stephanie Monks and Kathleen Kerr
Autumn 2005
Handout 4
Models of genetic inheritance
What are the basic parts to a model of genetic inheritance?



Population parameters e.g. allele/genotype frequencies
Transmission parameters e.g. P(A transmitted to offspring | AB parent),
recombination fraction
Penetrance parameters
o For a dichotomous trait, a penetrance parameter is defined for each genotype
as the P(trait | genotype).
Exercise: Complete the table below for a discrete and completely penetrant disease
mutation for dominant and recessive modes of inheritance.
Mode of
Inheritance
Dominant
Recessive
P(disease | DD)
P(disease | DN)
P(disease | NN)
o For a quantitative trait, Y, the penetrance function describes the distribution of
the trait conditional on an individual’s genotype, P(Y | genotype).
A quantitative trait controlled by a dominant gene:
A quantitative trait controlled by a recessive gene:
A quantitative trait controlled by an additive gene:
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BIOSTAT516 Statistical Methods in Genetic Epidemiology
Prepared by Stephanie Monks and Kathleen Kerr
Autumn 2005
Handout 4
Exercise: Consider a mutation with dominant mode of inheritance with allele frequency
Pr(D)=p. The goal is to write down the probability that the sibling of a diseased child will
be diseased. In other words, find the following:
P(sibling AND individual are diseased)
P(sibling has disease | diseased individual) 
P(diseased individual)
To figure this out, you need to go through a number of steps using different properties of
probabilities:
1. To calculate the denominator, we must figure out the probability of a diseased
individual. Note that
Pr(disease )   Pr(genotyp e)Pr(disea se | genotype)
ge notypes
2. What types of matings could produce a diseased child and how frequent is each
mating in the population? There will be 5 mating types.
3. For each mating type, what is the probability of producing a pair of diseased
children? Note that given the parental mating type, transmissions to offspring
are independent.
4. Based on the answers to parts 2 and 3, we can calculation the numerator. We often
will need to work with the following equality:
Pr(event ) 
 Pr(mating
type)Pr(e vent | mating type)
mating types
2. Mating Type
2. P(Mating Type)
3. P(affected sib pair|Mating Type)
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BIOSTAT516 Statistical Methods in Genetic Epidemiology
Prepared by Stephanie Monks and Kathleen Kerr
Autumn 2005
Handout 4
Why does it make sense that the probability is near ½ when the allele frequency is
almost 0?
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BIOSTAT516 Statistical Methods in Genetic Epidemiology
Prepared by Stephanie Monks and Kathleen Kerr
Autumn 2005
Handout 4
50
40
30
20
10
0
S ib lin g R isk o f D ise a se G ive n D ise a se d In d ivid u a l
We can also calculate what is referred to as the sibling risk ratio based on a
completely penetrant dominant mutation. The sibling risk ratio is
P(disease | sibling has disease)
. In general, the risk ratio is a function of both the
P(disease)
disease penetrances and the allele frequency of the disease locus. However, since we
assumed a completely dominant mutation (penetrance=1 in the presence of the disease
allele), we end up with a function of just p:
0.0
0.2
0.4
0.6
0.8
1.0
Pr(D)
We will go into detail about such “relative risk ratios” in another handout.
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