There are many different types of polymorphisms, e.g.:
single nucleotide polymorphism (SNP):
AAACATAG A CCGGTT
AAACATAG C CCGGTT
microsatellite/variable number of tandem repeat (VNTR):
AAACATAG CACACA---- CCGGTT
AAACATAG CACACACA CCGGTT
AAACATAG ACCA CCGGTT
AAACATAG -------- CCGGTT
restriction fragment length polymorphism (RFLP)
Genetic variation in numbers There are ~6 x 10 9 humans on earth, and thus ~12 x 10 9 copies of each autosomal chromosome. Assuming a mutation rate of ~1 x 10 8 , every single nucleotide will be mutated (~12 x 10 9 ) / (~1 x 10 8 ) = ~120 in each new generation of earthlings. Thus, every nucleotide will be polymorphic in Homo sapiens , except for those where variation is incompatible with life. Any 2 chromosomes differ from each other every ~1,000 bp. The 2 chromosomal sets inherited from the mother and the father (each with a length of 3 x 10 9 bp) therefore differ from each other at ~3 x 10 9 / ~1,000 = ~ 3 x 10 6 , or ~3 million, locations.
locus : a position in the DNA sequence, defined relative to others; in different contexts, this might mean a specific polymorphism or a very large region of DNA sequence in which a gene might be located gene : the sum total of the DNA sequence in a given region related to transcription of a given RNA, including introns, exons, and regulatory regions polymorphism : the existence of 2 or more variants of some locus allele the variant forms of either a gene or a polymorphism neutral allele : any allele which has no effect on reproductive fitness; a neutral allele could affect a phenotype, as long as the phenotype itself has no effect on fitness silent allele : any allele which has no effect on the phenotype under study; a silent allele can affect other phenotype(s) and reproductive fitness disease-predisposing allele : any allele which increases susceptibility to a given disease; this should not be called a mutation mutation : the process by which the DNA sequence is altered, resulting in a different allele Definitions of some important terms
Genetics vs. epidemiology: aggregate effects
The sharing of environmental factors among related (as well as unrelated) individuals is hard to quantify as an aggregate.
In contrast, the sharing of genetic factors among related (as well as unrelated) individuals is easy to quantify, because inheritance of genetic material follows very simple rules.
Aggregate sharing of genetic material can therefore be predicted fairly accurately w/o measurements: e.g.
a parent and his/her child share exactly 50% of their genetic material (autosomal DNA)
siblings share on average 50% of their genetic material
a grandparent and his/her grandchild (or half-sibs or avuncular individuals) share on average 25% of their genetic material
genome as aggregate “exposure”: While it is not clear whether an individual has been “exposed” to good or bad factors, “co-exposure” among relatives is predictable.
Use of genetic similarity of relatives
The genetic similarity of relatives, a result of inheritance of copies of the same DNA from a common ancestor, is the basis for
linkage disequilibrium analysis
between close relatives (e.g., identification of human remains, paternity disputes)
between distant groups of individuals from the same species (e.g., analysis of migration pattern)
between different species (e.g., analysis of phylogenetic trees)
identification of conserved DNA sequences through sequence alignment
Relatives are not i.i.d.
Unlike many random variables in many areas of statistics, the phenotypes and genotypes of related individuals are not independent and identically distributed (i.i.d.).
Many standard statistical tests can and/or should therefore not be applied in the analysis of relatives.
Most analyses on related individuals use likelihood-based statistical approaches, due to the modeling flexibility of this very general statistical framework.
“ Mendelian” vs. “complex” traits
“ simple mendelian” disease
genotypes of a single locus cause disease
often little genetic (locus) heterogeneity (sometimes even little allelic heterogeneity); little interaction between genotypes at different genes
often hardly any environmental effects
often low prevalence
often early onset
often clear mode of inheritance
“ good” pedigrees for gene mapping can often be found
often straightforward to map
“ complex multifactorial” disease
genotypes of a single locus merely increase risk of disease
genotypes of many different genes (and various environmental factors) jointly and often interactively determine the disease status
important environmental factors
often high prevalence
often late onset
no clear mode of inheritance
not easy to find “good” pedigrees for gene mapping
difficult to map
Genetic heterogeneity time locus homogeneity, allelic homogeneity locus homogeneity, allelic heterogeneity locus heterogeneity, allelic homogeneity (at each locus) time locus heterogeneity, allelic heterogeneity (at each locus)
Study design different traits different study designs different analytical methods
How to simplify the etiological architecture?
choose tractable trait
Are there sub-phenotypes within trait?
age of onset
combination of symptoms (syndrome)
“ endophenotype” or “biomarker ” vs. disease
quantitative vs. qualitative (discrete)
Dichotomizing quantitative phenotypes leads to loss of information.
simple/cheap measurement vs. uncertain/expensive diagnosis
not as clinically relevant, but with simpler etiology
given trait, choose appropriate study design/ascertainment protocol
“ random” ascertainment vs. ascertainment based on phenotype of interest
single or multiple probands
concordant or discordant probands
pedigrees with apparent “mendelian” inheritance?
singletons, small pedigrees, large pedigrees
account for/stratify by known genetic and environmental risk factors
for rare disease, limited variation in random sample; need for non-random ascertainment
for late-onset diseases, it is difficult/impossible to find multigenerational pedigrees
diagnosis: often difficult, subjective, arbitrary
treatment may cure disease or weaken symptoms, but original disease status is generally still known
of great clinical interest
often more complex etiologically
sufficient variation in random sample; non-random ascertainment may not be necessary or advisable
as no special ascertainment is necessary, any pedigree is suitable
measurement: often straight-forward, reliable
medications and other covariates may influence phenotype
often only of limited/indirect clinical interest
often simpler etiologically
Dichotomizing quantitative phenotypes generally leads to loss of information unaffected affected
Characterization of a quantitative trait center of distribution spread around center symmetry thickness of tails
How can a continuous trait result from discrete genetic variation? Suppose 4 genes influence the trait, each with 2 equally frequent alleles. Assume that at each locus allele 1 decreases the phenotype of an individual by 1, and that allele 2 increases the phenotype by 1. Now, let us obtain a random sample from the population - by coin tossing. Take 2 coins and toss them. 2 tails mean genotype 11, and phenotype of -2. 2 heads mean genotype 22, and phenotype contribution of +2. 1 head and 1 head is a heterozygote (genotype 12), with phenotype of 0. Repeat this experiment 4 times (once for each locus). Sum up the results to obtain the overall phenotype.
Variance decomposition p henotypic variance due to all causes phenotypic variance due to g enetic variation phenotypic variance due to e nvironmental variation
Decomposition of phenotypic variance attributable to genetic variation phenotypic variance due to g enetic variation phenotypic variance due to a dditive effects of genetic variation phenotypic variance due to d ominant effects of genetic variation
-a 0 phenotypic means of genotypes +a AA AB BB d
-a d=0 phenotypic means of genotypes +a AA AB BB If the phenotypic mean of the heterozygote is half way between the two homozygotes, there is “dose-response” effect, i.e. each dose of allele B increases the phenotype by the same amount. In this case, d = 0, and there is no dominance (interaction between alleles at the same polymorphism).
Decomposition of phenotypic variance attributable to environmental variation phenotypic variance due to e nvironmental variation phenotypic variance due to environmental variation c ommon among individuals (e.g., culture, household) phenotypic variance due to environmental variation u nique to an individual
Definition of heritability The proportion of the phenotypic variance in a trait that is attributable to the effects of genetic variation. The absolute values of variance attributable to a specific factor are not important, as they depend on the scale of the phenotype. It is the relative values of variance matter.
Broad sense and narrow-sense heritability The proportion of the phenotypic variance in a trait that is attributable to: - effects of genetic variation (broad sense) - additive effects of genetic variation (narrow sense)
Different degrees of relationship have different phenotypic covariance/correlation (assuming absence of effect of shared environment) first cousins half sibs full sibs parent child phenotypic correlation phenotypic covariance relative pair
MZ and DZ twins have different phenotypic covariance/correlation (assuming equal effect of shared environment) fraternal twins 2x difference identical twins phenotypic correlation phenotypic covariance relative pair
Normal distribution x f(x)
Variance components approach: multivariate normal distribution (MVN) In variance components analysis, the phenotype is generally assumed to follow a multivariate normal distribution: no. of individuals (in a pedigree) n n covariance matrix phenotype vector mean phenotype vector
Variance-covariance matrix The variance-covariance matrix describes the phenotypic covariance among pedigree members. n n structuring matrix scalar variance component (random effect)
“ Sporadic” model: no phenotypic resemblance between relatives In the simplest model, the phenotypic covariance among pedigree members is only influenced by environmental exposure unique to each individual. Shared factors among relatives, such as genetic and environmental factors, do not influence the trait. identity matrix:
Identity matrix f m 3 2 1 1 0 0 0 0 3 0 1 0 0 0 2 0 0 1 0 0 1 0 0 0 1 0 m 0 0 0 0 1 f 3 2 1 m f
Modeling phenotypic resemblance between relatives: “polygenic” model kinship matrix
Kinship and relationship matrix kinship matrix: Each element in the kinship matrix contains probability that the allele at a locus randomly drawn from the 2 chromosomal sets in a person is a copy of the same allele at the same locus randomly drawn from the 2 chromosomal sets in another person. For one individual, = 0.5, assuming absence of inbreeding. relationship matrix: This provides the probability that a given locus is shared identical-by-descent among 2 individuals. This is equivalent to the expected proportion of the genome that 2 individuals share in common due to common ancestry. For one individual, 2 = 1, assuming absence of inbreeding.
Relationship matrix: nuclear family f m 3 2 1 1 0.5 0.5 0.5 0.5 3 0.5 1 0.5 0.5 0.5 2 0.5 0.5 1 0.5 0.5 1 0.5 0.5 0.5 1 0 m 0.5 0.5 0.5 0 1 f 3 2 1 m f
Relationship matrix: half-sibs f1 m 2 1 f2 1 0.25 0.5 0.5 0 2 0.25 1 0 0.5 0.5 1 0.5 0 1 0 0 f2 0.5 0.5 0 1 0 m 0 0.5 0 0 1 f1 2 1 f2 m f1
The likelihood of a hypothesis (e.g. specific parameter value(s)) on a given dataset, L(hypothesis|data), is defined to be proportional to the probability of the data given the hypothesis, P(data|hypothesis):
Because of the proportionality constant, a likelihood by itself has no interpretation.
The likelihood ratio (LR) of 2 hypotheses is meaningful if the 2 hypotheses are nested (i.e., one hypothesis is contained within the other):
Under certain conditions, maximum likelihood estimates are asymptotically unbiased and asymptotically efficient. Likelihood theory describes how to interpret a likelihood ratio.
Inference in heritability analysis H 0 : (Additive) genetic variation does not contribute to phenotypic variation H 1 : (Additive) genetic variation does contribute to phenotypic variation heritability:
Modeling phenotypic resemblance between relatives: “polygenic” model allowing for dominance matrix of probabilities that 2 individuals inherited the same alleles on both chromosomes from 2 common ancestors
7 matrix: nuclear family f m 3 2 1 1 0.25 0.25 0 0 3 0.25 1 0.25 0 0 2 0.25 0.25 1 0 0 1 0 0 0 1 0 m 0 0 0 0 1 f 3 2 1 m f
Inference in heritability analysis H 0 : (Additive) genetic variation does not contribute to phenotypic variation H 1 : (Additive) genetic variation does contribute to phenotypic variation 2 degrees of freedom
Is it reasonable to assume that the only source for phenotypic resemblance among relatives is genetic? No. To overcome this problem, one can try to model shared environment, either in aggregate or broken into specific environmental factors. household matrix: accounts for aggregate of environmental factors shared among individuals living in the same household
Household matrix f m 3 2 1 1 0 0 0 0 3 0 1 0 0 0 2 0 0 1 1 1 1 0 0 1 1 1 m 0 0 1 1 1 f 3 2 1 m f
Inclusion of covariates Measured covariates can easily be incorporated as “fixed effects” in the multivariate normal model of the phenotype, by making the expected phenotype different for different individuals as a function of the measured covariates.
Inclusion of covariates If covariates are not of interest in and of themselves, one can “regress them out” before pedigree analysis. Then use residuals as phenotype of interest in pedigree analysis.
Inference regarding covariates in heritability analysis H 0 : measured covariate Y does not influence phenotype. H 1 : measured covariate Y does influence phenotype.
Inference regarding covariates in heritability analysis H 0 : measured covariate Y does not influence phenotype. H 1 : measured covariate Y does influence phenotype. CAUTION: Related individuals in pedigrees are treated as unrelated. This can easily lead to false positive findings regarding the effect of the covariate!
Choice of covariates Covariates ought to be included in the likelihood model if they are known to influence the phenotype of interest and if their own genetic regulation does not overlap the genetic regulation of the target phenotype. Typical examples include sex and age. In the analysis of height, information on nutrition during childhood should probably be included during analysis. However, known growth hormone levels probably should not be.
Choice of covariates
Choice of covariates
Choice of covariates: special case of treatment/medication
Before treatment/medication of affected individuals unaffected affected
After (partially effective) treatment / medication of affected individuals unaffected affected apparent effect of covariate
Choice of covariates: special case of treatment/medication
If medication is ineffective/partially effective, including treatment as a covariate is worse than ignoring it in the analysis.
If medication is very effective, such that the phenotypic mean of individuals after treatment is equal to the phenotypic mean of the population as a whole, then including medication as a covariate has no effect.
If medication is extremely effective, such that the phenotypic mean of individuals after treatment is “better” than the phenotypic mean of the population as a whole, then including medication as a covariate is better than ignoring it, but still far from satisfying.
Either censor individuals or, better, infer or integrate over their phenotypes before treatment, based on information on efficacy etc.
Be careful in interpretation of heritability estimates While one can attempt to account for shared environmental factors individually or in aggregate, it is notoriously difficult to do so. In contrast to genetics where “co-exposure” among relatives is predictable due to inheritance rules, this is not the case with environmental factors of interest in epidemiology. If environmental co-exposure is not adequately modeled, shared environmental effects tend to inflate the heritability estimate, because shared exposure is generally greater among relatives, such as mimicking the effects of genetic similarity among relatives. Heritability estimates thus are often overestimates.
Be careful in interpretation of heritability estimates Keep in mind that heritability estimates are applicable only to a specific population at a specific point in time.
Heritability of adult height (additive heritability, adjusted for sex and age) OK DK AZ 0.79 647 0.81 675 7449 total 0.63 616 Jiri 0.80 643 SHFS 0.92 737 SAFDS 0.76 903 SAFHS 0.88 324 GAIT 0.83 705 FLS 0.78 2199 TOPS heritability estimate sample size study
Be careful in interpretation of heritability estimates Heritability is a population level parameter, summarizing the strength of genetic influences on variation in a trait among members of the population. It does not provide any information regarding the phenotype in a given individual, such as risk of disease.
Relative risk The risk of disease (or another phenotype) in a relative of an affected individual as compared to the risk of disease in a randomly chosen person from the population.
Relative risk as a function of heritability
Heritability of adult height (additive heritability, adjusted for sex and age) <2 0.4 obesity 3 0.2 NIDDM 9 0.01 schizophrenia 15 0.004 IDDM 75 0.0004 autism sib p phenotype
Be careful in interpretation of heritability estimates
A heritability estimate is applicable only to a specific trait. If you alter the trait in any way, such as inclusion of additional/different covariates, this may alter the estimate and/or alter the interpretation of the finding.
left ventricular mass not adjusted for blood pressure