MCMC-Based Linkage Analysis for Complex Traits on General
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MCMC-Based Linkage Analysis for Complex Traits on General Pedigrees: Multipoint Analysis With a Two-Locus Model and a Polygenic Component. Yun Ju Sung Elizabeth A. Thompson and Ellen M. Wijsman. Motivation. Mendel law: A single locus influences a trait Complex Traits

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MCMC-Based Linkage Analysis for Complex Traits on GeneralPedigrees: Multipoint Analysis With a Two-Locus Modeland a Polygenic Component

Yun Ju Sung Elizabeth A. Thompson and Ellen M. Wijsman


Motivation
Motivation

  • Mendel law: A single locus influences a trait

  • Complex Traits

    • multiple loci influence them

    • Mendel law too restrictive

  • Current focus: Two trait Loci

  • Previous approaches have restrictions on

    • Number of markers

    • Pedigree sizes

  • Use of MCMC makes the method scalable.


Background
Background

  • Quantitativeinheritance refers to inheritance of a trait that is attributable to two or more genes and their interaction with the environment

  • Example of Traits:

    • Human Skin color

    • Diabetes

    • Autism

  • Many genes affect these traits and so changing one gene is not enough.


Quantitative trait locus
Quantitative Trait Locus

  • A quantitative trait locus (QTL) is a region of DNA that is associated with a particular trait - these QTLs are often found on different chromosomes

  • Typically, QTLs underlie continuous traits

    • E.g. Height which is continuous

  • Moreover, a single trait is usually determined by many genes. Consequently, many QTLs are associated with a single trait.


Model
Model

  • Z= Q1 + Q2 + V + E

    • Z: Quantitative Trait

    • Q1: QTL effects (discrete)

    • Q2: QTL effects (discrete)

    • V: Polygenic value (normally distributed)

    • E: Environmental Effects (normally distributed)


Now we derive 2 d lod score
Now we derive 2-D LOD score

  • Note that previously we were interested in LOD score of a single QTL (locus)

  • Now we want to derive LOD score of bi-variate QTLs.


My understanding as a bayesnet
My understanding as a Bayesnet

Query: Prob(Z|Y,Q1,Q2)=?

Trait Data

MarkerData

Z

Y

Polygenic value

P

Q1

Q2

S1

S2

G1

G2

Q1 and Q2 are QTL effects

S1 and S2 are segregation indicators at Q1 and Q2

G1 and G2 are genotypes of founders of Q1 and Q2


Sliced and profile lod scores
Sliced and Profile LOD scores

  • When Two QTLs are present, we need two-dimensional lod scores

  • To compare these to one-dimensional LOD scores, the two dimensional LOD scroes are summarized using

    • Sliced LOD score

    • Profile LOD score



Experiments data set
Experiments (Data set)

  • Example 1

    • 300 replicates of ped6 (300ped6)

    • 100 replicates of ped16 (100ped16)

    • 40 replicates of ped52 (40ped52)

  • Example 2

    • 600ped6

    • 100ped16


Experiments
Experiments

  • Competing schemes

    • 2Q+P (two QTLs + polygenic component)

    • 1Q+P

    • 1Q

    • VC model

  • Aim

    • Find Weak and Strong QTL


Example 1 parameters
Example 1 Parameters

QTL1 is weaker than QTL2.

Weak QTL at 15cM

Strong QTL at 55cM

Aim: Find the location of QTL1 and QTL2 using LOD scores





Example 2 paramters
Example 2 paramters

QTL1 is weaker than QTL2.

Weak QTL at 15, 25, 35 and 45 cM

Strong QTL at 55cM

Determine the location of strong and weak QTL using LOD scores





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