Mendel-Penetrance Module

Presenter: Joseph Kim

Mentors: Dr.Kenneth Lange Brian Dolan

What is Mendel?

Software package

Performs statistical analysis to solve a variety of genetic problems

http://www.biomath.medsch.ucla.edu/faculty/klange/software.html

Goal

Beta test Mendel’s new Penetrance module

Methods:Find data pertaining to penetrancePlug data into MendelSee if results agree with already established

results

Penetrance

Our definition:

the statistical relationship between genotype and phenotype; the likelihood of the phenotype given the genotype

Incomplete Penetrance-Example

not x-linked (male to male transmission)

Incompletely dominant

II-1 not affected

*color reflects phenotype, not genotype

http://www.uic.edu/classes/bms/bms655/lesson4.html

Mendel-Penetrance Module

Statistically models penetrance of alleles using pedigree data

Outputs parameters of the fitted model such as μ and σ (normal distribution)

Motivation

The output of Mendel can be used for finding disease genes by linkage analysis and association analysis

“Increase power of genetic analysis”

– Brian Dolan

Mendel can be used to determine who’s at risk of being affected with the genetic disease

Why is Mendel Better?

More versatile statistical models and a better ascertainment correction

Commercial software assume that the observations are independent

Better trait models enable better mapping of disease and trait genes

Background-Likelihood

Lange, Kenneth. Mathematical and Statistical Methods

1 { , , }

... Pen( | ) Prior( ) Tran( | , )n

i i j m k li j k l mG G

L X G G G G G

L: the likelihood of the pedigree datan:number of peopleXi:phenotype of ith personGi:possible genotype of ith person

product on j is taken over all foundersproduct on {k,l,m} is taken over all parent-offspring triples

Background-Pen Function

Contains all parameters to be optimizedExample: Probability Density Function

N(μ,σ )

                                           

http://en.wikipedia.org/wiki/Normal_distribution

Generalized Linear Models (GLM)

Normal Distribution is not sufficientIncorporate other GLM to overcome

deficiencies in the normal distributionBinomialPoissonExponentialGammaInverse NormalLognormal

Background-Prior Function

The frequencies of genotypes in population

Typically incorporate Hardy-Weinberg genotype frequenciesAssume different loci are independent

Ex: For two locus trait A/a and B/b,

P(A,b)=P(A)P(b)

Background-Tran Function

Punnett Square

Optimization

Maximize L with respect to parametersOnly concerned with parameters in

Penetrance functionUse Lagrange multipliers to limit values of

parametersUse iterative methods to solve for the

parameters

http://www.ecs.umass.edu/mie/labs/injection/research/process/

Distribution of Phenotypes

The values in the population fit a continuous distribution.

Courtesy of Dr. Janet Sinsheimer

http://en.wikipedia.org/wiki/Normal_distribution

Different curves have different parametersMendel will fit and give parameters for distribution of given data

Input filesInitialize

Parametersθ0

Calculate L underθm

Find θm+1 that increases L Output files

Repeat until convergence

Mendel Files

Input files: Control.in Ped.in Locus.in Map.in Var.in

Output file: Mendel.out

Mendel.out

What Do the Numbers Mean?

Parameters define the probability distribution function of the penetrance; it is a property of the penetrance of the trait

Knowing the parameters will allow more accurate results for research that requires knowledge in these properties (i.e. formulas that depend on these values)

Results

Verified the program using large pedigree segregating high triglycerides

Bugs found: 1Default Scaling factor causing underflow

(Truncation Error) resulting in early termination of the iterations

Acknowledgements

Dr. Kenneth LangeBrian DolanDr. Janet SinsheimerLara BaumanDr.Sharp and Dr.JohnstonDr. Richard JohnstonSocalbsi

Bibliography http://www.uic.edu/classes/bms/bms655/lesson4.html

Sobel E, Papp JC, Lange, K. “Detection and integration of genotyping errors in statistical genetics” Am J Hum Genet. 2002 Feb;70(2):496-508. Epub 2002 Jan 8. PMID: 11791215

Lange, Kenneth. Optimization. Springer-Verlag NY, LLC. New York: 2004.

Lange, Kenneth. Mathematical and Statistical Methods for Genetic Analysis. Second Edition. Springer-Verlag New York, Inc. New York: 2002.

Sinsheimer, Janet. Quantitative Traits slides

http://en.wikipedia.org/wiki/Normal_distribution

http://www.ecs.umass.edu/mie/labs/injection/research/process/