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)
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
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
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/