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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/kla
nge/software.html
Goal
Beta test Mendel’s new Penetrance module
Methods:
Find data pertaining to penetrance
Plug data into Mendel
See 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
L   ...
G1
Gn
 Pen( X
i
i
| Gi ) Prior(G j )
j
 Tran(G
m
| Gk , Gl )
{k ,l , m}
L: the likelihood of the pedigree data
n:number of people
Xi:phenotype of ith person
Gi:possible genotype of ith person
product on j is taken over all founders
product on {k,l,m} is taken over all parent-offspring triples
Lange, Kenneth. Mathematical and Statistical Methods
Background-Pen Function
Contains all parameters to be optimized
Example: Probability Density Function
N(μ,σ )
http://en.wikipedia.org/wiki/Normal_distribution
Generalized Linear Models (GLM)
Normal Distribution is not sufficient
Incorporate other GLM to overcome
deficiencies in the normal distribution
Binomial
Poisson
Exponential
Gamma
Inverse Normal
Lognormal
Background-Prior Function
The frequencies of genotypes in
population
Typically incorporate Hardy-Weinberg
genotype frequencies
Assume 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 parameters
Only concerned with parameters in
Penetrance function
Use Lagrange multipliers to limit values of
parameters
Use 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
Different curves have different
parameters
Mendel will fit and give parameters for
distribution of given data
http://en.wikipedia.org/wiki/Normal_distribution
Input files
Initialize
Parameters
θ0
Calculate L under
θm
Repeat until
convergence
Find θm+1 that
increases L
Output files
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: 1
Default Scaling factor causing underflow
(Truncation Error) resulting in early
termination of the iterations
Acknowledgements
Dr. Kenneth Lange
Brian Dolan
Dr. Janet Sinsheimer
Lara Bauman
Dr.Sharp and Dr.Johnston
Dr. Richard Johnston
Socalbsi
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/