1. Mendel-Penetrance Module Presenter: Joseph Kim Mentors: Dr.Kenneth Lange Brian Dolan

2. 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

3. 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

4. Penetrance Our definition: the statistical relationship between genotype and phenotype; the likelihood of the phenotype given the genotype

5. 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

6. Mendel-Penetrance Module  Statistically models penetrance of alleles using pedigree data  Outputs parameters of the fitted model such as μ and σ (normal distribution)

7. 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

8. 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

9. Background-Likelihood Lange, Kenneth. Mathematical and Statistical Methods 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

10. Background-Pen Function  Contains all parameters to be optimized  Example: Probability Density Function N(μ,σ ) http://en.wikipedia.org/wiki/Normal_distribution

11. 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

12. 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)

13. Background-Tran Function Punnett Square

14. 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

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

16. Distribution of Phenotypes The values in the population fit a continuous distribution. Courtesy of Dr. Janet Sinsheimer

17. http://en.wikipedia.org/wiki/Normal_distribution  Different curves have different parameters  Mendel will fit and give parameters for distribution of given data

18. Input files Initialize Parameters θ 0 Calculate L under θ m Find θ m+1 that increases L Output files Repeat until convergence

19. Mendel Files  Input files:  Control.in  Ped.in  Locus.in  Map.in  Var.in  Output file: Mendel.out

20. Mendel.out

21. 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)

22. 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

23. Acknowledgements  Dr. Kenneth Lange  Brian Dolan  Dr. Janet Sinsheimer  Lara Bauman  Dr.Sharp and Dr.Johnston  Dr. Richard Johnston  Socalbsi

24. Bibliography  http://www.uic.edu/classes/bms/bms655/lesson4.html 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://en.wikipedia.org/wiki/Normal_distribution  http://www.ecs.umass.edu/mie/labs/injection/research/process/