1. MMLS-C By : Laurence Bisht References : The Power to Detect Linkage in Complex Diseases Means of Simple LOD-score Analyses. By David A.,Paula Abreu and Susan E. hodge

2. Overview  Introducing the problem.  Goals..  Intuition.  What is MMLS?  What is MMLS-C?  Generating Models.  Results.  Discussion

3. Introducing The Problem … What is it? Analyzing Complex diseases, i.e. analyzing human linkage data.

4. Our Goal Is … Finding the disease gene’s locations.  Limitations : Complex Disease. MOI (Mode Of Inheritance) is unknown. Using all data available, somehow… Get a Powerful Method, stable and reliable one.

5.  What was in Lecture 8… Affected sib pair (ASP) Affected Pedigree Member (APM) Nonparametric linkage (NPL) Fact 1: We need to Exploit all data we have. But… These method’s use ONLY affected family members. Intuition To MMLS-C

6. Intuition Cont. Fact 2:  Maximum Likelihood analysis via LOD- score, assuming we have the inheritance model is most powerful method for finding linkage.

7. Solution 1. Use Maximum likelihood analyzes trying all modes of inheritance.. Why not?  Is it logical? Suppose given a super machine that can do it… how will this work? problem : 1. How will we compare?

8. Solution 2 – MMLS  Choose several models.  Run the Maximum likelihood analyzes for every chosen model- (LOD-score).  Take max(Z) as the test statistic for linkage. This is MMLS – Maximizing the Maximum LOD-Score

9. MMLS – analyzes  Negative sides. 1. Using Several parameters (models), Multiple tests … Result: Increase of type I error. 2. Unknown effect on the statistical power. 3. Most important: Is there a reason to believe that the models we used can lead us somewhere close to the true model?

10. Solving 1 Using Several parameters (models), Multiple tests … Result: Increase of type I error. We will show that: If we perform linkage analyzes twice, once assuming recessive and once assuming dominant, with an arbitrary penetrance of 50% Then : The Z threshold must be increased by at most ~0.3 for Z max <3.

11. Solution facts  Too stringent.. in most cases examined.. Suggestion:  Perform the test twice with the two models proposed.  take arbitrary penetrance (0.5 is good)  take the larger between the two resultant Z max  subtract 0.3 to “correct” the result  It has been shown that: when there is linkage, Z max relatively modest as the penetrance is varied. (relatively little information is lost assuming a single penetrance).

12. Points 2 and 3.  Simulation study will answer them …  Simulation will : Quantify the effect of correction for multiple testing. Examine the power to detect linkage in two cases discussed later…

13. Generating Models  D20,D80- Dominant with 20% and 80% penetrance.  R20,R80- Recessive with 20% and 80% penetrance.  Int10,Int30,Int50,Int80 – Intermediate (i.e. heterozygote penetrance is 10%, 30%, 50%, 80% while the homozygote will always be 90% and 0%).  note that when f2=0 (homozygote penetrance) its simple recessive

14. Generating Models Cont.  The MMLS power is expressed when f2=5-15%.. A hard case…  Additive-3, additive-2: Two loci models. when it is required at least 3, 2 (accordingly) disease alleles at the two loci.

15. Generating Models Cont.  Always one disease locus linked to the marker with recombination fraction (theta = 0.01).  for the additive model the other one is linked and for the other we will examine 3 recombination fractions: 0.1, 0.05, 0.01

16. Simulation Parameters  They examined 14 Generated Models one of each.  On modified version of the Two-locus simulation program for Greenberg (their program)  1000 datasets of 20 families.

17. Simple MMLS-C  Running MMLS for R50 and D50, as previously described.  Correction factor was varied* ~0.24 when Z max < 0.59 ~0.3 when Z max < 0.59 *(according to hodge (1997))

18. Results Table Notice that: Max[D50,R50] < E[raw MMLS] =~ E[MMLS-C]+0.30 < E[True]

19. Power Vs. LOD-Score

22. Power Table

23. Discussion …  Our main goal was : Examine the power to detect linkage using MMLS-C  After we passed over the results we can see the following: MMLS-C doesn’t substantially decrease the power compared with the True MOI. The range of the MMLS-C – TRUE was [0.3,0.7] (except for three case  )

24. ASP Vs. MMLS-C

25. Conclusions  Pro : MMLS-C is a simple method for analyzing complex diseases. Exploits all data available. Reliable. The assumption that the linkage at the locus being tested is critical.  Against : Was tested on small data set. not always the best method.

26. The End!