Tutorial #5 by Ma’ayan Fishelson Changes made by Anna Tzemach

1. Detecting Input Errors (Specifically, Genotyping Incompatibilities) Tutorial #5 by Ma’ayan Fishelson Changes made by Anna Tzemach

2. Input Format of Linkage Program • Marker data • Allele frequency • Map position • Pedigree data • Pedigree structure • Genotyping (person allele’s values) • Disease data • Frequency • Penetrance • Program data • What to run, which points and for how long

3. Possible Input Errors • Model errors • Databases are build on specific population: allele frequencies and marker positions can be wrong • Linkage analysis: wrong model • To close markers – Linkage disequilibrium

4. Possible Input Errors • Technology errors • Incorrect genotyping • By PCR: weight of TR (Tandom Repeat) marker • 272.5 is it 272 or 273 repeats • By chip (Affymetrix, Genechip ..) • Deletion are called as homozygote pair

5. Possible Input Errors • Type errors • Incompatibility between the 2 input files (in the number of loci, in the order of specification of the loci,…) • Errors in Locus File: probabilities don’t sum to 1, impossible values for recombination fractions or other probabilities, incompatibility between number of loci and number of loci descriptions… • Errors in Pedigree file: no correspondence between child and parent, pointer problems

6. # of disease loci (0 or 2) SuperlinkLocus File Program code # of loci Number of alleles for 1st locus 3 0 0 5 0 0 0.0 0.0 0 1 2 3 1 2 0.406000 0.594000 3 0.650000 0.322000 0.487000 0.635000 0.349000 0.203000 0.903000 0.473000 0.945000 3 4 0.132000 0.048000 0.299000 0.521000 3 5 0.138000 0.175000 0.055000 0.272000 0.360000 0 0 0.100000 0.100000 1 0.10000 0.30000 Chromosome order of the loci Number of penetrance classes for Affection Status locus Penetrances Affection Status locus (disease locus) Gene frequencies for 2nd locus Numbered Alleles locus (marker) Program-specific Parameters. Recombination values

7. Disease Status: 0=unknown 1=unaffected 2=affected SuperlinkPedigree File Pedigree Number Father’s ID Mother’s ID Next maternal sibling’s ID 1st marker 2nd marker 1 1 0 0 3 0 0 1 0 2 2 3 2 1 1 1 2 0 0 3 0 0 2 0 2 2 1 4 2 2 1 3 1 2 6 4 4 2 0 0 2 4 2 2 1 1 4 1 2 0 0 0 1 0 0 3 1 3 2 1 1 5 0 0 6 0 0 1 0 0 3 4 4 5 4 1 6 5 3 0 7 7 2 0 0 3 2 4 1 4 1 7 5 3 0 8 8 1 0 0 3 4 4 2 4 1 8 5 3 0 0 0 2 0 2 1 4 4 1 5 0 0 0 0 0 0 0 0 Individual’s ID Penetrance Class Sex: 1=male 2=female Marker Alleles (2 alleles per locus) Next paternal sibling’s ID First child’s ID

8. For More information on Superlink visit: http://bioinfo.cs.technion.ac.il/superlink/

9. Genotyping Errors Can be divided into 2 types: • Errors that can be detected when observing one marker. • Errors that can be detected only when observing several adjacent markers.

10. PedCheck (Jeffrey O’connell and Daniel Weeks) • A Program for identification of genotype incompatibilities in Linkage Analysis. • Genotype incompatibilities are detected in 4 stages: • Level 1: performs checks on the nuclear family level. • Level 2: Uses the Lange-Goradia algorithm to perform genotype elimination. • Level 3: Determines “critical genotypes”. • Level 4: Determines alternative typing for the critical genotypes, and finds the most likely person to be mistyped.

11. 1 2 6 3 5 4 4/3 2/1 5/1 4/9 7 4/3 Example 1a – Level 1 errors Assume there are 6 alleles at this marker.. List the errors.

12. 1 1 2 2 3 3 5 5 4 4 4/3 4/4 2/2 2/2 4/1 2/1 Example 1b – Level 1 errors List the errors here.

13. Level 1 Errors • Incompatibility between a child and a parent’s alleles. • A person is half-typed. • More than 4 alleles in a sibship. • More than 3 alleles in a sibship when there is a homozygous child. • More than 2 alleles in a sibship when there are 2 different homozygous children. • The allele is out of bounds.

14. Level 2 Errors • Performs genotype elimination via an extended version of the Lange-Goradia algorithm for set-recoded genotypes. • This algorithm recursively uses the nuclear-family relationships to eliminate invalid genotypes in the pedigree. Continues until no more genotypes can be eliminated. • For each pedigree and locus: identifies the first nuclear family with an error that hasn’t been detected in level 1, and outputs the inferred genotype lists.

15. 1 2 4/3 3/1 4 3 3/1 5 3/2 Example 2 – Level 2 errors

16. Genotype Elimination Algorithm • For each pedigree member, save only ordered genotypes compatible with his/her phenotype. • For each nuclear family: • Consider each mother-father genotype pair: • Determine which zygotes can arise from this pair. • If each child in the nuclear family has one or more of these zygote genotypes among his or her current genotype list, then save the parental genotypes and any child genotype matching one of the created zygote genotypes. • If any child has none of these zygote genotypes among his/her genotype list, then don’t save any genotypes. • For each person in the nuclear family, exclude any genotypes not saved during step (1). • Repeat part (B) until no more genotypes can be excluded.

17. 1 2 O 3 4 A 5 O Genotype Elimination Example

18. Complete Genotype-Elimination Algorithm • A genotype elimination algorithm is complete if it can detect that the set of given genotypes violates Mendelian laws of inheritance. • If a complete genotype elimination algorithm finds no errors  the genotypes are consistent with Menelian laws of inheritance.

19. 1 2 3 4 5 6 7 2/2 1/2 2/3 Genotype Elimination -Another Example.. Is the presented genotype elimination algorithm complete ?

20. Additional Problems.. • The inferred genotype lists don’t always permit easy identification of the source of the problem: • The genotype lists may be long. • More than one individual may be the error source. • The error may not be in the nuclear family reported.

21. Critical Genotypes • Genotypes of an individual that eliminate the pedigree inconsistency when removed from the data (i.e., treated as unknown). • Note: a critical genotype isn’t necessarily erroneous. • Degree n critical genotypes: an n-tuple of genotypes of typed individuals that when treated as unknown simultaneously, the inconsistency is eliminated. • The set of erroneous genotypes is a subset of the critical genotypes.

22. Critical-Genotype Algorithm (Level 3) • Attempts to identify the critical genotypes, if any, in the pedigree. • “Untypes” one typed individual at a time, and applies the genotype-elimination algorithm to determine if the inconsistency has been eliminated. • There may be one or more critical genotypes or there may be none. If there are none, higher-degree critical genotypes can be investigated at a higher cost. • If only one critical genotype is found  this genotype represents the error.

23. 1 2 2/2 3 4 5 1/2 1/1 2/2 Example 3 – Level 3 errors

24. Dilemma… Several critical genotypes have been identified at a locus There’s no way of deciding a priori which one is most likely to be erroneous..

25. Odds-Ratio Algorithm (Level 4) • Helps distinguish between alternative critical genotypes. • Based on single-locus likelihoods of the pedigree. Algorithm Outline: • For each individual with a critical genotype, identify valid typings that eliminate the inconsistency. • Compute the likelihood L of the pedigree data for each alternative typing at each critical genotype, holding all other critical genotypes at their original value. • Let Lmax be the largest likelihood obtained. For each alternative genotype compute the odds ratio Lmax/L. • Return each alternative typing together with its odds ratio.

26. 1 2 2/2 3 4 5 1/2 1/1 2/2 Example 3 – Level 4 Only one consistent alternative typing: 1/2 Two consistent alternative typings: 1/2 & 2/2

27. Odds-Ratio Algorithm (allele frequencies) There are 3 variations: • User-defined allele frequencies. • Assume all alleles are equally frequent. • Estimate allele-frequencies from typed individuals (leads to a bigger spread in odds ratio).

28. 2nd Type of Genotyping Errors • The pedigree data indicates a certain recombination event in an interval where Ө=0. • The pedigree data indicates more (or less) recombination events than expected according to the specified recombination fractions.

29. Error Detection in Merlin • Calculate L(G| Ө) and L(G| Ө=0.5). • For each genotype g: • Mark it as unknown. • Calculate L(G\g| Ө) and L(G\g| Ө=0.5) . • Compute the ratiorlinked = L(G\g| Ө) / L(G| Ө). • Compute the ratiorunlinked = L(G\g| Ө=0.5) / L(G| Ө=0.5). • Compute the statistic r = rlinked /runlinked. • Genotypes that cause inconsistency with neighboring markers result in large values of r.

30. Genotype Elimination in Superlink • Superlink’s algorithm is composed of 2 types of algorithms: • Downward traversal algorithm in which the children are updated according to the parents. • Upward traversal algorithm in which the parents are updated according to the children. • Genotypes are stores as 2 lists of alleles: • Possible paternal alleles. • Possible maternal alleles.

31. Downward Traversal Algorithm • Traverses the pedigree in such a manner that a child is updated by his parent only after the parent has been updated. • The update is performed as follows: • If nothing is known about the child’s genotype, add all the possible alleles of the parent to the child’s relevant allele. • Else, check for each possible allele of the child if it is possible according to the parent.

32. 1 2 1 | 2 3 Example: Downward Update The child 3 can only receive alleles 1 or 2 from his father (2).

33. Upward Traversal Algorithm • Traverses the pedigree in such a manner that a parent is updated by his child only after the child has been updated. • The update is performed as follows: • All the alleles that a child got from the parent for certain are marked. • If two alleles have been marked as certain, the rest of the alleles are erased (the genotype has been determined). • Sometimes the genotype is determined including phase.

34. Example: Upward Update The father (1) must have transmitted alleles 3 & 4 to the children. The mother (2) could only transmitted allele 1 to the children (3 & 4). 1 2 3 | 4 1 | 1 3 4 1 | 4 1 | 3

35. Downward-Upward Algorithm • For each person save possible paternal and maternal alleles • Downward – child updated only after parents • For trios: parents and child: • Update child: • If nothing is known about the child’s genotype, add all the possible alleles of the parent to the child’s relevant allele. • Else, check for each possible allele of the child if it is possible according to the parent. Save only possible. • Upward – parents updated only after child was updates • For trios: parent sand child: • All the alleles that a child got from the parent for certain are marked. • Update parents’ possible alleles. • If two alleles have been marked as certain (one maternal and one paternal), the rest of the alleles are erased (the genotype has been determined). • Repeat till no changes or no possible genotype for one of the people