Incorporating Heterogeneity of Maternal Effects for Precisely Detecting Parent-of-Origin Effects

1. Incorporating Heterogeneity of Maternal Effects for Precisely Detecting Parent-of-Origin Effects Jingyuan Yang, Prof. Shili Lin Department of Statistics Ohio State University JSM 2008, Denver, CO

2. Outline Background Existing methods: LL-LRT test and MFG test Proposed Generalized Linear Mixed-Effect Model Simulation Remarks

3. Background Parent-of-Origin Effect (POE): A characteristic follows either a maternal or paternal lineage, rather than following standard Mendelian inheritance patterns Causes of Parent-of-Origin Effect: Genomic imprinting Maternal effect X inactivation Transmission ratio distortion …

4. Background Genomic Imprinting: Unequal expression of the two parental alleles of a gene Maternal Effect: The genotype of a mother is expressed in the phenotype of her offspring, which is usually attributed to maternally-produced molecules, such as mRNAs that are deposited in the egg cell, and antigens that are passed to the offspring during pregnancy

5. Background Genomic imprinting and maternal effect may give rise to similar parent-of-origin patterns Models, which identify imprinting effects by detecting those parent-of-origin patterns, may report false positives that are actually due to maternal effects Goal: Incorporate maternal effects when trying to identify imprinting effects

6. A General Approach • Consider case-parent triads • M, F and C denote maternal, paternal and child’s genotype, respectively. Each takes a value among 0, 1 or 2, indicating the number of disease susceptibility alleles carried by that person • There are 15 possible combinations of familial genotypes. Given the child is a case, probabilities of those 15 combinations sum to 1. Counts of those 15 combinations follow a multinomial distribution

7. Familial Genotype Combinations

8. Existing Methods For each specific MFC combination: Weinberg’s (1998): Log Linear Likelihood Ratio Test Sinsheimer’s (2003): Maternal-Fetal Genotype Incompatibility Test:

9. When maternal effects exist, power of detecting paternal imprinting (excessive maternal expression) is consistently lower.

10. Proposed Method • Multiple sibling • Trimming the nuclear families to get case-parent triads discards some information • Heterogeneity of maternal effects • Different amount of mRNAs and antigens may cause heterogeneous maternal effects

11. Proposed Method • Multiple sibling • Generalized Linear Mixed-Effect Model for Testing Parent-of-Origin Effect (PO-GLMM)

12. Simulation The likelihood for the familial genotype combination given vector D can be decomposed as following: Compute , and simulate the parental genotypes according to the number of affected sibling in that family. Then useto generate the genotype of each child.

13. Remarks Performance of PO-GLMM is under investigation Assess robustness of PO-GLMM under different distributions (discrete, continuous, mixture…) Different support: [0, +∞): Adverse Maternal Effect (-∞, 0]: Protective Maternal Effect (-∞, +∞): Adverse or Protective