Over the past decade the technique of choice for identifying disease loci has been association analysis, particularly genome wide association studies (GWAS). Such studies which involve thousands of subjects, assume that finding highly significant statistical differences between marker allele frequencies in case and control populations guarantee that a gene influencing disease expression would be discovered. The statistical tests for single locus disease association are mostly under-powered. If a disease associated causal single nucleotide polymorphism (SNP) operates essentially through a complex mechanism that involves multiple SNPs or possible environmental factors, its effect might be missed if the causal SNP is studied in isolation without accounting for these unknown genetic influences. Single gene studies alone are not adequate when it comes to complex diseases. Most common diseases have a substantial complex genetic etiology and are the outcome of interplay of either more than one genetic factors or possible environmental factors such as SNPs interacting with each other or potential interactions between genes and environmental factors. One could conceivably do a pair-wise test of all SNPs in a GWAS to search for an association but achieving a result with enough statistical significance to survive correction for the number of tests would be difficult. Moreover immense sample size and overwhelming statistical significance is required to correct for number of tests. The amount of time needed to carry such analysis even with advanced CPU power and space is huge. The power to detect association is also reduced in the face of allelic heterogeneity. Thus the existence of multiple alleles at a locus with differing influences on disease affect association detection. Parametric approaches such as logistic regression and various non-parametric approaches have been used
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through years for carrying out genetic interaction studies. None has proved to be the best for all scenarios. Combining multiple tests to get an optimum result may balance pros and cons of existing methods. Varying amounts of LD between disease alleles and marker SNP and differing interactions with alleles at other loci, interaction detection becomes difficult.
Another approach may be to convert the disease-gene or disease SNP model into a one-locus model by adjusting for gene-gene interaction or other epistatic effects that can possibly have a negative effect on the power. The degree of freedom of tests is controlled simultaneously, accounting for the epistatic effect, if any, of the other SNPs or environmental factors on the SNP under study. These SNPs might be in linkage disequilibrium (LD) and/or epistatic with the target-SNP and have a joint interactive influence on the disease under study.

Contents
English Abstract -------------------------------------------------------------------------------------- i
Acknowledgement ------------------------------------------------------------------------------------vii
Table of Contents-------------------------------------------------------------------------------------- viii
List of Figures------------------------------------------------------------------------------------------- xi
List of Tables-------------------------------------------------------------------------------------------- xii
Chapter 1 Introduction -------------------------------------------------------------------------1~11
1.1 Background -------------------------------------------------------------------------1
1.2 Literature Review ------------------------------------------------------------------3
1.3 Specific Aims -----------------------------------------------------------------------8
1.4 Significance -------------------------------------------------------------------------9
Chapter 2 Materials and Methods ---------------------------------------------------------12~26
2.1 Materials ---------------------------------------------------------------------------12
2.2 Methods --------------------------------------------------------------------------- 12
2.3 Ranked Summarizing Scores using non parametric methods ---------------14
2.3.1 Three Non-parametric methods ------------------------------------------14
2.3.2 Summarizing Methods ----------------------------------------------------17
2.3.3 Comparison Methods ----------------------------------------------------- 18
2.3.4 Hypothesis testing ---------------------------------------------------------19
2.3.5 Permutation ----------------------------------------------------------------20
2.4 Propensity Score Adjustment Method -----------------------------------------21
2.4.1 Selection of subset of SNPs ---------------------------------------------23
2.4.2 Estimating PS for SNP--------------------------------------------------- 23
2.4.3 Testing disease association of SNP-------------------------------------24
2.4.4 Repeat step -----------------------------------------------------------------24
2.4.5 Methods of Comparison --------------------------------------------------24
Chapter 3 Results -----------------------------------------------------------------------27~42
3.1 Simulation studies for Ranked Summarized Scores
Using Non-parametric Methods ------------------------------------------------ 27
3.1.1 Design used in SNaP to generate disease associated
interacting SNP--------------------------------------------------------------27
3.1.2 Comparison of Power based on simulation case-control
data with one disease associated loci------------------------------------28
3.1.3 Comparison of Type-I-Error rates based on simulated
case – control data with no disease marker ----------------------------30
3.2 Authentic data analysis using Ranked Summarized Scores
Using Non-parametric Methods--------- ----------------------------------------30
3.2.1 Whole Genome SNP- SNP interactions--------------------------------31
3.2.2 Candidate-region study of 2-way SNP – SNP interaction----------32
3.3 Simulation studies for Propensity Score Adjustment Method --------------34
3.3.1 Design used in SNaP to generate Disease Associated
interacting SNP----------------------------------------------------------35
3.3.2 Comparison of power based on simulated case-control data
with one disease marker---------------------------------------------------35
3.3.3 Comparison of power based on simulated case-control data
with two disease markers which have epistatic
effect on each other------------------------------------------------------36
3.3.4 Comparison of Type-I-Error rates based on simulated case – control
data with no disease marker---------------------------------------------38
3.4 Comparison of P-values using the open source MDR data------------------39
3.5 Application of propensity score adjustment method on
the GAW16 NARAC dataset-----------------------------------------------------40
Chapter 4. Discussions-----------------------------------------------------------------------43~53
Chapter 5. Conclusions and Prospect------------------------------------------------------54~58
References---------------------------------------------------------------------------------------59~68
Appendices -------------------------------------------------------------------69~
Figures ------------------------------------------------------------69
Tables -------------------------------------------------------------71
Programming Code ----------------------------------------------88
Publications ------------------------------------------------------ 96

List of Figures
Figure 1. Power evaluation of Ranked Summarized Score Using
Non-parametric Methods with SSS, MDR and original Non-parametric
scores under 8 epistatic scenarios--------------------------------------------------------------- 69
Figure 2. Power comparison of PSAM, with ULRM, S-MLRM and
PLINK using simulation studies-------------------------------------------------------------------70

List of Tables
Table 1. Methods for detecting disease associated gene-gene interaction--------------71
Table 2. Example of a contingency table using an epistasis scenario-------------------72
Table 3. Penetrance for eight interaction models------------------------------------------73
Table 4. A comparison of Type-I-Error rates for GS, APDS, ES, ZSS,
PCS, SSS, and MDR-----------------------------------------------------------------74
Table 5. Top ranked interactions for a whole genome study using
PCS/ZSS on GAW16 RA dataset--------------------------------------------------75
Table 6. Top ranked interactions for a candidate gene study using
PCS/ZSS on GAW16 RA dataset---------------------------------------------------76
Table 7. Top ranked (Rank = 1) interacting SNPs (Gene) for higher
order interactions using both ZSS and PCS---------------------------------------78
Table 8. Gene functions for genes identified using ZSS/PCS-----------------------------80
Table 9. Parameter specifications for Model1 ~ Model7 for
simulation study using PSAM------------------------------------------------------82
Table 10. Comparison of Type-I-Error rates for PSAM with
ULRM, S-MLRM, and PLINK---------------------------------------------------83
Table 11. Comparison study of P-values of disease-associated
SNPs of PSAM, ULRM, S- MLRM, and PLINK with
Base using open-access MDR dataset------------------------------------------- 84
Table 12. Significant SNPs list reported by PSAM-----------------------------------------85

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