  Genetic variants identified to date by genome-wide association studies only
explain a small fraction of total heritability. Gene-by-gene interaction is one
important potential source of unexplained heritability. In the first part of
this dissertation, a novel approach to detect such interactions is proposed.
This approach utilizes penalized regression and sparse estimation principles,
and incorporates outside biological knowledge through a network-based penalty.
The method is tested on simulated data under various scenarios. Simulations
show that with reasonable outside biological knowledge, the new method performs
noticeably better than current stage-wise strategies, especially when the
marginal strength of main effects is weak.
  The proposed method is designed for single-cohort analyses. However, it is
generally acknowledged that only multi-cohort analyses have sufficient power to
uncover genes and gene-by-gene interactions with moderate effects on traits,
such as likely underlie complex diseases. Multi-cohort, meta-analysis
approaches for penalized regressions are developed and investigated in the
second part of this dissertation. Specifically, I propose two different ways of
utilizing data-splitting principles in multi-cohort settings and develop three
procedures to conduct meta-analysis. Using the method developed in the first
part of this dissertation as an example of penalized regressions, three
proposed meta-analysis procedures are compared to mega-analysis using a
simulation study. The results suggest that the best approach is to split the
participating cohorts into two groups.
  In the last part of this dissertation, the novel method developed in the
first part is applied to the Framingham Heart Study measures on total plasma
Immunoglobulin E (IgE) concentrations, C-reactive protein levels, and Fasting
Glucose.
