  Obesity is widely recognized as a critical and pervasive health concern. We
strive to identify important genetic risk factors from hundreds of thousands of
single nucleotide polymorphisms (SNPs) for obesity. We propose and apply a
novel Quantile Regression with Insight Fusion (QRIF) approach that can
integrate insights from established studies or domain knowledge to
simultaneously select variables and modeling for ultra-high dimensional genetic
data, focusing on high conditional quantiles of body mass index (BMI) that are
of most interest. We discover interesting new SNPs and shed new light on a
comprehensive view of the underlying genetic risk factors for different levels
of BMI. This may potentially pave the way for more precise and targeted
treatment strategies. The QRIF approach intends to balance the trade-off
between the prior insights and the observed data while being robust to
potential false information. We further establish the desirable asymptotic
properties under the challenging non-differentiable check loss functions via
Huber loss approximation and nonconvex SCAD penalty via local linear
approximation. Finally, we develop an efficient algorithm for the QRIF
approach. Our simulation studies further demonstrate its effectiveness.
