| It is widely recognized that genome-wide association studies suffer from inflation of the risk estimates (commonly known as the "winner's curse" or "significance bias") for genetic variants, usually single nucleotide polymorphisms (SNP)s, identified as significant in the genome scan. To handle such significance bias, a number of investigators have proposed using likelihoods that condition on the declared significance of the outcome. We describe an approximate conditional likelihood approach that can be applied using estimates of odds ratios and their standard errors provided by standard statistical software. We also discuss extensions to the situation where, to supplement the primary analysis, risk estimation is performed for multiple correlated phenotypes or gene-environment interactions in the genome scan. The results have considerable importance for the proper design of follow-up studies and risk characterization. Our conditional likelihood approach also lends itself naturally to regression settings, in which shrinkage of multiple coefficients is performed. We use our conditional likelihood to propose a new regression penalty function, and demonstrate that it is competitive with other penalized regression procedures in both low-dimensional and high-dimensional settings. |
