Logistic Bayesian LASSO for Identifying Association with Rare Haplotypes and Application to Age‐Related Macular Degeneration

Abstract

Rare variants have been heralded as key to uncovering "missing heritability" in complex diseases. These variants can now be genotyped using next-generation sequencing technologies; nonetheless, rare haplotypes may also result from combination of common single nucleotide polymorphisms available from genome-wide association studies (GWAS). The National Eye Institute's data on age-related macular degeneration (AMD) is such an example. Studies on AMD had identified potential rare variants; however, due to lack of appropriate statistical tools, effects of individual rare haplotypes were never studied. Here we develop a method for identifying association with rare haplotypes for case-control design. A logistic regression based retrospective likelihood is formulated and is regularized using logistic Bayesian LASSO (LBL). In particular, we penalize the regression coefficients using appropriate priors to weed out unassociated haplotypes, making it possible for the rare associated ones to stand out. We applied LBL to the AMD data and identified common and rare haplotypes in the complement factor H gene, gaining insights into rare variants' contributions to AMD beyond the current literature. This analysis also demonstrates the richness of GWAS data for mapping rare haplotypes-a potential largely unexplored. Additionally, we conducted simulations to investigate the performance of LBL and compare it with Hapassoc. Our results show that LBL is much more powerful in identifying rare associated haplotypes when the false positive rates for both approaches are kept the same.

Kullback–Leibler divergence for detection of rare haplotype common disease association

“…However, there is a continuing realization that rare haplotype variants resulting from common SNVs may also have an important role in understanding complex disease etiology. [2][3][4][5][6][7][8][9][10] The interest in detecting rare haplotype association with common diseases is further fueled by the recognition that rare haplotype may tag rare causal SNVs. [7][8][9][10] There are advantages pursuing rare haplotypes instead of rare SNVs.…”

“…Among such new approaches, the majority use likelihood-based regularization methods (eg, Lasso 15 ) to weed out unassociated haplotypes [3][4][5]7,8 so that those that are associated with the disease, especially the rare ones, can be more precisely estimated for their effects on the trait. However, owing to the difficulty in evaluating the effect of the uncertainty of regularization parameters on assessing association, the Bayesian counterpart of Lasso has been proposed for studying rare haplotype association, 6,9,10 as well as the Bayesian hierarchical GLM approach. 5 Regardless of whether a method is likelihood based or Bayesian formulated, such a method relies on assuming an underlying model connecting the haplotypes to the disease, which, unfortunately, is unknown.…”

“…Although the reference haplotype is typically assumed to be the one with the largest frequency, such an assumption can be erroneous and can lead to incorrect interpretation of results. 6 Departing from the model-based methods discussed above is a twostep, model-free, approach, 16 which is simple and easy to implement. However, the method is susceptible to the existence of both 'risk' and 'protective' haplotypes; the approach will lose power as the effects of these two types of haplotypes will cancel out one another.…”

“…However, the method is susceptible to the existence of both 'risk' and 'protective' haplotypes; the approach will lose power as the effects of these two types of haplotypes will cancel out one another. 6,11 In this paper, we attempt to reap the benefits of a simple nonparametric approach without the need to specify a null haplotype, yet being able to accommodate both risk and protective variants. Specifically, we propose a model-free approach for detecting haplotype association based on Kullback-Leibler divergence (hapKL) for case-control samples.…”

“…This is an especially good benchmark data set for evaluating nonparametric methods such as hapKL, as rare associated haplotypes have been successfully detected by modeling-based methods. 6,9 …”