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Penalized Logistic Regression Analysis for Genetic Association Studies of Binary Phenotypes
Author(s) -
Yu Ying,
Chen Siyuan,
Jones Samantha Jean,
Hoque Rawnak,
Vishnyakova Olga,
Brooks-Wilson Angela,
McNeney Brad
Publication year - 2022
Publication title -
human heredity
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.423
H-Index - 62
eISSN - 1423-0062
pISSN - 0001-5652
DOI - 10.1159/000525650
Subject(s) - research article
Increasingly, logistic regression methods for genetic association studies of binary phenotypes must be able to accommodate data sparsity, which arises from unbalanced case-control ratios and/or rare genetic variants. Sparseness leads to maximum likelihood estimators (MLEs) of log-OR parameters that are biased away from their null value of zero and tests with inflated type I errors. Different penalized likelihood methods have been developed to mitigate sparse data bias. We study penalized logistic regression using a class of log- F priors indexed by a shrinkage parameter m to shrink the biased MLE toward zero. Methods: We proposed a two-step approach to the analysis of a genetic association study: first, a set of variants that show evidence of association with the trait is used to estimate m ; second, the estimated m is used for log- F -penalized logistic regression analyses of all variants using data augmentation with standard software. Our estimate of m is the maximizer of a marginal likelihood obtained by integrating the latent log-ORs out of the joint distribution of the parameters and observed data. We consider two approximate approaches to maximizing the marginal likelihood: (i) a Monte Carlo EM algorithm and (ii) a Laplace approximation to each integral, followed by derivative-free optimization of the approximation. Results: We evaluated the statistical properties of our proposed two-step method and compared its performance to other shrinkage methods by a simulation study. Our simulation studies suggest that the proposed log- F -penalized approach has lower bias and mean squared error than other methods considered. We also illustrated the approach on data from a study of genetic associations with “Super Senior” cases and middle-aged controls. Discussion/Conclusion: We have proposed a method for single rare variant analysis with binary phenotypes by logistic regression penalized by log- F priors. Our method has the advantage of being easily extended to correct for confounding due to population structure and genetic relatedness through a data augmentation approach.

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