For statistical inference on regression models with a diverging number of covariates, the existing literature typically makes sparsity assumptions on the inverse of the Fisher information matrix. Such assumptions, however, are often violated under Cox proportion hazards models, leading to biased estimates with under‐coverage confidence intervals. We propose a modified debiased lasso method, which solves a series of quadratic programming problems to approximate the inverse information matrix without posing sparse matrix assumptions. We establish asymptotic results for the estimated regression coefficients when the dimension of covariates diverges with the sample size. As demonstrated by extensive simulations, our proposed method provides consistent estimates and confidence intervals with nominal coverage probabilities. The utility of the method is further demonstrated by assessing the effects of genetic markers on patients' overall survival with the Boston Lung Cancer Survival Cohort, a large‐scale epidemiology study investigating mechanisms underlying the lung cancer.
Modeling and drawing inference on the joint associations between single‐nucleotide polymorphisms and a disease has sparked interest in genome‐wide associations studies. In the motivating Boston Lung Cancer Survival Cohort (BLCSC) data, the presence of a large number of single nucleotide polymorphisms of interest, though smaller than the sample size, challenges inference on their joint associations with the disease outcome. In similar settings, we find that neither the debiased lasso approach (van de Geer et al., 2014), which assumes sparsity on the inverse information matrix, nor the standard maximum likelihood method can yield confidence intervals with satisfactory coverage probabilities for generalized linear models. Under this “large
- NSF-PAR ID:
- 10364139
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Biometrics
- Volume:
- 79
- Issue:
- 1
- ISSN:
- 0006-341X
- Format(s):
- Medium: X Size: p. 344-357
- Size(s):
- ["p. 344-357"]
- Sponsoring Org:
- National Science Foundation
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Abstract Background Alzheimer's disease (AD), the most prevalent form of dementia, affects 6.5 million Americans and over 50 million people globally. Clinical, genetic, and phenotypic studies of dementia provide some insights of the observed progressive neurodegenerative processes, however, the mechanisms underlying AD onset remain enigmatic.
Aims This paper examines late‐onset dementia‐related cognitive impairment utilizing neuroimaging‐genetics biomarker associations.
Materials and Methods The participants, ages 65–85, included 266 healthy controls (HC), 572 volunteers with mild cognitive impairment (MCI), and 188 Alzheimer's disease (AD) patients. Genotype dosage data for AD‐associated single nucleotide polymorphisms (SNPs) were extracted from the imputed ADNI genetics archive using sample‐major additive coding. Such 29 SNPs were selected, representing a subset of independent SNPs reported to be highly associated with AD in a recent AD meta‐GWAS study by Jansen and colleagues
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Background Markov chains (MC) have been widely used to model molecular sequences. The estimations of MC transition matrix and confidence intervals of the transition probabilities from long sequence data have been intensively studied in the past decades. In next generation sequencing (NGS), a large amount of short reads are generated. These short reads can overlap and some regions of the genome may not be sequenced resulting in a new type of data. Based on NGS data, the transition probabilities of MC can be estimated by moment estimators. However, the classical asymptotic distribution theory for MC transition probability estimators based on long sequences is no longer valid.
Methods In this study, we present the asymptotic distributions of several statistics related to MC based on NGS data. We show that, after scaling by the effective coverage
d defined in a previous study by the authors, these statistics based on NGS data approximate to the same distributions as the corresponding statistics for long sequences.Results We apply the asymptotic properties of these statistics for finding the theoretical confidence regions for MC transition probabilities based on NGS short reads data. We validate our theoretical confidence intervals using both simulated data and real data sets, and compare the results with those by the parametric bootstrap method.
Conclusions We find that the asymptotic distributions of these statistics and the theoretical confidence intervals of transition probabilities based on NGS data given in this study are highly accurate, providing a powerful tool for NGS data analysis.
