Optimal multiple testing under a Gaussian prior on the effect sizes

Anonic Silicon Hydrogels Affect the Concentration of Proteins in Tears during Wear

PURPOSE

The objective of this study was to quantitatively assess the concentration of human tear proteins in patients wearing contact lenses of various ionicities and determine whether differences were related to the incidence of corneal infiltrative events (CIE).

METHODS

24 subjects (samples) were randomly selected for spectral count analysis to obtain protein concentrations using LCMS analysis. The subjects were neophyte and ametropic with ages between 18 and 40; 6 wore control lenses, 8 wore TestLens1, and 10 wore TestLens2. 16 subjects experienced CIEs during the study.

RESULTS

A pairwise multiple hypothesis test identified 7 proteins that significantly differed in concentration between TestLens1 and control, and 11 proteins that differed between TestLens2 and control. Of the 12 unique proteins, 9 were at increased concentration and 3 were at lower concentration in the tears of test lens wearers compared to the control lens group. Bootstrap clustering confirmed these findings, showing 3 similar clusters to the original sample groups which separated people wearing control lenses from those wearing TestLens1 or TestLens2 with 83% accuracy and between TestLens1 and TestLens2 with 45% accuracy. Permutation testing identified 5 proteins that had significantly changed in concentration between people wearing TestLens2 and Control lenses. There was no difference in protein concentrations between those subjects who experienced a CIE and those who did not.

CONCLUSION

Wearing contact lenses of different ionicities can affect the concentration of proteins in the tear film. The current study did not find any associations of the concentration of proteins with CIEs. Future tests with increased sample size are needed to establish any relations between these changes and clinical performance.

Optimal multiple testing and design in clinical trials

A central goal in designing clinical trials is to find the test that maximizes power (or equivalently minimizes required sample size) for finding a false null hypothesis subject to the constraint of type I error. When there is more than one test, such as in clinical trials with multiple endpoints, the issues of optimal design and optimal procedures become more complex. In this paper, we address the question of how such optimal tests should be defined and how they can be found. We review different notions of power and how they relate to study goals, and also consider the requirements of type I error control and the nature of the procedures. This leads us to an explicit optimization problem with objective and constraints that describe its specific desiderata. We present a complete solution for deriving optimal procedures for two hypotheses, which have desired monotonicity properties, and are computationally simple. For some of the optimization formulations this yields optimal procedures that are identical to existing procedures, such as Hommel's procedure or the procedure of Bittman et al. (2009), while for other cases it yields completely novel and more powerful procedures than existing ones. We demonstrate the nature of our novel procedures and their improved power extensively in a simulation and on the APEX study (Cohen et al., 2016).

Covariate adaptive familywise error rate control for genome-wide association studies

The familywise error rate has been widely used in genome-wide association studies. With the increasing availability of functional genomics data, it is possible to increase detection power by leveraging these genomic functional annotations. Previous efforts to accommodate covariates in multiple testing focused on false discovery rate control, while covariate-adaptive procedures controlling the familywise error rate remain underdeveloped. Here, we propose a novel covariate-adaptive procedure to control the familywise error rate that incorporates external covariates which are potentially informative of either the statistical power or the prior null probability. An efficient algorithm is developed to implement the proposed method. We prove its asymptotic validity and obtain the rate of convergence through a perturbation-type argument. Our numerical studies show that the new procedure is more powerful than competing methods and maintains robustness across different settings. We apply the proposed approach to the UK Biobank data and analyse 27 traits with 9 million single-nucleotide polymorphisms tested for associations. Seventy-five genomic annotations are used as covariates. Our approach detects more genome-wide significant loci than other methods in 21 out of the 27 traits.

Adaptive penalization in high-dimensional regression and classification with external covariates using variational Bayes

Penalization schemes like Lasso or ridge regression are routinely used to regress a response of interest on a high-dimensional set of potential predictors. Despite being decisive, the question of the relative strength of penalization is often glossed over and only implicitly determined by the scale of individual predictors. At the same time, additional information on the predictors is available in many applications but left unused. Here, we propose to make use of such external covariates to adapt the penalization in a data-driven manner. We present a method that differentially penalizes feature groups defined by the covariates and adapts the relative strength of penalization to the information content of each group. Using techniques from the Bayesian tool-set our procedure combines shrinkage with feature selection and provides a scalable optimization scheme. We demonstrate in simulations that the method accurately recovers the true effect sizes and sparsity patterns per feature group. Furthermore, it leads to an improved prediction performance in situations where the groups have strong differences in dynamic range. In applications to data from high-throughput biology, the method enables re-weighting the importance of feature groups from different assays. Overall, using available covariates extends the range of applications of penalized regression, improves model interpretability and can improve prediction performance.

Fast and covariate-adaptive method amplifies detection power in large-scale multiple hypothesis testing

Multiple hypothesis testing is an essential component of modern data science. In many settings, in addition to the p-value, additional covariates for each hypothesis are available, e.g., functional annotation of variants in genome-wide association studies. Such information is ignored by popular multiple testing approaches such as the Benjamini-Hochberg procedure (BH). Here we introduce AdaFDR, a fast and flexible method that adaptively learns the optimal p-value threshold from covariates to significantly improve detection power. On eQTL analysis of the GTEx data, AdaFDR discovers 32% more associations than BH at the same false discovery rate. We prove that AdaFDR controls false discovery proportion and show that it makes substantially more discoveries while controlling false discovery rate (FDR) in extensive experiments. AdaFDR is computationally efficient and allows multi-dimensional covariates with both numeric and categorical values, making it broadly useful across many applications.

Weighted mining of massive collections of [Formula: see text]-values by convex optimization

Researchers in data-rich disciplines-think of computational genomics and observational cosmology-often wish to mine large bodies of [Formula: see text]-values looking for significant effects, while controlling the false discovery rate or family-wise error rate. Increasingly, researchers also wish to prioritize certain hypotheses, for example, those thought to have larger effect sizes, by upweighting, and to impose constraints on the underlying mining, such as monotonicity along a certain sequence. We introduce Princessp, a principled method for performing weighted multiple testing by constrained convex optimization. Our method elegantly allows one to prioritize certain hypotheses through upweighting and to discount others through downweighting, while constraining the underlying weights involved in the mining process. When the [Formula: see text]-values derive from monotone likelihood ratio families such as the Gaussian means model, the new method allows exact solution of an important optimal weighting problem previously thought to be non-convex and computationally infeasible. Our method scales to massive data set sizes. We illustrate the applications of Princessp on a series of standard genomics data sets and offer comparisons with several previous 'standard' methods. Princessp offers both ease of operation and the ability to scale to extremely large problem sizes. The method is available as open-source software from github.com/dobriban/pvalue_weighting_matlab (accessed 11 October 2017).

Data-driven hypothesis weighting increases detection power in genome-scale multiple testing

Hypothesis weighting improves the power of large-scale multiple testing. We describe independent hypothesis weighting (IHW), a method that assigns weights using covariates independent of the P-values under the null hypothesis but informative of each test's power or prior probability of the null hypothesis (http://www.bioconductor.org/packages/IHW). IHW increases power while controlling the false discovery rate and is a practical approach to discovering associations in genomics, high-throughput biology and other large data sets.

Genome-Wide Scan Informed by Age-Related Disease Identifies Loci for Exceptional Human Longevity

We developed a new statistical framework to find genetic variants associated with extreme longevity. The method, informed GWAS (iGWAS), takes advantage of knowledge from large studies of age-related disease in order to narrow the search for SNPs associated with longevity. To gain support for our approach, we first show there is an overlap between loci involved in disease and loci associated with extreme longevity. These results indicate that several disease variants may be depleted in centenarians versus the general population. Next, we used iGWAS to harness information from 14 meta-analyses of disease and trait GWAS to identify longevity loci in two studies of long-lived humans. In a standard GWAS analysis, only one locus in these studies is significant (APOE/TOMM40) when controlling the false discovery rate (FDR) at 10%. With iGWAS, we identify eight genetic loci to associate significantly with exceptional human longevity at FDR < 10%. We followed up the eight lead SNPs in independent cohorts, and found replication evidence of four loci and suggestive evidence for one more with exceptional longevity. The loci that replicated (FDR < 5%) included APOE/TOMM40 (associated with Alzheimer’s disease), CDKN2B/ANRIL (implicated in the regulation of cellular senescence), ABO (tags the O blood group), and SH2B3/ATXN2 (a signaling gene that extends lifespan in Drosophila and a gene involved in neurological disease). Our results implicate new loci in longevity and reveal a genetic overlap between longevity and age-related diseases and traits, including coronary artery disease and Alzheimer’s disease. iGWAS provides a new analytical strategy for uncovering SNPs that influence extreme longevity, and can be applied more broadly to boost power in other studies of complex phenotypes.

Longevity is a complex phenotype, and few genetic variants that affect lifespan have been identified. However, aging and disease are closely related, and a great deal is known about the genetic basis of disease risk. Here, we show using genome-wide association studies (GWAS) of longevity and disease that there is an overlap between loci involved in longevity and loci involved in several diseases, such as Alzheimer’s disease and coronary artery disease. We then develop a new statistical framework to find genetic variants associated with extreme longevity. The method, informed GWAS (iGWAS), takes advantage of knowledge from 14 large studies of disease and disease-related traits in order to narrow the search for SNPs associated with longevity. Using iGWAS, we found eight SNPs that are significant in our discovery cohorts, and we were able to validate four of these in replication studies of long-lived subjects. Our results implicate new loci in longevity and reveal a genetic overlap between longevity and age-related diseases and traits. Beyond the study of human longevity, iGWAS can be applied to boost statistical power in any GWAS of a target phenotype by using larger GWAS of genetically-related conditions.