Investigators from a large consortium of scientists recently performed a multi-year study in which they replicated 100 psychology experiments. Although statistically significant results were reported in 97% of the original studies, statistical significance was achieved in only 36% of the replicated studies. This article presents a reanalysis of these data based on a formal statistical model that accounts for publication bias by treating outcomes from unpublished studies as missing data, while simultaneously estimating the distribution of effect sizes for those studies that tested nonnull effects. The resulting model suggests that more than 90% of tests performed in eligible psychology experiments tested negligible effects, and that publication biases based on p-values caused the observed rates of nonreproducibility. The results of this reanalysis provide a compelling argument for both increasing the threshold required for declaring scientific discoveries and for adopting statistical summaries of evidence that account for the high proportion of tested hypotheses that are false. Supplementary materials for this article are available online.

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We consider the problem of high-dimensional classification between two groups with unequal covariance matrices. Rather than estimating the full quadratic discriminant rule, we propose to perform simultaneous variable selection and linear dimension reduction on the original data, with the subsequent application of quadratic discriminant analysis on the reduced space. In contrast to quadratic discriminant analysis, the proposed framework doesn’t require the estimation of precision matrices; it scales linearly with the number of measurements, making it especially attractive for the use on high-dimensional datasets. We support the methodology with theoretical guarantees on variable selection consistency, and empirical comparisons with competing approaches. We apply the method to gene expression data of breast cancer patients, and confirm the crucial importance of the ESR1 gene in differentiating estrogen receptor status.

We take a functional data approach to longitudinal studies with complex bivariate outcomes. This work is motivated by data from a physical activity study that measured 2 responses over time in 5-minute intervals. One response is the proportion of time active in each interval, a continuous proportions with excess zeros and ones. The other response, energy expenditure rate in the interval, is a continuous variable with excess zeros and skewness. This outcome is complex because there are 3 possible activity patterns in each interval (inactive, partially active, and completely active), and those patterns, which are observed, induce both nonrandom and random associations between the responses. More specifically, the inactive pattern requires a zero value in both the proportion for active behavior and the energy expenditure rate; a partially active pattern means that the proportion of activity is strictly between zero and one and that the energy expenditure rate is greater than zero and likely to be moderate, and the completely active pattern means that the proportion of activity is exactly one, and the energy expenditure rate is greater than zero and likely to be higher. To address these challenges, we propose a 3-part functional data joint modeling approach. The first part is a continuation-ratio model to reorder the ordinal valued 3 activity patterns. The second part models the proportions when they are in interval (0,1). The last component specifies the skewed continuous energy expenditure rate with Box-Cox transformations when they are greater than zero. In this 3-part model, the regression structures are specified as smooth curves measured at various time points with random effects that have a correlation structure. The smoothed random curves for each variable are summarized using a few important principal components, and the association of the 3 longitudinal components is modeled through the association of the principal component scores. The difficulties in handling the ordinal and proportional variables are addressed using a quasi-likelihood type approximation. We develop an efficient algorithm to fit the model that also involves the selection of the number of principal components. The method is applied to physical activity data and is evaluated empirically by a simulation study.

Motivation Most existing microbiome association analyses focus on the association between microbiome and conditional mean of health or disease-related outcomes, and within this vein, vast computational tools and methods have been devised for standard binary or continuous outcomes. However, these methods tend to be limited either when the underlying microbiome-outcome association occurs somewhere other than the mean level, or when distribution of the outcome variable is irregular (e.g., zero-inflated or mixtures) such that conditional outcome mean is less meaningful. We address this gap by investigating association analysis between microbiome compositions and conditional outcome quantiles. Results We introduce a new association analysis tool named MiRKAT-IQ within the Microbiome Regression-based Kernel Association Test framework using Integrated Quantile regression models to examine the association between microbiome and the distribution of outcome. For an individual quantile, we utilize the existing kernel machine regression framework to examine the association between that conditional outcome quantile and a group of microbial features (e.g., microbiome community compositions). Then, the goal of examining microbiome association with the whole outcome distribution is achieved by integrating all outcome conditional quantiles over a process, and thus our new MiRKAT-IQ test is robust to both the location of association signals (e.g.,mean, variance, median) and the heterogeneous distribution of the outcome. Extensive numerical simulation studies have been conducted to show the validity of the new MiRKAT-IQ test. We demonstrate the potential usefulness of MiRKAT-IQ with applications to actual biological data collected from a previous microbiome study. Availability R codes to implement the proposed methodology is provided in the MiRKAT package, which is available on CRAN. Supplementary information Supplementary data are available at Bioinformatics online.