Marginal false discovery rate control for likelihood‐based penalized regression models

The popularity of penalized regression in high‐dimensional data analysis has led to a demand for new inferential tools for these models. False discovery rate control is widely used in high‐dimensional hypothesis testing, but has only recently been considered in the context of penalized regression. Almost all of this work, however, has focused on lasso‐penalized linear regression. In this paper, we derive a general method for controlling the marginal false discovery rate that can be applied to any penalized likelihood‐based model, such as logistic regression and Cox regression. Our approach is fast, flexible and can be used with a variety of penalty functions including lasso, elastic net, MCP, and MNet. We derive theoretical results under which the proposed method is valid, and use simulation studies to demonstrate that the approach is reasonably robust, albeit slightly conservative, when these assumptions are violated. Despite being conservative, we show that our method often offers more power to select causally important features than existing approaches. Finally, the practical utility of the method is demonstrated on gene expression datasets with binary and time‐to‐event outcomes.     

Concave likelihood-based regression with finite-support response variables

We propose a unified framework for likelihood-based regression modeling when the response variable has finite support. Our work is motivated by the fact that, in practice, observed data are discrete and bounded. The proposed methods assume a model which includes models previously considered for interval-censored variables with log-concave distributions as special cases. The resulting log-likelihood is concave, which we use to establish asymptotic normality of its maximizer as the number of observations n tends to infinity with the number of parameters d fixed, and rates of convergence of L₁-regularized estimators when the true parameter vector is sparse and d and n both tend to infinity with $\log (d)/n\to 0$. We consider an inexact proximal Newton algorithm for computing estimates and give theoretical guarantees for its convergence. The range of possible applications is wide, including but not limited to survival analysis in discrete time, the modeling of outcomes on scored surveys and questionnaires, and, more generally, interval-censored regression. The applicability and usefulness of the proposed methods are illustrated in simulations and data examples.     

Fair Innings

In many societies, the aging of the population is becoming a major problem. This raises difficult issues for ethics and public policy. On what is known as the fair innings view, it is not impermissible to give lower priority to policies that primarily benefit the elderly. Philosophers have tried to justify this view on various grounds. In this article, I look at a consequentialist, a fairness‐based, and a contractarian justification. I argue that all of them have implausible implications and fail to correspond to our moral intuitions. I end by outlining a different kind of consequentialist justification that avoids those implications and corresponds better to our considered moral judgments.     

Asynchronous functional linear regression models for longitudinal data in reproducing kernel Hilbert space

Motivated by the analysis of longitudinal neuroimaging studies, we study the longitudinal functional linear regression model under asynchronous data setting for modeling the association between clinical outcomes and functional (or imaging) covariates. In the asynchronous data setting, both covariates and responses may be measured at irregular and mismatched time points, posing methodological challenges to existing statistical methods. We develop a kernel weighted loss function with roughness penalty to obtain the functional estimator and derive its representer theorem. The rate of convergence, a Bahadur representation, and the asymptotic pointwise distribution of the functional estimator are obtained under the reproducing kernel Hilbert space framework. We propose a penalized likelihood ratio test to test the nullity of the functional coefficient, derive its asymptotic distribution under the null hypothesis, and investigate the separation rate under the alternative hypotheses. Simulation studies are conducted to examine the finite-sample performance of the proposed procedure. We apply the proposed methods to the analysis of multitype data obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) study, which reveals significant association between 21 regional brain volume density curves and the cognitive function. Data used in preparation of this paper were obtained from the ADNI database (adni.loni.usc.edu).     

Fair Resource Allocation to Health Research: Priority Topics for Bioethics Scholarship

This article draws attention to the limited amount of scholarship on what constitutes fairness and equity in resource allocation to health research by individual funders. It identifies three key decisions of ethical significance about resource allocation that research funders make regularly and calls for prioritizing scholarship on those topics – namely, how health resources should be fairly apportioned amongst public health and health care delivery versus health research, how health research resources should be fairly allocated between health problems experienced domestically versus other health problems typically experienced by disadvantaged populations outside the funder's country, and how domestic and non‐domestic health research funding should be further apportioned to different areas, e.g. types of research and recipients. These three topics should be priorities for bioethics research because their outcomes have a substantial bearing on the achievement of health justice. The proposed agenda aims to move discussion on the ethics of health research funding beyond its current focus on the mismatch between worldwide basic and clinical research investment and the global burden of disease. Individual funders’ decision‐making on whether and to what extent to allocate resources to non‐domestic health research, health systems research, research on the social determinants of health, capacity development, and recipients in certain countries should also be the focus of ethical scrutiny.     

Offspring-parent regression for a binary trait

Summary Offspring-parent regression is often used to estimate the heritability of a quantitative trait. It is shown that for a purely binary trait, the regression of offspring on one parent is always linear, while that on both parents or mid-parent is generally nonlinear. However, the regressions are linear on a logistic scale.     

Screening methods for linear errors-in-variables models in high dimensions

Microarray studies, in order to identify genes associated with an outcome of interest, usually produce noisy measurements for a large number of gene expression features from a small number of subjects. One common approach to analyzing such high-dimensional data is to use linear errors-in-variables (EIV) models; however, current methods for fitting such models are computationally expensive. In this paper, we present two efficient screening procedures, namely, corrected penalized marginal screening (PMSc) and corrected sure independence screening (SISc), to reduce the number of variables for final model building. Both screening procedures are based on fitting corrected marginal regression models relating the outcome to each contaminated covariate separately, which can be computed efficiently even with a large number of features. Under mild conditions, we show that these procedures achieve screening consistency and reduce the number of features substantially, even when the number of covariates grows exponentially with sample size. In addition, if the true covariates are weakly correlated, we show that PMSc can achieve full variable selection consistency. Through a simulation study and an analysis of gene expression data for bone mineral density of Norwegian women, we demonstrate that the two new screening procedures make estimation of linear EIV models computationally scalable in high-dimensional settings, and improve finite sample estimation and selection performance compared with estimators that do not employ a screening stage.     

A goodness-of-fit test for multinomial logistic regression

This article presents a score test to check the fit of a logistic regression model with two or more outcome categories. The null hypothesis that the model fits well is tested against the alternative that residuals of samples close to each other in covariate space tend to deviate from the model in the same direction. We propose a test statistic that is a sum of squared smoothed residuals, and show that it can be interpreted as a score test in a random effects model. By specifying the distance metric in covariate space, users can choose the alternative against which the test is directed, making it either an omnibus goodness-of-fit test or a test for lack of fit of specific model variables or outcome categories.