我们提出了一种新的方法，稀疏回归和边际测试，相关功能的数据。我们的程序首先聚类的功能，然后选择集群原型中最丰富的功能。然后我们对这些原型应用稀疏回归（lasso）或边际显著性检验。虽然这种策略并不完全是新的，但我们建议的一个关键特征是使用Taylor et al.（2014）和Lee et al.（2014）的后选择推理理论来计算精确的p值和置信区间，以正确解释原型的选择。我们还应用最近的“山寨”的想法巴伯和坎迪斯提供确切的有限样本控制的FDR我们的回归过程。我们说明我们的建议，真实和模拟数据。
英文摘要：
We propose a new approach for sparse regression and marginal testing, for data with correlated features. Our procedure first clusters the features, and then chooses as the cluster prototype the most informative feature in that cluster. Then we apply either sparse regression (lasso) or marginal significance testing to these prototypes. While this kind of strategy is not entirely new, a key feature of our proposal is its use of the post-selection inference theory of Taylor et al. (2014) and Lee et al. (2014) to compute exact p-values and confidence intervals that properly account for the selection of prototypes.
We also apply the recent "knockoff" idea of Barber and Candès to provide exact finite sample control of the FDR of our regression procedure. We illustrate our proposals on both real and simulated data.
Leading methods for support recovery in high-dimensional regression, such as Lasso, have been well-studied and their limitations in the context of correlated design have been characterized with precise incoherence conditions. In this work, we present a similar treatment of selection consistency for marginal regression (MR), a computationally efficient family of methods with connections to decision trees. Selection based on marginal regression is also referred to as covariate screening or independence screening and is a popular approach in applied work, especially in ultra high-dimensional sett…
Capturing complex dependence structures between outcome variables (e.g., study endpoints) is of high relevance in contemporary biomedical data problems and medical research. Distributional copula regression provides a flexible tool to model the joint distribution of multiple outcome variables by disentangling the marginal response distributions and their dependence structure. In a regression setup each parameter of the copula model, i.e. the marginal distribution parameters and the copula dependence parameters, can be related to covariates via structured additive predictors. We propose a frame…
In many applications, we need to study a linear regression model that consists of a response variable and a large number of potential explanatory variables and determine which variables are truly associated with the response. In 2015, Barber and Candes introduced a new variable selection procedure called the knockoff filter to control the false discovery rate (FDR) and proved that this method achieves exact FDR control. In this paper, we propose a prototype knockoff filter for group selection by extending the Reid-Tibshirani prototype method. Our prototype knockoff filter improves the computat…
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 …
Clustered multistate process data are commonly encountered in multicenter observational studies and clinical trials. A clinically important estimand with such data is the marginal probability of being in a particular transient state as a function of time. However, there is currently no method for nonparametric marginal regression analysis of these probabilities with clustered multistate process data. To address this problem, we propose a weighted functional generalized estimating equations approach which does not impose Markov assumptions or assumptions regarding the structure of the within-cl…
We present a method to infer on joint regression coefficients obtained from marginal regressions using a reference panel. This type of scenario is common in genetic fine-mapping, where the estimated marginal associations are reported in genomewide association studies (GWAS), and a reference panel is used for inference on the association in a joint regression model. We show that ignoring the uncertainty due to the use of a reference panel instead of the original design matrix, can lead to a severe inflation of false discoveries and a lack of replicable findings. We derive the asymptotic distrib…
This paper deals with robust marginal estimation under a general regression model when missing data occur in the response and also in some of covariates. The target is a marginal location parameter which is given through an $M-$functional. To obtain robust Fisher--consistent estimators, properly defined marginal distribution function estimators are considered. These estimators avoid the bias due to missing values by assuming a missing at random condition. Three methods are considered to estimate the marginal distribution function which allows to obtain the $M-$location of interest: the well-kn…
Flexible estimation of multiple conditional quantiles is of interest in numerous applications, such as studying the effect of pregnancy-related factors on low and high birth weight. We propose a Bayesian non-parametric method to simultaneously estimate non-crossing, non-linear quantile curves. We expand the conditional distribution function of the response in I-spline basis functions where the covariate-dependent coefficients are modeled using neural networks. By leveraging the approximation power of splines and neural networks, our model can approximate any continuous quantile function. Compa…
Population adjustment methods such as matching-adjusted indirect comparison (MAIC) are increasingly used to compare marginal treatment effects when there are cross-trial differences in effect modifiers and limited patient-level data. MAIC is sensitive to poor covariate overlap and cannot extrapolate beyond the observed covariate space. Current outcome regression-based alternatives can extrapolate but target a conditional treatment effect that is incompatible in the indirect comparison. When adjusting for covariates, one must integrate or average the conditional estimate over the population of …
Clustered competing risks data are commonly encountered in multicenter studies. The analysis of such data is often complicated due to informative cluster size, a situation where the outcomes under study are associated with the size of the cluster. In addition, cause of failure is frequently incompletely observed in real-world settings. To the best of our knowledge, there is no methodology for population-averaged analysis with clustered competing risks data with informative cluster size and missing causes of failure. To address this problem, we consider the semiparametric marginal proportional …
Marginal generalized raking with parametric working models
Kaiser Permanente Washington Health Research Institute（凯撒永久华盛顿健康研究所）；University of Washington（华盛顿大学）；Fred Hutchinson Cancer Center（弗雷德·哈钦森癌症中心）；University of Auckland（奥克兰大学）；Vanderbilt University（范德堡大学）
A marginalized three-part interrupted time series regression model for proportional data
Oregon Health & Science University（俄勒冈健康与科学大学）；Kaiser Permanente Washington Health Research Institute（凯撒永久华盛顿健康研究所）；University of Washington（华盛顿大学）；King’s College London（伦敦国王学院）
Motivation: The discovery of relationships between gene expression measurements and phenotypic responses is hampered by both computational and statistical impediments. Conventional statistical methods are less than ideal because they either fail to select relevant genes, predict poorly, ignore the unknown interaction structure between genes, or are computationally intractable. Thus, the creation of new methods which can handle many expression measurements on relatively small numbers of patients while also uncovering gene-gene relationships and predicting well is desirable. Results: We develop …
Deep neural network (DNN) regression models are widely used in applications requiring state-of-the-art predictive accuracy. However, until recently there has been little work on accurate uncertainty quantification for predictions from such models. We add to this literature by outlining an approach to constructing predictive distributions that are `marginally calibrated'. This is where the long run average of the predictive distributions of the response variable matches the observed empirical margin. Our approach considers a DNN regression with a conditionally Gaussian prior for the final layer…
Improved Methods for Moment Restriction Models with Marginally Incompatible Data Combination and an Application to Two-sample Instrumental Variable Estimation
We consider penalized regression models under a unified framework where the particular method is determined by the form of the penalty term. We propose a fully Bayesian approach that incorporates both sparse and dense settings and show how to use a type of model averaging approach to eliminate the nuisance penalty parameters and perform inference through the marginal posterior distribution of the regression coefficients. We establish tail robustness of the resulting estimator as well as conditional and marginal posterior consistency. We develop an efficient component-wise Markov chain Monte Ca…
A new class of copulas, termed the MGL copula class, is introduced. The new copula originates from extracting the dependence function of the multivariate generalized log-Moyal-gamma distribution whose marginals follow the univariate generalized log-Moyal-gamma (GLMGA) distribution as introduced in \citet{li2019jan}. The MGL copula can capture nonelliptical, exchangeable, and asymmetric dependencies among marginal coordinates and provides a simple formulation for regression applications. We discuss the probabilistic characteristics of MGL copula and obtain the corresponding extreme-value copula…
Turku School of Economics, University of Turku（图尔库经济学院，图尔库大学）；Miguel Hernández University of Elche（埃尔切米格尔·埃尔南德斯大学）；Surrey Business School, University of Surrey（萨里商学院，萨里大学）
Bivariate observations of binary and ordinal data arise frequently and require a bivariate modelling approach in cases where one is interested in aspects of the marginal distributions as separate outcomes along with the association between the two. We consider methods for constructing such bivariate models with logistic marginals and propose a model based on the Ali-Mikhail-Haq bivariate logistic distribution. We motivate the model as an extension of that based on the Gumbel type 2 distribution as considered by other authors and as a bivariate extension of the logistic distribution which prese…
Longitudinal data are common in clinical trials and observational studies, where missing outcomes due to dropouts are always encountered. Under such context with the assumption of missing at random, the weighted generalized estimating equations (WGEE) approach is widely adopted for marginal analysis. Model selection on marginal mean regression is a crucial aspect of data analysis, and identifying an appropriate correlation structure for model fitting may also be of interest and importance. However, the existing information criteria for model selection in WGEE have limitations, such as separate…
Population adjustment methods such as matching-adjusted indirect comparison (MAIC) are increasingly used to compare marginal treatment effects when there are cross-trial differences in effect modifiers and limited patient-level data. MAIC is based on propensity score weighting, which is sensitive to poor covariate overlap and cannot extrapolate beyond the observed covariate space. Current outcome regression-based alternatives can extrapolate but target a conditional treatment effect that is incompatible in the indirect comparison. When adjusting for covariates, one must integrate or average th…
A fully nonparametric approach for making probabilistic predictions in multi-response regression problems is introduced. Random forests are used as marginal models for each response variable and, as novel contribution of the present work, the dependence between the multiple response variables is modeled by a generative neural network. This combined modeling approach of random forests, corresponding empirical marginal residual distributions and a generative neural network is referred to as RafterNet. Multiple datasets serve as examples to demonstrate the flexibility of the approach and its impa…
In this work we consider Bayesian inference problems with intractable likelihood functions. We present a method to compute an approximate of the posterior with a limited number of model simulations. The method features an inverse Gaussian Process regression (IGPR), i.e., one from the output of a simulation model to the input of it. Within the method, we provide an adaptive algorithm with a tempering procedure to construct the approximations of the marginal posterior distributions. With examples we demonstrate that IGPR has a competitive performance compared to some commonly used algorithms, es…
Modern high-throughput biomedical devices routinely produce data on a large scale, and the analysis of high-dimensional datasets has become commonplace in biomedical studies. However, given thousands or tens of thousands of measured variables in these datasets, extracting meaningful features poses a challenge. In this article, we propose a procedure to evaluate the strength of the associations between a nominal (categorical) response variable and multiple features simultaneously. Specifically, we propose a framework of large-scale multiple testing under arbitrary correlation dependency among t…
Thanks to their ability to capture complex dependence structures, copulas are frequently used to glue random variables into a joint model with arbitrary marginal distributions. More recently, they have been applied to solve statistical learning problems such as regression or classification. Framing such approaches as solutions of estimating equations, we generalize them in a unified framework. We can then obtain simultaneous, coherent inferences across multiple regression-like problems. We derive consistency, asymptotic normality, and validity of the bootstrap for corresponding estimators. The…
Hybrid Bernstein Normalizing Flows for Flexible Multivariate Density Regression with Interpretable Marginals
Institute for Applied Research HTWG - University of Applied Sciences（应用研究研究所 HTWG - 高等专业学院）；Chair of Statistics and Campus Institute Data Science (CIDAS) University of Göttingen（统计学教授及校园数据科学研究所 (CIDAS) 雷姆森大学）；Department of Statistics LMU Munich（统计学系 慕尼黑大学）；Munich Center for Machine Learning (MCML)（慕尼黑机器学习中心）
In this article, we analyze perinatal data with birth weight (BW) as primarily interesting response variable. Gestational age (GA) is usually an important covariate and included in polynomial form. However, in opposition to this univariate regression, bivariate modeling of BW and GA is recommended to distinguish effects on each, on both, and between them. Rather than a parametric bivariate distribution, we apply conditional copula regression, where marginal distributions of BW and GA (not necessarily of the same form) can be estimated independently, and where the dependence structure is modele…
We propose a versatile joint regression framework for count responses. The method is implemented in the R add-on package GJRM and allows for modelling linear and non-linear dependence through the use of several copulae. Moreover, the parameters of the marginal distributions of the count responses and of the copula can be specified as flexible functions of covariates. Motivated by a football application, we also discuss an extension which forces the regression coefficients of the marginal (linear) predictors to be equal via a suitable penalisation. Model fitting is based on a trust region algor…
