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Qiang Sun, Ruoqing Zhu, Tao Wang, Donglin Zeng
We propose counting process-based dimension reduction methods for right-censored survival data. Semiparametric estimating equations are constructed to estimate the dimension reduction subspace for the failure time model. Our methods address two limitations of existing approaches. First, using the counting process formulation, they do not require estimation of the censoring distribution to compensate for the bias in estimating the dimension reduction subspace. Second, the nonparametric estimation involved adapts to the structural dimension, so our methods circumvent the curse of dimensionality...
March 2019: Biometrika
Yiping Yuan, Xiaotong Shen, Wei Pan, Zizhuo Wang
Directed acyclic graphs are widely used to describe directional pairwise relations. Such relations are estimated by reconstructing a directed acyclic graph's structure, which is challenging when the ordering of nodes of the graph is unknown. In such a situation, existing methods such as the neighbourhood and search-and-score methods have high estimation errors or computational complexities, especially when a local or sequential approach is used to enumerate edge directions by testing or optimizing a criterion locally, as a local method may break down even for moderately sized graphs...
March 2019: Biometrika
S W Jewell, D M Witten
No abstract text is available yet for this article.
March 2019: Biometrika
M Sesia, C Sabatti, E J Candès
Modern scientific studies often require the identification of a subset of explanatory variables. Several statistical methods have been developed to automate this task, and the framework of knockoffs has been proposed as a general solution for variable selection under rigorous Type I error control, without relying on strong modelling assumptions. In this paper, we extend the methodology of knockoffs to problems where the distribution of the covariates can be described by a hidden Markov model. We develop an exact and efficient algorithm to sample knockoff variables in this setting and then argue that, combined with the existing selective framework, this provides a natural and powerful tool for inference in genome-wide association studies with guaranteed false discovery rate control...
March 2019: Biometrika
Susan Wei, Michael R Kosorok
We propose a projection pursuit technique in survival analysis for finding lower-dimensional projections that exhibit differentiated survival outcome. This idea is formally introduced as the change-plane Cox model, a non-regular Cox model with a change-plane in the covariate space dividing the population into two subgroups whose hazards are proportional. The proposed technique offers a potential framework for principled subgroup discovery. Estimation of the change-plane is accomplished via likelihood maximization over a data-driven sieve constructed using sliced inverse regression...
December 2018: Biometrika
I Díaz, O Savenkov, K Ballman
We consider estimation of an optimal individualized treatment rule when a high-dimensional vector of baseline variables is available. Our optimality criterion is with respect to delaying the expected time to occurrence of an event of interest. We use semiparametric efficiency theory to construct estimators with properties such as double robustness. We propose two estimators of the optimal rule, which arise from considering two loss functions aimed at directly estimating the conditional treatment effect and recasting the problem in terms of weighted classification using the 0-1 loss function...
September 2018: Biometrika
Quan Zhou, Philip A Ernst, Kari Lock Morgan, Donald B Rubin, Anru Zhang
The seminal work of Morgan & Rubin (2012) considers rerandomization for all the units at one time.In practice, however, experimenters may have to rerandomize units sequentially. For example, a clinician studying a rare disease may be unable to wait to perform an experiment until all the experimental units are recruited. Our work offers a mathematical framework for sequential rerandomization designs, where the experimental units are enrolled in groups. We formulate an adaptive rerandomization procedure for balancing treatment/control assignments over some continuous or binary covariates, using Mahalanobis distance as the imbalance measure...
September 2018: Biometrika
Jiwei Zhao, Yanyuan Ma
Tang et al. (2003) considered a regression model with missing response, where the missingness mechanism depends on the value of the response variable and hence is nonignorable. They proposed three pseudolikelihood estimators, based on different treatments of the probability distribution of the completely observed covariates. The first assumes the distribution of the covariate to be known, the second estimates this distribution parametrically, and the third estimates the distribution nonparametrically. While it is not hard to show that the second estimator is more efficient than the first, Tang et al...
June 2018: Biometrika
Yin Xia, T Tony Cai, Hongzhe Li
Multivariate regression with high-dimensional covariates has many applications in genomic and genetic research, in which some covariates are expected to be associated with multiple responses. This paper considers joint testing for regression coefficients over multiple responses and develops simultaneous testing methods with false discovery rate control. The test statistic is based on inverse regression and bias-corrected group lasso estimates of the regression coefficients and is shown to have an asymptotic chi-squared null distribution...
June 2018: Biometrika
Marco Avella-Medina, Heather S Battey, Jianqing Fan, Quefeng Li
High-dimensional data are often most plausibly generated from distributions with complex structure and leptokurtosis in some or all components. Covariance and precision matrices provide a useful summary of such structure, yet the performance of popular matrix estimators typically hinges upon a sub-Gaussianity assumption. This paper presents robust matrix estimators whose performance is guaranteed for a much richer class of distributions. The proposed estimators, under a bounded fourth moment assumption, achieve the same minimax convergence rates as do existing methods under a sub-Gaussianity assumption...
June 1, 2018: Biometrika
J E Johndrow, K Lum, D B Dunson
There has been substantial recent interest in record linkage, where one attempts to group the records pertaining to the same entities from one or more large databases that lack unique identifiers. This can be viewed as a type of microclustering, with few observations per cluster and a very large number of clusters. We show that the problem is fundamentally hard from a theoretical perspective and, even in idealized cases, accurate entity resolution is effectively impossible unless the number of entities is small relative to the number of records and/or the separation between records from different entities is extremely large...
June 2018: Biometrika
Jian Kang, Brian J Reich, Ana-Maria Staicu
This work concerns spatial variable selection for scalar-on-image regression. We propose a new class of Bayesian nonparametric models and develop an efficient posterior computational aigorithm. The proposed soft-thresholded Gaussian process provides large prior support over the class of piecewise-smooth, sparse, and continuous spatially-varying regression coefficient functions. In addition, under some mild regularity conditions the soft-thresholded Gaussian proess prior leads to the posterior consistency for parameter estimation and variable selection for scalar-on-image regression, even when the number of predictors is larger than the sample size...
March 2018: Biometrika
Raymond K W Wong, Kwun Chuen Gary Chan
Covariate balance is often advocated for objective causal inference since it mimics randomization in observational data. Unlike methods that balance specific moments of covariates, our proposal attains uniform approximate balance for covariate functions in a reproducing-kernel Hilbert space. The corresponding infinite-dimensional optimization problem is shown to have a finite-dimensional representation in terms of an eigenvalue optimization problem. Large-sample results are studied, and numerical examples show that the proposed method achieves better balance with smaller sampling variability than existing methods...
March 2018: Biometrika
Yunro Chung, Anastasia Ivanova, Michael G Hudgens, Jason P Fine
We consider the estimation of the semiparametric proportional hazards model with an unspecified baseline hazard function where the effect of a continuous covariate is assumed to be monotone. Previous work on nonparametric maximum likelihood estimation for isotonic proportional hazard regression with right-censored data is computationally intensive, lacks theoretical justification, and may be prohibitive in large samples. In this paper, partial likelihood estimation is studied. An iterative quadratic programming method is considered, which has performed well with likelihoods for isotonic parametric regression models...
March 1, 2018: Biometrika
K Schorning, H Dette, K Kettelhake, W K Wong, F Bretz
We derive optimal designs to estimate efficacy and toxicity in active controlled dose-finding trials when the bivariate continuous outcomes are described using nonlinear regression models. We determine upper bounds on the required number of different doses and provide conditions under which the boundary points of the design space are included in the optimal design. We provide an analytical description of minimally supported optimal designs and show that they do not depend on the correlation between the bivariate outcomes...
December 2017: Biometrika
Byeong Yeob Choi, Jason P Fine, M Alan Brookhart
Two-stage least squares estimation is popular for structural equation models with unmeasured confounders. In such models, both the outcome and the exposure are assumed to follow linear models conditional on the measured confounders and instrumental variable, which is related to the outcome only via its relation with the exposure. We consider data where both the outcome and the exposure may be incompletely observed, with particular attention to the case where both are censored event times. A general class of two-stage minimum distance estimators is proposed that separately fits linear models for the outcome and exposure and then uses a minimum distance criterion based on the reduced-form model for the outcome to estimate the regression parameters of interest...
December 2017: Biometrika
D Benkeser, M Carone, M J Van Der Laan, P B Gilbert
Doubly robust estimators are widely used to draw inference about the average effect of a treatment. Such estimators are consistent for the effect of interest if either one of two nuisance parameters is consistently estimated. However, if flexible, data-adaptive estimators of these nuisance parameters are used, double robustness does not readily extend to inference. We present a general theoretical study of the behaviour of doubly robust estimators of an average treatment effect when one of the nuisance parameters is inconsistently estimated...
December 2017: Biometrika
Liping Zhu, Kai Xu, Runze Li, Wei Zhong
We propose the use of projection correlation to characterize dependence between two random vectors. Projection correlation has several appealing properties. It equals zero if and only if the two random vectors are independent, it is not sensitive to the dimensions of the two random vectors, it is invariant with respect to the group of orthogonal transformations, and its estimation is free of tuning parameters and does not require moment conditions on the random vectors. We show that the sample estimate of the projection correction is [Formula: see text]-consistent if the two random vectors are independent and root-[Formula: see text]-consistent otherwise...
December 2017: Biometrika
Fang Han, Shizhe Chen, Han Liu
We consider the testing of mutual independence among all entries in a [Formula: see text]-dimensional random vector based on [Formula: see text] independent observations. We study two families of distribution-free test statistics, which include Kendall's tau and Spearman's rho as important examples. We show that under the null hypothesis the test statistics of these two families converge weakly to Gumbel distributions, and we propose tests that control the Type I error in the high-dimensional setting where [Formula: see text]...
December 2017: Biometrika
Odile Stalder, Alex Asher, Liang Liang, Raymond J Carroll, Yanyuan Ma, Nilanjan Chatterjee
Many methods have recently been proposed for efficient analysis of case-control studies of gene-environment interactions using a retrospective likelihood framework that exploits the natural assumption of gene-environment independence in the underlying population. However, for polygenic modelling of gene-environment interactions, which is a topic of increasing scientific interest, applications of retrospective methods have been limited due to a requirement in the literature for parametric modelling of the distribution of the genetic factors...
December 2017: Biometrika
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