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Ultrahigh and high dimensional data are common in regression analysis for various fields, such as omics data, finance, and biological engineering. In addition to the problem of dimension, the data might also be contaminated. There are two main types of contamination: outliers and model misspecification. We develop an unique method that takes into account the ultrahigh or high dimensional issues and both types of contamination. In this article, we propose a framework for feature screening and selection based on the minimum Lq-likelihood estimation (MLqE), which accounts for the model misspecification contamination issue and has also been shown to be robust to outliers. In numerical analysis, we explore the robustness of this framework under different outliers and model misspecification scenarios. To examine the performance of this framework, we conduct real data analysis using the skin cutaneous melanoma data. When comparing with traditional screening and feature selection methods, the proposed method shows superiority in both variable identification effectiveness and parameter estimation accuracy.

In this article, we introduce the concept of model confidence bounds (MCB) for variable selection in the context of nested models. Similarly to the endpoints in the familiar confidence interval for parameter estimation, the MCB identifies two nested models (upper and lower confidence bound models) containing the true model at a given level of confidence. Instead of trusting a single selected model obtained from a given model selection method, the MCB proposes a group of nested models as candidates and the MCB's width and composition enable the practitioner to assess the overall model selection uncertainty. A new graphical tool-the model uncertainty curve (MUC)-is introduced to visualize the variability of model selection and to compare different model selection procedures. The MCB methodology is implemented by a fast bootstrap algorithm that is shown to yield the correct asymptotic coverage under rather general conditions. Our Monte Carlo simulations and real data examples confirm the validity and illustrate the advantages of the proposed method.

Variable screening plays an important role in ultra-high-dimensional data analysis. Most of the previous analyses have focused on individual predictor screening using marginal correlation or other rank-based techniques. When predictors can be naturally grouped, the structure information should be incorporated while applying variable screening. This study presents a group screening procedure that is based on maximum Lq-likelihood estimation, which is being increasingly used for robust estimation. The proposed method is robust against data contamination, including a heavy-tailed distribution of the response and a mixture of observations from different distributions. The sure screening property is rigorously established. Simulations demonstrate the competitive performance of the proposed method, especially in terms of its robustness against data contamination. Two real data analyses are presented to further illustrate its performance.

In this article, we introduce the concept of confidence graphs (CG) for graphical model selection. CG first identifies two nested graphical models—called small and large confidence graphs (SCG and LCG)—trapping the true graphical model in between at a given level of confidence, just like the endpoints of traditional confidence interval capturing the population parameter. Therefore, SCG and LCG provide us with more insights about the simplest and most complex forms of dependence structure the true model can possibly be, and their difference also offers us a measure of model selection uncertainty. In addition, rather than relying on a single selected model, CG consists of a group of graphical models between SCG and LCG as the candidates. The proposed method can be coupled with many popular model selection methods, making it an ideal tool for comparing model selection uncertainty as well as measuring reproducibility. We also propose a new residual bootstrap procedure for graphical model settings to approximate the sampling distribution of the selected models and to obtain CG. To visualize the distribution of selected models and its associated uncertainty, we further develop new graphical tools, such as grouped model selection distribution plot. Numerical studies further illustrate the advantages of the proposed method.

In the research on complex diseases, gene expression (GE) data have been extensively used for clustering samples. The clusters so generated can serve as the basis for disease subtype identification, risk stratification, and many other purposes. With the small sample sizes of genetic profiling studies and noisy nature of GE data, clustering analysis results are often unsatisfactory. In the most recent studies, a prominent trend is to conduct multidimensional profiling, which collects data on GEs and their regulators (copy number alterations, microRNAs, methylation, etc.) on the same subjects. With the regulation relationships, regulators contain important information on the properties of GEs. We develop a novel assisted clustering method, which effectively uses regulator information to improve clustering analysis using GE data. To account for the fact that not all GEs are informative, we propose a weighted strategy, where the weights are determined data-dependently and can discriminate informative GEs from noises. The proposed method is built on the NCut technique and effectively realized using a simulated annealing algorithm. Simulations demonstrate that it can well outperform multiple direct competitors. In the analysis of TCGA cutaneous melanoma and lung adenocarcinoma data, biologically sensible findings different from the alternatives are made.

Concerns have been expressed over the validity of statistical inference under covariate-adaptive randomization despite the extensive use in clinical trials. In the literature, the inferential properties under covariate-adaptive randomization have been mainly studied for continuous responses; in particular, it is well known that the usual two sample t-test for treatment effect is typically conservative, in the sense that the actual test size is smaller than the nominal level. This phenomenon of invalid tests has also been found for generalized linear models without adjusting for the covariates and are sometimes more worrisome due to inflated Type I error. The purpose of this study is to examine the unadjusted test for treatment effect under generalized linear models and covariate-adaptive randomization. For a large class of covariate-adaptive randomization methods, we obtain the asymptotic distribution of the test statistic under the null hypothesis and derive the conditions under which the test is conservative, valid, or anti-conservative. Several commonly used generalized linear models, such as logistic regression and Poisson regression, are discussed in detail. An adjustment method is also proposed to achieve a valid size based on the asymptotic results. Numerical studies confirm the theoretical findings and demonstrate the effectiveness of the proposed adjustment method., Comment: Updated to the published version

In this article, we consider a semiparametric additive partially linear interaction model for the integrative analysis of multiple genetic datasets. The goals are to identify important genetic predictors and gene-gene interactions and to estimate the nonparametric functions that describe the environmental effects at the same time. To find the similarities and differences of the genetic effects across different datasets, we impose a group structure on the regression coefficients matrix under the homogeneity assumption, ie, models for different datasets share the same sparsity structure, but the coefficients may differ across datasets. We develop an iterative approach to estimate the parameters of main effects, interactions and nonparametric functions, where a reparametrization of interaction parameters is implemented to meet the strong hierarchy assumption. We demonstrate the advantages of the proposed method in identification, estimation, and prediction in a series of numerical studies. We also apply the proposed method to the Skin Cutaneous Melanoma data and the lung cancer data from the Cancer Genome Atlas.

Expanding on the zero-inflated Poisson model, the multiple-inflated Poisson model is applied to analyze count data with multiple inflated values. The existing studies on the multiple-inflated Poisson model determined the inflated values by inspecting the histogram of count response and fitting the model with different combinations of inflated values, which leads to relatively complicated computations and may overlook some real inflated points. We address a two-stage inflated values selection method, which takes all values of count response as potential inflated values and adopts the adaptive lasso regularization on the mixing proportion of those values. Numerical studies demonstrate the excellent performance both on inflated values selection and parameters estimation. Moreover, a specially designed simulation, based on the structure of data from a randomized clinical trial of an HIV sexual risk education intervention, performs well and ensures our method could be generalized to the real situation. An empirical analysis of a clinical trial dataset is used to elucidate the multiple-inflated Poisson model.

Covariate-adaptive randomization (CAR) procedures are frequently used in comparative studies to increase the covariate balance across treatment groups. However, because randomization inevitably uses the covariate information when forming balanced treatment groups, the validity of classical statistical methods after such randomization is often unclear. In this article, we derive the theoretical properties of statistical methods based on general CAR under the linear model framework. More importantly, we explicitly unveil the relationship between covariate-adaptive and inference properties by deriving the asymptotic representations of the corresponding estimators. We apply the proposed general theory to various randomization procedures such as complete randomization, rerandomization, pairwise sequential randomization, and Atkinson's $D_A$-biased coin design and compare their performance analytically. Based on the theoretical results, we then propose a new approach to obtain valid and more powerful tests. These results open a door to understand and analyze experiments based on CAR. Simulation studies provide further evidence of the advantages of the proposed framework and the theoretical results. Supplementary materials for this article are available online., Updated to the published version

In this paper, we propose an adaptive stochastic gradient boosting tree for classification studies with imbalanced data. The adjustment of cost-sensitivity and the predictive threshold are integrated together with a composite criterion into the original stochastic gradient boosting tree to deal with the issues of the imbalanced data structure. Numerical study shows that the proposed method can significantly enhance the classification accuracy for the minority class with only a small loss in the true negative rate for the majority class. We discuss the relation of the cost-sensitivity to the threshold manipulation using simulations. An illustrative example of the analysis of suboptimal health-state data in traditional Chinese medicine is discussed.

In this paper, we consider the variable selection problem in semiparametric additive partially linear models for longitudinal data. Our goal is to identify relevant main effects and corresponding interactions associated with the response variable. Meanwhile, we enforce the strong hierarchical restriction on the model, that is, an interaction can be included in the model only if both the associated main effects are included. Based on B-splines basis approximation for the nonparametric components, we propose an iterative estimation procedure for the model by penalizing the likelihood with a partial group minimax concave penalty (MCP), and use BIC to select the tuning parameter. To further improve the estimation efficiency, we specify the working covariance matrix by maximum likelihood estimation. Simulation studies indicate that the proposed method tends to consistently select the true model and works efficiently in estimation and prediction with finite samples, especially when the true model obeys the strong hierarchy. Finally, the China Stock Market data are fitted with the proposed model to illustrate its effectiveness.

Imbalanced data brings biased classification and causes the low accuracy of the classification of the minority class. In this article, we propose a methodology to select grouped variables using the area under the ROC with an adjustable prediction cut point. The proposed method enhance the accuracy of classification for the minority class by maximizing the true positive rate. Simulation results show that the proposed method is appropriate for both the categorical and continuous covariates. An illustrative example of the analysis of the SHS data in TCM is discussed to show the reasonable application of the proposed method.

It is well known that statistical classifiers trained from imbalanced data lead to low true positive rates and select inconsistent significant variables. In this article, an improved method is proposed to enhance the classification accuracy for the minority class by differentiating misclassification cost for each group. The overall error rate is replaced by an alternative composite criterion. Furthermore, we propose an approach to estimate the tuning parameter, the composite criterion, and the cut-point simultaneously. Simulations show that the proposed method achieves a high true positive rate on prediction and a good performance on variable selection for both continuous and categorical predictors, even with highly imbalanced data. An illustrative example of the analysis of the suboptimal health state data in traditional Chinese medicine is discussed to show the reasonable application of the proposed method.

We introduce a maximum Lq-likelihood estimation (MLqE) of mixture models using our proposed expectation-maximization (EM) algorithm, namely the EM algorithm with Lq-likelihood (EM-Lq). Properties of the MLqE obtained from the proposed EM-Lq are studied through simulated mixture model data. Compared with the maximum likelihood estimation (MLE), which is obtained from the EM algorithm, the MLqE provides a more robust estimation against outliers for small sample sizes. In particular, we study the performance of the MLqE in the context of the gross error model, where the true model of interest is a mixture of two normal distributions, and the contamination component is a third normal distribution with a large variance. A numerical comparison between the MLqE and the MLE for this gross error model is presented in terms of Kullback–Leibler (KL) distance and relative efficiency.

Both continuous and categorical covariates are common in traditional Chinese medicine (TCM) research, especially in the clinical syndrome identification and in the risk prediction research. For groups of dummy variables which are generated by the same categorical covariate, it is important to penalize them group-wise rather than individually. In this paper, we discuss the group lasso method for a risk prediction analysis in TCM osteoporosis research. It is the first time to apply such a group-wise variable selection method in this field. It may lead to new insights of using the grouped penalization method to select appropriate covariates in the TCM research. The introduced methodology can select categorical and continuous variables, and estimate their parameters simultaneously. In our application of the osteoporosis data, four covariates (including both categorical and continuous covariates) are selected out of 52 covariates. The accuracy of the prediction model is excellent. Compared with the prediction ...

Copula modeling has gained much attention in many fields recently with the advantage of separating dependence structure from marginal distributions. In real data, however, serious ties are often present in one or multiple margins, which cause problems to many rank-based statistical methods developed under the assumption of continuous data with no ties. Simple methods such as breaking the ties at random or using average rank introduce independence into the data and, hence, lead to biased estimation. We propose an estimation method that treats the ranks of tied data as being interval censored and maximizes a pseudo-likelihood based on interval censored pseudo-observations. A parametric bootstrap procedure that preserves the observed tied ranks in the data is adapted to assess the estimation uncertainty and perform goodness-of-fit tests. The proposed approach is shown to be very competitive in comparison to the simple treatments in a large scale simulation study. Application to a bivariate insurance data illustrates the methodology.

This article introduces a robust hypothesis testing procedure: the Lq-likelihood-ratio-type test (LqRT). By deriving the asymptotic distribution of this test statistic, the authors demonstrate its robustness both analytically and numerically, and they investigate the properties of both its influence function and its breakdown point. A proposed method to select the tuning parameter q offers a good efficiency/robustness trade-off, compared with the traditional likelihood ratio test (LRT) and other robust tests. A simulation and real data analysis provides further evidence of the advantages of the proposed LqRT method. In particular, for the special case of testing the location parameter in the presence of gross error contamination, the LqRT dominates the Wilcoxon-Mann-Whitney test and the sign test at various levels of contamination., 32 pages, 11 figures

The syndrome is one of the most important concepts and ingredients in the theoretical and clinical research of traditional Chinese medicine (TCM). TCM doctors believe that all diseases are caused by an imbalance in the patient's body, which is called syndrome. All the therapies and formulas in TCM are decided according to the patients' syndrome situation. To quantitatively evaluate the level of syndrome, many statistical methodologies have been discussed in recent years. In this article, we introduce a second-order latent variable model to evaluate the level of patients' syndrome with many clinical symptoms. An objective evaluation score can be easily derived by the proposed model, with a high speed of convergence and without joint-distribution assumption. We illustrate the application of this model by an analysis of premenstrual disorder syndrome of liver-qi invasion syndrome evaluation research.