One of the most fundamental problems in network study is community detection. The stochastic block model (SBM) is a widely used model, for which various estimation methods have been developed with their community detection consistency results unveiled. However, the SBM is restricted by the strong assumption that all nodes in the same community are stochastically equivalent, which may not be suitable for practical applications. We introduce a pairwise covariates-adjusted stochastic block model (PCABM), a generalization of SBM that incorporates pairwise covariate information. We study the maximum likelihood estimates of the coefficients for the covariates as well as the community assignments. It is shown that both the coefficient estimates of the covariates and the community assignments are consistent under suitable sparsity conditions. Spectral clustering with adjustment (SCWA) is introduced to efficiently solve PCABM. Under certain conditions, we derive the error bound of community detection under SCWA and show that it is community detection consistent. In addition, we investigate model selection in terms of the number of communities and feature selection for the pairwise covariates, and propose two corresponding algorithms. PCABM compares favorably with the SBM or degree-corrected stochastic block model (DCBM) under a wide range of simulated and real networks when covariate information is accessible.
Nonparametric covariate adjustment is considered for log-rank type tests of treatment effect with right-censored time-to-event data from clinical trials applying covariate-adaptive randomization. Our proposed covariate-adjusted log-rank test has a simple explicit formula and a guaranteed efficiency gain over the unadjusted test. We also show that our proposed test achieves universal applicability in the sense that the same formula of test can be universally applied to simple randomization and all commonly used covariate-adaptive randomization schemes such as the stratified permuted block and P…
It is often important to incorporating covariate information in the design of clinical trials. In literature, there are many designs of using stratification and covariate-adaptive randomization to balance on certain known covariate. Recently Zhang, Hu, Cheung and Chan (2007) have proposed a family of covariate-adjusted response-adaptive (CARA) designs and studied their asymptotic properties. However, these CARA designs often have high variabilities. In this paper, we propose a new family of covariate-adjusted response-adaptive (CARA) designs. We show that the new designs have smaller variabili…
We often seek to estimate the causal effect of an exposure on a particular outcome in both randomized and observational settings. One such estimation method is the covariate-adjusted residuals estimator, which was designed for individually or cluster randomized trials. In this manuscript, we study the properties of this estimator and develop a new estimator that utilizes both covariate adjustment and inverse probability weighting We support our theoretical results with a simulation study and an application in an infectious disease setting. The covariate-adjusted residuals estimator is an effic…
A tuning-free procedure is proposed to estimate the covariate-adjusted Gaussian graphical model. For each finite subgraph, this estimator is asymptotically normal and efficient. As a consequence, a confidence interval can be obtained for each edge. The procedure enjoys easy implementation and efficient computation through parallel estimation on subgraphs or edges. We further apply the asymptotic normality result to perform support recovery through edge-wise adaptive thresholding. This support recovery procedure is called ANTAC, standing for Asymptotically Normal estimation with Thresholding af…
Response-adaptive designs have been extensively studied and used in clinical trials. However, there is a lack of a comprehensive study of response-adaptive designs that include covariates, despite their importance in clinical experiments. Because the allocation scheme and the estimation of parameters are affected by both the responses and the covariates, covariate-adjusted response-adaptive (CARA) designs are very complex to formulate. In this paper, we overcome the technical hurdles and lay out a framework for general CARA designs for the allocation of subjects to $K (\geq 2)$ treatments. The…
To maximize clinical benefit, clinicians routinely tailor treatment to the individual characteristics of each patient, where individualized treatment rules are needed and are of significant research interest to statisticians. In the covariate-adjusted randomization clinical trial with many covariates, we model the treatment effect with an unspecified function of a single index of the covariates and leave the baseline response completely arbitrary. We devise a class of estimators to consistently estimate the treatment effect function and its associated index while bypassing the estimation of th…
Differences between biological networks corresponding to disease conditions can help delineate the underlying disease mechanisms. Existing methods for differential network analysis do not account for dependence of networks on covariates. As a result, these approaches may detect spurious differential connections induced by the effect of the covariates on both the disease condition and the network. To address this issue, we propose a general covariate-adjusted test for differential network analysis. Our method assesses differential network connectivity by testing the null hypothesis that the net…
We consider the problem of identifying sub-groups of participants in a clinical trial that have enhanced treatment effect. Recursive partitioning methods that recursively partition the covariate space based on some measure of between groups treatment effect difference are popular for such sub-group identification. The most commonly used recursive partitioning method, the classification and regression tree algorithm, first creates a large tree by recursively partitioning the covariate space using some splitting criteria and then selects the final tree from all subtrees of the large tree. In the…
To improve precision of estimation and power of testing hypothesis for an unconditional treatment effect in randomized clinical trials with binary outcomes, researchers and regulatory agencies recommend using g-computation as a reliable method of covariate adjustment. However, the practical application of g-computation is hindered by the lack of an explicit robust variance formula that can be used for different unconditional treatment effects of interest. To fill this gap, we provide explicit and robust variance estimators for g-computation estimators and demonstrate through simulations that t…
We consider nonparametric estimation of a regression curve when the data are observed with multiplicative distortion which depends on an observed confounding variable. We suggest several estimators, ranging from a relatively simple one that relies on restrictive assumptions usually made in the literature, to a sophisticated piecewise approach that involves reconstructing a smooth curve from an estimator of a constant multiple of its absolute value, and which can be applied in much more general scenarios. We show that, although our nonparametric estimators are constructed from predictors of the…
This paper investigates the high-dimensional linear regression with highly correlated covariates. In this setup, the traditional sparsity assumption on the regression coefficients often fails to hold, and consequently many model selection procedures do not work. To address this challenge, we model the variations of covariates by a factor structure. Specifically, strong correlations among covariates are explained by common factors and the remaining variations are interpreted as idiosyncratic components of each covariate. This leads to a factor-adjusted regression model with both common factors …
In this paper we propose a general class of covariate-adjusted response-adaptive (CARA) designs based on a new functional urn model. We prove strong consistency concerning the functional urn proportion and the proportion of subjects assigned to the treatment groups, in the whole study and for each covariate profile, allowing the distribution of the responses conditioned on covariates to be estimated nonparametrically. In addition, we establish joint central limit theorems for the above quantities and the sufficient statistics of features of interest, which allow to construct procedures to make…
Accurate diagnosis of disease is of fundamental importance in clinical practice and medical research. Before a medical diagnostic test is routinely used in practice, its ability to distinguish between diseased and nondiseased states must be rigorously assessed through statistical analysis. The receiver operating characteristic (ROC) curve is the most popular used tool for evaluating the discriminatory ability of continuous-outcome diagnostic tests. It has been acknowledged that several factors (e.g., subject-specific characteristics, such as age and/or gender) can affect the test's accuracy be…
Fisher's randomization test (FRT) delivers exact $p$-values under the strong null hypothesis of no treatment effect on any units whatsoever and allows for flexible covariate adjustment to improve the power. Of interest is whether the procedure could also be valid for testing the weak null hypothesis of zero average treatment effect. Towards this end, we evaluate two general strategies for FRT with covariate-adjusted test statistics: that based on the residuals from an outcome model with only the covariates, and that based on the output from an outcome model with both the treatment and the cova…
In this paper, we present three estimators of the ROC curve when missing observations arise among the biomarkers. Two of the procedures assume that we have covariates that allow to estimate the propensity and the estimators are obtained using an inverse probability weighting method or a smoothed version of it. The other one assumes that the covariates are related to the biomarkers through a regression model which enables us to construct convolution--based estimators of the distribution and quantile functions. Consistency results are obtained under mild conditions. Through a numerical study we …
We present an objective Bayes method for covariance selection in Gaussian multivariate regression models whose error term has a covariance structure which is Markov with respect to a Directed Acyclic Graph (DAG). The scope is covariate-adjusted sparse graphical model selection, a topic of growing importance especially in the area of genetical genomics (eQTL analysis). Specifically, we provide a closed-form expression for the marginal likelihood of any DAG (with small parent sets) whose computation virtually requires no subjective elicitation by the user and involves only conjugate matrix norma…
Datasets from field experiments with covariate-adaptive randomizations (CARs) usually contain extra covariates in addition to the strata indicators. We propose to incorporate these additional covariates via auxiliary regressions in the estimation and inference of unconditional quantile treatment effects (QTEs) under CARs. We establish the consistency and limit distribution of the regression-adjusted QTE estimator and prove that the use of multiplier bootstrap inference is non-conservative under CARs. The auxiliary regression may be estimated parametrically, nonparametrically, or via regulariza…
We present a general framework for using existing data to estimate the efficiency gain from using a covariate-adjusted estimator of a marginal treatment effect in a future randomized trial. We describe conditions under which it is possible to define a mapping from the distribution that generated the existing external data to the relative efficiency of a covariate-adjusted estimator compared to an unadjusted estimator. Under conditions, these relative efficiencies approximate the ratio of sample size needed to achieve a desired power. We consider two situations where the outcome is either fully…
In contemporary scientific research, it is of great interest to predict a categorical response based on a high-dimensional tensor (i.e. multi-dimensional array) and additional covariates. This mixture of different types of data leads to challenges in statistical analysis. Motivated by applications in science and engineering, we propose a comprehensive and interpretable discriminant analysis model, called CATCH model (in short for Covariate-Adjusted Tensor Classification in High-dimensions), which efficiently integrates the covariates and the tensor to predict the categorical outcome. The CATCH…
Identifying a biomarker or treatment-dose threshold that marks a specified level of risk is an important problem, especially in clinical trials. This risk, viewed as a function of thresholds and possibly adjusted for covariates, we call the threshold-response function. Extending the work of Donovan, Hudgens and Gilbert (2019), we propose a nonparametric efficient estimator for the covariate-adjusted threshold-response function, which utilizes machine learning and Targeted Minimum-Loss Estimation (TMLE). We additionally propose a more general estimator, based on sequential regression, that also…
Dissecting Microbial Community Structure and Heterogeneity via Multivariate Covariate-Adjusted Clustering
University of Connecticut Health Center（康涅狄格大学健康中心）；Department of Biostatistics, University of Michigan（密歇根大学生物统计系）；Department of Statistics, University of Connecticut（康涅狄格大学统计学系）
In this article, we propose the outcome-adjusted balance measure to perform model selection for the generalized propensity score (GPS), which serves as an essential component in estimation of the pairwise average treatment effects (ATEs) in observational studies with more than two treatment levels. The primary goal of the balance measure is to identify the GPS model specification such that the resulting ATE estimator is consistent and efficient. Following recent empirical and theoretical evidence, we establish that the optimal GPS model should only include covariates related to the outcomes. G…
Anchored covariate-adjusted indirect comparisons inform reimbursement decisions where there are no head-to-head trials between the treatments of interest, there is a common comparator arm shared by the studies, and there are patient-level data limitations. Matching-adjusted indirect comparison (MAIC) is the most widely used covariate-adjusted indirect comparison method. MAIC has poor precision and is inefficient when the effective sample size after weighting is small. A modular extension to MAIC, termed two-stage matching-adjusted indirect comparison (2SMAIC), is proposed. This uses two parame…
In variable selection, most existing screening methods focus on marginal effects and ignore dependence between covariates. To improve the performance of selection, we incorporate pairwise effects in covariates for screening and penalization. We achieve this by studying the asymptotic distribution of the maximal absolute pairwise sample correlation among independent covariates. The novelty of the theory is in that the convergence is with respect to the dimensionality $p$, and is uniform with respect to the sample size $n$. Moreover, we obtain an upper bound for the maximal pairwise R squared wh…
We consider inference for the mean and covariance functions of covariate adjusted functional data using Local Linear Kernel (LLK) estimators. By means of a double asymptotic, we differentiate between sparse and dense covariate adjusted functional data - depending on the relative order of m (the discretization points per function) and n (the number of functions). Our simulation results demonstrate that the existing asymptotic normality results can lead to severely misleading inferences in finite samples. We explain this phenomenon based on our theoretical results and propose finite-sample corre…
Covariate-adjusted win statistics in randomized clinical trials with ordinal outcomes
Shenzhen Technology University（深圳理工大学）；Feinberg School of Medicine, Northwestern University（西北大学费恩伯格医学院）；University of Wisconsin - Madison（威斯康星大学麦迪逊分校）；Yale University School of Public Health（耶鲁大学公共卫生学院）；Yale Center for Analytical Sciences, Yale University School of Public Health（耶鲁大学公共卫生学院分析科学中心）；University of Washington（华盛顿大学）；Clinical Learning, Evidence, and Research (CLEAR) Center, University of Washington（华盛顿大学临床学习、证据与研究（CLEAR）中心）；Section of Cardiovascular Medicine, Department of Internal Medicine, Yale School of Medicine（耶鲁医学院内科学系心血管医学部）；Cardiovascular Medicine Analytics Center, Yale School of Medicine（耶鲁医学院心血管医学分析中心）；Center for Methods in Implementation and Prevention Science, Yale School of Public Health（耶鲁大学公共卫生学院实施与预防科学方法中心）
Two-stage least squares (TSLS) estimators and variants thereof are widely used to infer the effect of an exposure on an outcome using instrumental variables (IVs). They belong to a wider class of two-stage IV estimators, which are based on fitting a conditional mean model for the exposure, and then using the fitted exposure values along with the covariates as predictors in a linear model for the outcome. We show that standard TSLS estimators enjoy greater robustness to model misspecification than more general two-stage estimators. However, by potentially using a wrong exposure model, e.g. when…
This paper studies model selection consistency for high dimensional sparse regression when data exhibits both cross-sectional and serial dependency. Most commonly-used model selection methods fail to consistently recover the true model when the covariates are highly correlated. Motivated by econometric studies, we consider the case where covariate dependence can be reduced through factor model, and propose a consistent strategy named Factor-Adjusted Regularized Model Selection (FarmSelect). By separating the latent factors from idiosyncratic components, we transform the problem from model sele…
In comparative studies, such as in causal inference and clinical trials, balancing important covariates is often one of the most important concerns for both efficient and credible comparison. However, chance imbalance still exists in many randomized experiments. This phenomenon of covariate imbalance becomes much more serious as the number of covariates $p$ increases. To address this issue, we introduce a new randomization procedure, called pairwise sequential randomization (PSR). The proposed method allocates the units sequentially and adaptively, using information on the current level of imb…
Functional Principal Component Analysis (FPCA) has become a widely-used dimension reduction tool for functional data analysis. When additional covariates are available, existing FPCA models integrate them either in the mean function or in both the mean function and the covariance function. However, methods of the first kind are not suitable for data that display second-order variation, while those of the second kind are time-consuming and make it difficult to perform subsequent statistical analyses on the dimension-reduced representations. To tackle these issues, we introduce an eigen-adjusted…
The receiver operating characteristic (ROC) curve is the most popular tool used to evaluate the discriminatory capability of diagnostic tests/biomarkers measured on a continuous scale when distinguishing between two alternative disease states (e.g, diseased and nondiseased). In some circumstances, the test's performance and its discriminatory ability may vary according to subject-specific characteristics or different test settings. In such cases, information-specific accuracy measures, such as the covariate-specific and the covariate-adjusted ROC curve are needed, as ignoring covariate informa…
