Community detection has attracted tremendous interests in network analysis, which aims at finding group of nodes with similar characteristics. Various detection methods have been developed to detect homogeneous communities in multi-layer networks, where inter-layer dependence is a widely acknowledged but severely under-investigated issue. In this paper, we propose a novel stochastic block Ising model (SBIM) to incorporate the inter-layer dependence to help with community detection in multi-layer networks. The community structure is modeled by the stochastic block model (SBM) and the inter-layer dependence is incorporated via the popular Ising model. Furthermore, we develop an efficient variational EM algorithm to tackle the resultant optimization task and establish the asymptotic consistency of the proposed method. Extensive simulated examples and a real example on gene co-expression multi-layer network data are also provided to demonstrate the advantage of the proposed method.

Quantile regression has emerged as a useful and effective tool in modeling survival data, especially for cases where noises demonstrate heterogeneity. Despite recent advancements, non-smooth components involved in censored quantile regression estimators may often yield numerically unstable results, which, in turn, lead to potentially self-contradicting conclusions. We propose an estimating equation-based approach to obtain consistent estimators of the regression coefficients of interest via the induced smoothing technique to circumvent the difficulty. Our proposed estimator can be shown to be asymptotically equivalent to its original unsmoothed version, whose consistency and asymptotic normality can be readily established. Extensions to handle functional covariate data and recurrent event data are also discussed. To alleviate the heavy computational burden of bootstrap-based variance estimation, we also propose an efficient resampling procedure that reduces the computational time considerably. Our numerical studies demonstrate that our proposed estimator provides substantially smoother model parameter estimates across different quantile levels and can achieve better statistical efficiency compared to a plain estimator under various finite-sample settings. The proposed method is also illustrated via four survival datasets, including the HMO (health maintenance organizations) HIV (human immunodeficiency virus) data, the primary biliary cirrhosis (PBC) data, and so forth.

We propose a Bayesian model selection approach for generalized linear mixed models (GLMMs). We consider covariance structures for the random effects that are widely used in areas such as longitudinal studies, genome-wide association studies, and spatial statistics. Since the random effects cannot be integrated out of GLMMs analytically, we approximate the integrated likelihood function using a pseudo-likelihood approach. Our Bayesian approach assumes a flat prior for the fixed effects and includes both approximate reference prior and half-Cauchy prior choices for the variances of random effects. Since the flat prior on the fixed effects is improper, we develop a fractional Bayes factor approach to obtain posterior probabilities of the several competing models. Simulation studies with Poisson GLMMs with spatial random effects and overdispersion random effects show that our approach performs favorably when compared to widely used competing Bayesian methods including deviance information criterion and Watanabe-Akaike information criterion. We illustrate the usefulness and flexibility of our approach with three case studies including a Poisson longitudinal model, a Poisson spatial model, and a logistic mixed model. Our proposed approach is implemented in the R package GLMMselect that is available on CRAN.

Sample size and power determination are crucial design considerations for biomedical studies intending to formally test the effects of key variables on an outcome. Other known prognostic factors may exist, necessitating the use of techniques for covariate adjustment when conducting this evaluation. Moreover, the main interest often includes assessing the impact of more than one variable on an outcome, such as multiple treatments or risk factors. Regression models are frequently employed for these purposes, formalizing this assessment as a test of multiple regression parameters. But, the presence of multiple variables of primary interest and correlation between covariates can complicate sample size/power calculation. Given the paucity of available sample size formulas for this context, these calculations are often performed via simulation, which can be both time-consuming as well as demanding extensive probability modeling. We propose a simpler, general approach to sample size and power determination that may be applied when testing multiple parameters in commonly used regression models, including generalized linear models as well as ordinary and stratified versions of the Cox and Fine-Gray models. Through both rigorous simulations and theoretical derivations, we demonstrate the formulas' accuracy in producing sample sizes that will meet the type I error rate and power specifications of the study design.

The prevalence of data collected on the same set of samples from multiple sources (i.e., multi-view data) has prompted significant development of data integration methods based on low-rank matrix factorizations. These methods decompose signal matrices from each view into the sum of shared and individual structures, which are further used for dimension reduction, exploratory analyses, and quantifying associations across views. However, existing methods have limitations in modeling partially-shared structures due to either too restrictive models, or restrictive identifiability conditions. To address these challenges, we propose a new formulation for signal structures that include partially-shared signals based on grouping the views into so-called hierarchical levels with identifiable guarantees under suitable conditions. The proposed hierarchy leads us to introduce a new penalty, hierarchical nuclear norm (HNN), for signal estimation. In contrast to existing methods, HNN penalization avoids scores and loadings factorization of the signals and leads to a convex optimization problem, which we solve using a dual forward-backward algorithm. We propose a simple refitting procedure to adjust the penalization bias and develop an adapted version of bi-cross-validation for selecting tuning parameters. Extensive simulation studies and analysis of the genotype-tissue expression data demonstrate the advantages of our method over existing alternatives.

In longitudinal studies, it is not uncommon to make multiple attempts to collect a measurement after baseline. Recording whether these attempts are successful provides useful information for the purposes of assessing missing data assumptions. This is because measurements from subjects who provide the data after numerous failed attempts may differ from those who provide the measurement after fewer attempts. Previous models for these designs were parametric and/or did not allow sensitivity analysis. For the former, there are always concerns about model misspecification and for the latter, sensitivity analysis is essential when conducting inference in the presence of missing data. Here, we propose a new approach which minimizes issues with model misspecification by using Bayesian nonparametrics for the observed data distribution. We also introduce a novel approach for identification and sensitivity analysis. We re-analyze the repeated attempts data from a clinical trial involving patients with severe mental illness and conduct simulations to better understand the properties of our approach.

The problem of how to best select variables for confounding adjustment forms one of the key challenges in the evaluation of exposure effects in observational studies, and has been the subject of vigorous recent activity in causal inference. A major drawback of routine procedures is that there is no finite sample size at which they are guaranteed to deliver exposure effect estimators and associated confidence intervals with adequate performance. In this work, we will consider this problem when inferring conditional causal hazard ratios from observational studies under the assumption of no unmeasured confounding. The major complication that we face with survival data is that the key confounding variables may not be those that explain the censoring mechanism. In this paper, we overcome this problem using a novel and simple procedure that can be implemented using off-the-shelf software for penalized Cox regression. In particular, we will propose tests of the null hypothesis that the exposure has no effect on the considered survival endpoint, which are uniformly valid under standard sparsity conditions. Simulation results show that the proposed methods yield valid inferences even when covariates are high-dimensional.

Mendelian randomization (MR) is a widely used method to estimate the causal effect of an exposure on an outcome by using genetic variants as instrumental variables. MR analyses that use variants from only a single genetic region (cis-MR) encoding the protein target of a drug are able to provide supporting evidence for drug target validation. This paper proposes methods for cis-MR inference that use many correlated variants to make robust inferences even in situations, where those variants have only weak effects on the exposure. In particular, we exploit the highly structured nature of genetic correlations in single gene regions to reduce the dimension of genetic variants using factor analysis. These genetic factors are then used as instrumental variables to construct tests for the causal effect of interest. Since these factors may often be weakly associated with the exposure, size distortions of standard t-tests can be severe. Therefore, we consider two approaches based on conditional testing. First, we extend results of commonly-used identification-robust tests for the setting where estimated factors are used as instruments. Second, we propose a test which appropriately adjusts for first-stage screening of genetic factors based on their relevance. Our empirical results provide genetic evidence to validate cholesterol-lowering drug targets aimed at preventing coronary heart disease.

In clinical follow-up studies with a time-to-event end point, the difference in the restricted mean survival time (RMST) is a suitable substitute for the hazard ratio (HR). However, the RMST only measures the survival of patients over a period of time from the baseline and cannot reflect changes in life expectancy over time. Based on the RMST, we study the conditional restricted mean survival time (cRMST) by estimating life expectancy in the future according to the time that patients have survived, reflecting the dynamic survival status of patients during follow-up. In this paper, we introduce the estimation method of cRMST based on pseudo-observations, the statistical inference concerning the difference between two cRMSTs (cRMSTd), and the establishment of the robust dynamic prediction model using the landmark method. Simulation studies are conducted to evaluate the statistical properties of these methods. The results indicate that the estimation of the cRMST is accurate, and the dynamic RMST model has high accuracy in coefficient estimation and good predictive performance. In addition, an example of patients with chronic kidney disease who received renal transplantations is employed to illustrate that the dynamic RMST model can predict patients' expected survival times from any prediction time, considering the time-dependent covariates and time-varying effects of covariates.

Causal inference practitioners have increasingly adopted machine learning techniques with the aim of producing principled uncertainty quantification for causal effects while minimizing the risk of model misspecification. Bayesian nonparametric approaches have attracted attention as well, both for their flexibility and their promise of providing natural uncertainty quantification. Priors on high-dimensional or nonparametric spaces, however, can often unintentionally encode prior information that is at odds with substantive knowledge in causal inference-specifically, the regularization required for high-dimensional Bayesian models to work can indirectly imply that the magnitude of the confounding is negligible. In this paper, we explain this problem and provide tools for (i) verifying that the prior distribution does not encode an inductive bias away from confounded models and (ii) verifying that the posterior distribution contains sufficient information to overcome this issue if it exists. We provide a proof-of-concept on simulated data from a high-dimensional probit-ridge regression model, and illustrate on a Bayesian nonparametric decision tree ensemble applied to a large medical expenditure survey.

The study of how the number of spikes in a middle temporal visual area (MT/V5) neuron is tuned to the direction of a visual stimulus has attracted considerable attention over the years, but recent studies suggest that the variability of the number of spikes might also be influenced by the directional stimulus. This entails that Poisson regression models are not adequate for this type of data, as the observations usually present over/underdispersion (or both) with respect to the Poisson distribution. This paper makes use of the double exponential family and presents a flexible model to estimate, jointly, the mean and dispersion functions, accounting for the effect of a circular covariate. The empirical performance of the proposal is explored via simulations and an application to a neurological data set is shown.

In Duchenne muscular dystrophy (DMD) and other rare diseases, recruiting patients into clinical trials is challenging. Additionally, assigning patients to long-term, multi-year placebo arms raises ethical and trial retention concerns. This poses a significant challenge to the traditional sequential drug development paradigm. In this paper, we propose a small-sample, sequential, multiple assignment, randomized trial (snSMART) design that combines dose selection and confirmatory assessment into a single trial. This multi-stage design evaluates the effects of multiple doses of a promising drug and re-randomizes patients to appropriate dose levels based on their Stage 1 dose and response. Our proposed approach increases the efficiency of treatment effect estimates by (i) enriching the placebo arm with external control data, and (ii) using data from all stages. Data from external control and different stages are combined using a robust meta-analytic combined (MAC) approach to consider the various sources of heterogeneity and potential selection bias. We reanalyze data from a DMD trial using the proposed method and external control data from the Duchenne Natural History Study (DNHS). Our method's estimators show improved efficiency compared to the original trial. Also, the robust MAC-snSMART method most often provides more accurate estimators than the traditional analytic method. Overall, the proposed methodology provides a promising candidate for efficient drug development in DMD and other rare diseases.

It has been increasingly appealing to evaluate whether expression levels of two genes in a gene coexpression network are still dependent given samples' clinical information, in which the conditional independence test plays an essential role. For enhanced robustness regarding model assumptions, we propose a class of double-robust tests for evaluating the dependence of bivariate outcomes after controlling for known clinical information. Although the proposed test relies on the marginal density functions of bivariate outcomes given clinical information, the test remains valid as long as one of the density functions is correctly specified. Because of the closed-form variance formula, the proposed test procedure enjoys computational efficiency without requiring a resampling procedure or tuning parameters. We acknowledge the need to infer the conditional independence network with high-dimensional gene expressions, and further develop a procedure for multiple testing by controlling the false discovery rate. Numerical results show that our method accurately controls both the type-I error and false discovery rate, and it provides certain levels of robustness regarding model misspecification. We apply the method to a gastric cancer study with gene expression data to understand the associations between genes belonging to the transforming growth factor β signaling pathway given cancer-stage information.