Matching is a commonly used causal inference study design in observational studies. Through matching on measured confounders between different treatment groups, valid randomization inferences can be conducted under the no unmeasured confounding assumption, and sensitivity analysis can be further performed to assess robustness of results to potential unmeasured confounding. However, for many common matched designs, there is still a lack of valid downstream randomization inference and sensitivity analysis methods. Specifically, in matched observational studies with treatment doses (eg, continuous or ordinal treatments), with the exception of some special cases such as pair matching, there is no existing randomization inference or sensitivity analysis method for studying analogs of the sample average treatment effect (ie, Neyman-type weak nulls), and no existing valid sensitivity analysis approach for testing the sharp null of no treatment effect for any subject (ie, Fisher's sharp null) when the outcome is nonbinary. To fill these important gaps, we propose new methods for randomization inference and sensitivity analysis that can work for general matched designs with treatment doses, applicable to general types of outcome variables (eg, binary, ordinal, or continuous), and cover both Fisher's sharp null and Neyman-type weak nulls. We illustrate our methods via comprehensive simulation studies and a real data application. All the proposed methods have been incorporated into $\tt {R}$ package $\tt {doseSens}$.

In many genomic studies, gene co-expression graphs are influenced by subject-level covariates like single nucleotide polymorphisms. Traditional Gaussian graphical models ignore these covariates and estimate only population-level networks, potentially masking important heterogeneity. Covariate-dependent Gaussian graphical regressions address this limitation by regressing the precision matrix on covariates, thereby modeling how graph structures vary with high-dimensional subject-specific covariates. To fit the model, we adopt a multi-task learning approach that achieves lower error rates than node-wise regressions. Yet, the important problem of statistical inference in this setting remains largely unexplored. We propose a class of debiased estimators based on multi-task learners, which can be computed quickly and separately. In a key step, we introduce a novel projection technique for estimating the inverse covariance matrix, reducing optimization costs to scale with the sample size n. Our debiased estimators achieve fast convergence and asymptotic normality, enabling valid inference. Simulations demonstrate the utility of the method, and an application to a brain cancer gene-expression dataset reveals meaningful biological relationships.

Clustering is widely used in biomedical research for meaningful subgroup identification. However, most existing clustering algorithms do not account for the statistical uncertainty of the resulting clusters and consequently may generate spurious clusters due to natural sampling variation. To address this problem, the Statistical Significance of Clustering (SigClust) method was developed to evaluate the significance of clusters in high-dimensional data. While SigClust has been successful in assessing clustering significance for continuous data, it is not specifically designed for discrete data, such as count data in genomics. Moreover, SigClust and its variations can suffer from reduced statistical power when applied to non-Gaussian high-dimensional data. To overcome these limitations, we propose SigClust-DEV, a method designed to evaluate the significance of clusters in count data. Through extensive simulations, we compare SigClust-DEV against other existing SigClust approaches across various count distributions and demonstrate its superior performance. Furthermore, we apply our proposed SigClust-DEV to Hydra single-cell RNA sequencing (scRNA) data and electronic health records (EHRs) of cancer patients to identify meaningful latent cell types and patient subgroups, respectively.

ABSTRACTInvestigators often focus on predicting extreme random effects from mixed effects models fitted to longitudinal or clustered data, and on identifying or “flagging” outliers such as poorly performing hospitals or rapidly deteriorating patients. Our recent work with Gaussian outcomes showed that weighted prediction methods can substantially reduce mean square error of prediction for extremes and substantially increase correct flagging rates compared to previous methods, while controlling the incorrect flagging rates. This paper extends the weighted prediction methods to non-Gaussian outcomes such as binary and count data. Closed-form expressions for predicted random effects and probabilities of correct and incorrect flagging are not available for the usual non-Gaussian outcomes, and the computational challenges are substantial. Therefore, our results include the development of theory to support algorithms that tune predictors that we call “self-calibrated” (which control the incorrect flagging rate using very simple flagging rules) and innovative numerical methods to calculate weighted predictors as well as to evaluate their performance. Comprehensive numerical evaluations show that the novel weighted predictors for non-Gaussian outcomes have substantially lower mean square error of prediction at the extremes and considerably higher correct flagging rates than previously proposed methods, while controlling the incorrect flagging rates. We illustrate our new methods using data on emergency room readmissions for children with asthma.

In studies of medical treatments, individuals often experience post-treatment events that predict their future outcomes. In this work, we study how to use initial observations of a recurrent event-a type of post-treatment event-to offer updated treatment recommendations in settings where no, or few, individuals are observed to switch between treatment arms. Specifically, we formulate an estimand quantifying the average effect of switching treatment on subsequent events. We derive bounds on the value of this estimand under plausible conditions and propose non-parametric estimators of the bounds. Furthermore, we define a value and regret function for a dynamic treatment-switching regime, and use these to determine 3 types of optimal regimes under partial identification: the pessimist (maximin value), optimist (maximax value), and opportunist (minimax regret) regimes. The pessimist regime is guaranteed to perform at least as well as the standard of care. We apply our methods to data from the Systolic Blood Pressure Intervention Trial.

Quantifying associations between short-term exposure to ambient air pollution and health outcomes is an important public health priority. Many studies have investigated the association considering delayed effects within the past few days. Adaptive cumulative exposure distributed lag non-linear models (ACE-DLNMs) quantify associations between health outcomes and cumulative exposure that is specified in a data-adaptive way. While the ACE-DLNM framework is highly interpretable, it is limited to continuous outcomes and does not scale well to large datasets. Motivated by a large analysis of daily pollution and respiratory hospitalization counts in Canada between 2001 and 2018, we propose a generalized ACE-DLNM incorporating penalized splines, improving upon existing ACE-DLNM methods to accommodate general response types. We then develop a computationally efficient estimation strategy based on profile likelihood and Laplace approximate marginal likelihood with Newton-type methods. We demonstrate the performance and practical advantages of the proposed method through simulations. In application to the motivating analysis, the proposed method yields more stable inferences compared to generalized additive models with fixed exposures, while retaining interpretability.

Inspired by logistic regression, we introduce a regression model for data tuples consisting of a binary response and a set of covariates residing in a metric space without vector structures. Based on the proposed model, we also develop a binary classifier for metric-space valued data. We propose a maximum likelihood estimator for the metric-space valued regression coefficient in the model, and provide upper bounds on the estimation error under various metric entropy conditions that quantify complexity of the underlying metric space. Matching lower bounds are derived for the important metric spaces commonly seen in statistics, establishing optimality of the proposed estimator in such spaces. A finer upper bound and a matching lower bound, and thus optimality of the proposed classifier, are established for Riemannian manifolds. To the best of our knowledge, the proposed regression model and the above minimax bounds are the first of their kind for analyzing a binary response with covariates residing in general metric spaces. We also investigate the numerical performance of the proposed estimator and classifier via simulation studies, and illustrate their practical merits via an application to task-related fMRI data.

The joint spatial distribution of two count outcomes (eg, counts of two diseases) is usually studied using a Poisson shared component model (P-SCM), which uses geographically structured latent variables to model spatial variations that are specific and shared by both outcomes. In this model, the correlation between the outcomes is assumed to be fully accounted for by the latent variables. However, in this article, we show that when the outcomes have an unknown number of cases in common, the bivariate counts exhibit a positive "residual" correlation, which the P-SCM wrongly attributes to the covariance of the latent variables, leading to biased inference and degraded predictive performance. Accordingly, we propose a new SCM based on the Bivariate-Poisson distribution (BP-SCM hereafter) to study such correlated bivariate data. The BP-SCM decomposes each count into counts of common and distinct cases, and then models each of these three counts (two distinct and one common) using Gaussian Markov Random Fields. The model is formulated in a Bayesian framework using Hamiltonian Monte Carlo inference. Simulations and a real-world application showed the good inferential and predictive performances of the BP-SCM and confirm the bias in P-SCM. BP-SCM provides rich epidemiological information, such as the mean levels of the unknown counts of common and distinct cases, and their shared and specific spatial variations.