Deep Treatment Learning (deepTL), a robust yet efficient deep learning-based semiparametric regression approach, is proposed to adjust the complex confounding structures in comparative effectiveness analysis of observational data, for example, electronic health record (EHR) data in which complex confounding structures are often embedded. Specifically, we develop a deep learning neural network with a score-based ensembling scheme for flexible function approximation. An improved semiparametric procedure is further developed to enhance the performance of the proposed method under finite sample settings. Comprehensive numerical studies have demonstrated the superior performance of the proposed methods, as compared with existing methods, with a remarkably reduced bias and mean squared error in parameter estimates. The proposed research is motivated by a postsurgery pain study, which is also used to illustrate the practical application of deepTL. Finally, an R package, “deepTL,” is developed to implement the proposed method.

Structural health monitoring (SHM) often involves instrumenting structures with distributed sensor networks. These networks typically provide high frequency data describing the spatiotemporal behaviour of the assets. A main objective of SHM is to reason about changes in structures’ behaviour using sensor data. We construct a streaming anomaly detection method for data from a railway bridge instrumented with a fibre-optic sensor network. The data exhibits trend over time, which may be partially attributable to environmental factors, calling for temporally adaptive estimation. Exploiting a latent structure present in the data motivates a quantity of interest for anomaly detection. This quantity is estimated, sequentially and adaptively, using a new formulation of streaming principal component analysis. Anomaly detection for this quantity is then provided using conformal prediction. Like all streaming methods, the proposed method has free control parameters which are set using simulations based on bridge data. Experiments demonstrate that this method can operate at the sampling frequency of the data while providing accurate tracking of the target quantity. Further, the anomaly detection is able to detect train passage events. Finally, the method reveals a previously unreported cyclic structure present in the data.

Improving existing widely-adopted prediction models is often a more efficient and robust way toward progress than training new models from scratch. Existing models may: (a) incorporate complex mechanistic knowledge, (b) leverage proprietary information, and (c) have surmounted barriers to adoption. Compared to model training, model improvement and modification receive little attention. In this paper we propose a general approach to model improvement: we combine gradient boosting with any previously developed model to improve model performance while retaining important existing characteristics. To exemplify, we consider the context of Mendelian models which estimate the probability of carrying genetic mutations that confer susceptibility to disease by using family pedigrees and health histories of family members. Via simulations, we show that integration of gradient boosting with an existing Mendelian model can produce an improved model that outperforms both that model and the model built using gradient boosting alone. We illustrate the approach on genetic testing data from the USC–Stanford Cancer Genetics Hereditary Cancer Panel (HCP) study.

For concertgoers, musical interpretation is the most important factor in determining whether or not we enjoy a classical performance. Every performance includes mistakes—intonation issues, a lost note, an unpleasant sound—but these are all easily forgotten (or unnoticed) when a performer engages her audience, imbuing a piece with novel emotional content beyond the vague instructions inscribed on the printed page. In this research we use data from the CHARM Mazurka Project—46 professional recordings of Chopin’s Mazurka Op. 68 No. 3 by consummate artists—with the goal of elucidating musically interpretable performance decisions. We focus specifically on each performer’s use of tempo by examining the interonset intervals of the note attacks in the recording. To explain these tempo decisions, we develop a switching state space model and estimate it by maximum likelihood, combined with prior information gained from music theory and performance practice. We use the estimated parameters to quantitatively describe individual performance decisions and compare recordings. These comparisons suggest methods for informing music instruction, discovering listening preferences and analyzing performances.

We propose to model time-varying periodic and oscillatory processes by means of a hidden Markov model where the states are defined through the spectral properties of a periodic regime. The number of states is unknown along with the relevant periodicities, the role and number of which may vary across states. We address this inference problem by a Bayesian nonparametric hidden Markov model, assuming a sticky hierarchical Dirichlet process for the switching dynamics between different states while the periodicities characterizing each state are explored by means of a transdimensional Markov chain Monte Carlo sampling step. We develop the full Bayesian inference algorithm and illustrate the use of our proposed methodology for different simulation studies as well as an application related to respiratory research which focuses on the detection of apnea instances in human breathing traces.

We introduce Targeted Smooth Bayesian Causal Forests (tsBCF), a nonparametric Bayesian approach for estimating heterogeneous treatment effects which vary smoothly over a single covariate in the observational data setting. The tsBCF method induces smoothness by parameterizing terminal tree nodes with smooth functions and allows for separate regularization of treatment effects vs. prognostic effect of control covariates. Smoothing parameters for prognostic and treatment effects can be chosen to reflect prior knowledge or tuned in a data-dependent way.

We use tsBCF to analyze a new clinical protocol for early medical abortion. Our aim is to assess the relative effectiveness of simultaneous vs. interval administration of mifepristone and misoprostol over the first nine weeks of gestation. Our analysis yields important clinical insights into how to best counsel patients seeking early medical abortion, where understanding even small differences in relative effectiveness can yield dramatic returns to public health. The model reflects our expectation that the treatment effect varies smoothly over gestation but not necessarily over other covariates. We demonstrate the performance of the tsBCF method on benchmarking experiments. Software for tsBCF is available at https://github.com/jestarling/tsbcf/ and in the Supplementary Material (Starling (2020)).

We consider regression in which one predicts a response Y with a set of predictors X across different experiments or environments. This is a common setup in many data-driven scientific fields, and we argue that statistical inference can benefit from an analysis that takes into account the distributional changes across environments. In particular, it is useful to distinguish between stable and unstable predictors, that is, predictors which have a fixed or a changing functional dependence on the response, respectively. We introduce stabilized regression which explicitly enforces stability and thus improves generalization performance to previously unseen environments. Our work is motivated by an application in systems biology. Using multiomic data, we demonstrate how hypothesis generation about gene function can benefit from stabilized regression. We believe that a similar line of arguments for exploiting heterogeneity in data can be powerful for many other applications as well. We draw a theoretical connection between multi-environment regression and causal models which allows to graphically characterize stable vs. unstable functional dependence on the response. Formally, we introduce the notion of a stable blanket which is a subset of the predictors that lies between the direct causal predictors and the Markov blanket. We prove that this set is optimal in the sense that a regression based on these predictors minimizes the mean squared prediction error, given that the resulting regression generalizes to unseen new environments.

Uplift models provide a solution to the problem of isolating the marketing effect of a campaign. For customer churn reduction, uplift models are used to identify the customers who are likely to respond positively to a retention activity, only if targeted, and to avoid wasting resources on customers that are very likely to switch to another company. In practice, the uplift models performance is measured by the Qini coefficient. We introduce a Qini-based uplift regression model to analyze a large insurance company’s retention marketing campaign. Our approach is based on logistic regression models. We show that a Qini-optimized uplift model acts as a regularizing factor for uplift, much as a penalized likelihood model does for regression. This results in interpretable models with few relevant explanatory variables. Our results show that Qini-based parameter estimation significantly improves the Qini prediction performance of uplift models.

The dramatic growth of big datasets presents a new challenge to data storage and analysis. Data reduction, or subsampling, that extracts useful information from datasets is a crucial step in big-data analysis. We propose an orthogonal subsampling (OSS) approach for big data with a focus on linear regression models. The approach is inspired by the fact that an orthogonal array of two levels provides the best experimental design for linear regression models in the sense that it minimizes the average variance of the estimated parameters and provides the best predictions. The merits of OSS are three-fold: (i) it is easy to implement and fast; (ii) it is suitable for distributed parallel computing and ensures the subsamples selected in different batches have no common data points, and (iii) it outperforms existing methods in minimizing the mean squared errors of the estimated parameters and maximizing the efficiencies of the selected subsamples. Theoretical results and extensive numerical results show that the OSS approach is superior to existing subsampling approaches. It is also more robust to the presence of interactions among covariates, and, when they do exist, OSS provides more precise estimates of the interaction effects than existing methods. The advantages of OSS are also illustrated through analysis of real data.

For certain subtypes of breast cancer, study findings show that their level of estrogen receptor expression is associated with their risk of cancer death and also suggest a nonlinear effect on the hazard of death. A flexible form of the proportional hazards model, $\mathit{\lambda }(\mathit{t}|\mathit{x},\mathit{z})=\mathit{\lambda }(\mathit{t})exp({\mathit{z}}^{\mathit{T}}\mathit{\beta })\mathit{q}(\mathit{x})$, is desirable to facilitate a rich class of covariate effect on a survival outcome to provide meaningful insight, where the functional form of $\mathit{q}(\mathit{x})$ is not specified except for its shape. Prior biologic knowledge on the shape of the underlying distribution of the covariate effect in regression models can be used to enhance statistical inference. Despite recent progress, major challenges remain for the semiparametric shape-restricted inference due to lack of practical and efficient computational algorithms to accomplish nonconvex optimization. We propose an alternative algorithm to maximize the full log-likelihood with two sets of parameters iteratively under monotone constraints. The first set consists of the nonparametric estimation of the monotone-restricted function $\mathit{q}(\mathit{x})$, while the second set includes estimating the baseline hazard function and other covariate coefficients. The iterative algorithm, in conjunction with the pool-adjacent-violators algorithm, makes the computation efficient and practical. The jackknife resampling effectively reduces the estimator bias, when sample size is small. Simulations show that the proposed method can accurately capture the underlying shape of $\mathit{q}(\mathit{x})$ and outperforms the estimators when $\mathit{q}(\mathit{x})$ in the Cox model is misspecified. We apply the method to model the effect of estrogen receptor on breast cancer patients’ survival.

In cardiovascular studies we often observe ordered multiple events along disease progression which are, essentially, a series of recurrent events and terminal events with competing risk structure. One of the main interests is to explore the event specific association with the dynamics of longitudinal biomarkers. A new statistical challenge arises when the biomarkers carry information from the past event history, providing feedbacks for the occurrences of future events and, particularly, when these biomarkers are only intermittently observed with measurement errors. In this paper we propose a novel modeling framework where the recurrent events and terminal events are modeled as multistate processes and the longitudinal covariates that account for event feedbacks are described by random effects models. Considering the nature of long-term observation in cardiac studies, flexible models with semiparametric coefficients are adopted. To improve computation efficiency, we develop an one-step estimator of the regression coefficients and derive their asymptotic variances for the computation of the confidence intervals, based on the proposed asymptotically unbiased estimating equation. Simulation studies show that the naive estimators, which either ignore the past event feedbacks or the measurement errors, are biased. Our method achieves better coverage probability, compared to the naive methods. The model is motivated and applied to a dataset from the Atherosclerosis Risk in Communities Study.

Ohio is one of the states most impacted by the opioid epidemic and experienced the second highest age-adjusted fatal drug overdose rate in 2017. Initially it was believed prescription opioids were driving the opioid crisis in Ohio. However, as the epidemic evolved, opioid overdose deaths due to fentanyl have drastically increased. In this work we develop a Bayesian multivariate spatiotemporal model for Ohio county overdose death rates from 2007 to 2018 due to different types of opioids. The log-odds are assumed to follow a spatially varying change point regression model. By assuming the regression coefficients are a multivariate conditional autoregressive process, we capture spatial dependence within each drug type and also dependence across drug types. The proposed model allows us to not only study spatiotemporal trends in overdose death rates but also to detect county-level shifts in these trends over time for various types of opioids.

This paper considers the modeling of zero-inflated circular measurements concerning real case studies from medical sciences. Circular-circular regression models have been discussed in the statistical literature and illustrated with various real-life applications. However, there are no models to deal with zero-inflated response as well as a covariate simultaneously. The Möbius transformation based two-stage circular-circular regression model is proposed, and the Bayesian estimation of the model parameters is suggested using the MCMC algorithm. Simulation results show the superiority of the performance of the proposed method over the existing competitors. The method is applied to analyse real datasets on astigmatism due to cataract surgery and abnormal gait related to orthopaedic impairment. The methodology proposed can assist in efficient decision making during treatment or postoperative care.

The ability to identify time periods when individuals are most susceptible to exposures as well as the biological mechanisms through which these exposures act is of great public health interest. Growing evidence supports an association between prenatal exposure to air pollution and epigenetic marks, such as DNA methylation, but the timing and gene-specific effects of these epigenetic changes are not well understood. Here, we present the first study that aims to identify prenatal windows of susceptibility to air pollution exposures in cord blood DNA methylation. In particular, we propose a function-on-function regression model that leverages data from nearby DNA methylation probes to identify epigenetic regions that exhibit windows of susceptibility to ambient particulate matter less than 2.5 microns (PM${}_{2.5}$). By incorporating the covariance structure among both the multivariate DNA methylation outcome and the time-varying exposure under study, this framework yields greater power to detect windows of susceptibility and greater control of false discoveries than methods that model probes independently. We compare our method to a distributed lag model approach that models DNA methylation in a probe-by-probe manner, both in simulation and by application to motivating data from the Project Viva birth cohort. We identify a window of susceptibility to PM${}_{2.5}$ exposure in the middle of the third trimester of pregnancy in an epigenetic region selected based on prior studies of air pollution effects on epigenome-wide methylation.

In this article we investigate group differences in phthalate exposure profiles using NHANES data. Phthalates are a family of industrial chemicals used in plastics and as solvents. There is increasing evidence of adverse health effects of exposure to phthalates on reproduction and neurodevelopment and concern about racial disparities in exposure. We would like to identify a single set of low-dimensional factors summarizing exposure to different chemicals, while allowing differences across groups. Improving on current multigroup additive factor models, we propose a class of Perturbed Factor Analysis (PFA) models that assume a common factor structure after perturbing the data via multiplication by a group-specific matrix. Bayesian inference algorithms are defined using a matrix normal hierarchical model for the perturbation matrices. The resulting model is just as flexible as current approaches in allowing arbitrarily large differences across groups but has substantial advantages that we illustrate in simulation studies. Applying PFA to NHANES data, we learn common factors summarizing exposures to phthalates, while showing clear differences across groups.

Today there are approximately 85,000 chemicals regulated under the Toxic Substances Control Act, with around 2,000 new chemicals introduced each year. It is impossible to screen all of these chemicals for potential toxic effects, either via full organism in vivo studies or in vitro high-throughput screening (HTS) programs. Toxicologists face the challenge of choosing which chemicals to screen, and predicting the toxicity of as yet unscreened chemicals. Our goal is to describe how variation in chemical structure relates to variation in toxicological response to enable in silico toxicity characterization designed to meet both of these challenges. With our Bayesian partially Supervised Sparse and Smooth Factor Analysis (${\mathrm{BS}}^3\mathrm{FA}$) model, we learn a distance between chemicals targeted to toxicity, rather than one based on molecular structure alone. Our model also enables the prediction of chemical dose-response profiles based on chemical structure (i.e., without in vivo or in vitro testing) by taking advantage of a large database of chemicals that have already been tested for toxicity in HTS programs. We show superior simulation performance in distance learning and modest to large gains in predictive ability compared to existing methods. Results from the high-throughput screening data application elucidate the relationship between chemical structure and a toxicity-relevant high-throughput assay. An $\mathsf{R}$ package for ${\mathrm{BS}}^3\mathrm{FA}$ is available online at https://github.com/kelrenmor/bs3fa.

As advances in technology allow the acquisition of complementary information, it is increasingly common for scientific studies to collect multiple datasets. Large-scale neuroimaging studies often include multiple modalities (e.g., task functional MRI, resting-state fMRI, diffusion MRI, and/or structural MRI) with the aim to understand the relationships between datasets. In this study, we seek to understand whether regions of the brain activated in a working memory task relate to resting-state correlations. In neuroimaging, a popular approach uses principal component analysis for dimension reduction prior to canonical correlation analysis with joint independent component analysis, but this may discard biological features with low variance and/or spuriously associate structure unique to a dataset with joint structure. We introduce SImultaneous Non-Gaussian component analysis (SING) in which dimension reduction and feature extraction are achieved simultaneously, and shared information is captured via subject scores. We apply our method to a working memory task and resting-state correlations from the Human Connectome Project. We find joint structure as evident from joint scores whose loadings highlight resting-state correlations involving regions associated with working memory. Moreover, some of the subject scores are related to fluid intelligence.

Human intelligence is usually measured by well-established psychometric tests through a series of problem solving. The recorded cognitive scores are continuous but usually heavy-tailed with potential outliers and violating the normality assumption. Meanwhile, magnetic resonance imaging (MRI) provides an unparalleled opportunity to study brain structures and cognitive ability. Motivated by association studies between MRI images and human intelligence, we propose a tensor quantile regression model, which is a general and robust alternative to the commonly used scalar-on-image linear regression. Moreover, we take into account rich spatial information of brain structures, incorporating low-rankness and piecewise smoothness of imaging coefficients into a regularized regression framework. We formulate the optimization problem as a sequence of penalized quantile regressions with a generalized Lasso penalty, based on tensor decomposition, and develop a computationally efficient alternating direction method of multipliers algorithm (ADMM) to estimate the model components. Extensive numerical studies are conducted to examine the empirical performance of the proposed method and its competitors. Finally, we apply the proposed method to a large-scale important dataset—the Human Connectome Project. We find that the tensor quantile regression can serve as a prognostic tool to assess future risk of cognitive impairment progression. More importantly, with the proposed method we are able to identify the most activated brain subregions associated with quantiles of human intelligence. The prefrontal and anterior cingulate cortex are found to be mostly associated with lower and upper quantile of fluid intelligence. The insular cortex associated with median of fluid intelligence is a rarely reported region.

Thirty-day rehospitalization rate is a well-studied and important measure reflecting the overall performance of health systems. Recently, transitional care (TC) programs have been initiated to reduce avoidable rehospitalizations. These programs typically ask nurses to follow-up with patients after the hospitalization to manage issues and reduce the risk of rehospitalizations during health care transitions. As rehospitalization is a complex process that depends on many factors, it is unlikely that these interventions are effective for all patients across a diverse population. In this paper we consider individualized intervention or treatment recommendation rules (ITRs) aimed at maximizing overall treatment effectiveness. We investigate our approach in a setting where patients are divided into two diagnosis related groups, medically complicated and uncomplicated. As the treatment effects can greatly vary between the two groups, we allow our recommendation rules to be group specific. In particular, our approach can accommodate scale differences in treatment effects and utilize a tuning parameter to drive the similarity of the estimated ITRs between groups. Computation is achieved by transforming our problem into a form solvable by existing software, and a wrapper R package is developed for our proposed treatment recommendation framework. We conduct extensive evaluation through both simulation studies and analysis of a TC program.

The sex ratio at birth (SRB) is defined as the ratio of male to female live births. The SRB imbalance in parts of the world over the past several decades is a direct consequence of sex-selective abortion, driven by the coexistence of son preference, readily available technology of prenatal sex determination and fertility decline. Estimation and projection of the degree of SRB imbalance is complicated because of variability in SRB reference levels and because of the uncertainty associated with SRB observations.

We develop Bayesian hierarchical time series mixture models for SRB estimation and scenario-based projections for all countries from 1950 to 2100. We model the SRB regional and national reference levels and the fluctuation around national reference levels. We identify countries at risk of SRB imbalances and model both: (i) the absence or presence of sex ratio transitions in such countries and, if present, (ii) the transition process. The transition model of SRB imbalance captures three stages (increase, stagnation and convergence back to SRB baselines). The model identifies countries with statistical evidence of SRB inflation in a fully Bayesian approach. The scenario-based SRB projections are based on the sex ratio transition model with varying assumptions regarding the occurrence of a sex ratio transition in at-risk countries. Projections are used to quantify the future burden of missing female births due to sex-selective abortions under different scenarios.

Cognitive diagnosis models (CDMs) are a family of discrete latent attribute models that serve as statistical basis in educational and psychological cognitive diagnosis assessments. CDMs aim to achieve fine-grained inference on individuals’ latent attributes, based on their observed responses to a set of designed diagnostic items. In the literature CDMs usually assume that items require mastery of specific latent attributes and that each attribute is either fully mastered or not mastered by a given subject. We propose a new class of models, partial mastery CDMs (PM-CDMs), that generalizes CDMs by allowing for partial mastery levels for each attribute of interest. We demonstrate that PM-CDMs can be represented as restricted latent class models. Relying on the latent class representation, we propose a Bayesian approach for estimation. We present simulation studies to demonstrate parameter recovery, to investigate the impact of model misspecification with respect to partial mastery and to develop diagnostic tools that could be used by practitioners to decide between CDMs and PM-CDMs. We use two examples of real test data—the fraction subtraction and the English tests—to demonstrate that employing PM-CDMs not only improves model fit, compared to CDMs, but also can make substantial difference in conclusions about attribute mastery. We conclude that PM-CDMs can lead to more effective remediation programs by providing detailed individual-level information about skills learned and skills that need to study.

Selection bias is a serious potential problem for inference about relationships of scientific interest based on samples without well-defined probability sampling mechanisms. Motivated by the potential for selection bias in: (a) estimated relationships of polygenic scores (PGSs) with phenotypes in genetic studies of volunteers and (b) estimated differences in subgroup means in surveys of smartphone users, we derive novel measures of selection bias for estimates of the coefficients in linear and probit regression models fitted to nonprobability samples, when aggregate-level auxiliary data are available for the selected sample and the target population. The measures arise from normal pattern-mixture models that allow analysts to examine the sensitivity of their inferences to assumptions about nonignorable selection in these samples. We examine the effectiveness of the proposed measures in a simulation study and then use them to quantify the selection bias in: (a) estimated PGS-phenotype relationships in a large study of volunteers recruited via Facebook and (b) estimated subgroup differences in mean past-year employment duration in a nonprobability sample of low-educated smartphone users. We evaluate the performance of the measures in these applications using benchmark estimates from large probability samples.