National health insurance schemes are generally impractical in low-income countries due to limited resources and low organizational capacity. In response to such obstacles, community-based health insurance (CBHI) schemes have emerged over the past 20 years. CBHIs are designed to reduce the financial burden generated by unanticipated treatment cost among individuals falling sick, and thus are expected to make health care more affordable. In this paper, we investigate whether CBHI schemes effectively protect individuals against large financial shocks using a stepped-wedge cluster-randomized design on data from a CBHI program rolled out in rural Burkina Faso. We investigate statistical properties of the stepped-wedge design following the parametric mixed model approach proposed by Hussey and Hughes in 2007. We find that testing for the treatment effect is generally sensitive to specification of the parametric model. For instance, if we fail to account for cluster-by-time interactions present in the data, the Type I error rate is severely inflated. We develop a more robust and efficient strategy—randomization inference. We demonstrate how to apply randomization inference to test for constant treatment effects and discuss test statistics suitable for the stepped-wedge design. Randomization inference guarantees a valid Type I error rate; simulation studies show that randomization inference test statistics also have power that is comparable to the currently used procedures that do not guarantee a valid Type I error rate. Finally, we apply our proposed method to the Burkina Faso CBHI dataset. We conclude that the insurance had limited effects on reducing the likelihood of low to moderate levels of catastrophic health expenditure, but substantially reduced the likelihood of extremely high health expenditure that exceeds half of a person’s monthly income.

We present a Bayesian nonparametric approach for modelling wildlife migration patterns using capture–recapture (CR) data. Arrival times of individuals are modelled in continuous time and assumed to be drawn from a Poisson process with unknown intensity function, which is modelled via a flexible nonparametric mixture model. The proposed CR framework allows us to estimate the following: (i) the total number of individuals that arrived at the site, (ii) their times of arrival and departure, and hence their stopover duration, and (iii) the density of arrival times, providing a smooth representation of the arrival pattern of the individuals at the site. We apply the model to data on breeding great crested newts (Triturus cristatus) and on migrating reed warblers (Acrocephalus scirpaceus). For the former, the results demonstrate the staggered arrival of individuals at the breeding ponds and suggest that males tend to arrive earlier than females. For the latter, they demonstrate the arrival of migrating flocks at the stopover site and highlight the considerable difference in stopover duration between caught and not-caught individuals.

Reconstructing a gene network from high-throughput molecular data is an important but challenging task, as the number of parameters to estimate easily is much larger than the sample size. A conventional remedy is to regularize or penalize the model likelihood. In network models, this is often done locally in the neighborhood of each node or gene. However, estimation of the many regularization parameters is often difficult and can result in large statistical uncertainties. In this paper we propose to combine local regularization with global shrinkage of the regularization parameters to borrow strength between genes and improve inference. We employ a simple Bayesian model with nonsparse, conjugate priors to facilitate the use of fast variational approximations to posteriors. We discuss empirical Bayes estimation of hyperparameters of the priors, and propose a novel approach to rank-based posterior thresholding. Using extensive model- and data-based simulations, we demonstrate that the proposed inference strategy outperforms popular (sparse) methods, yields more stable edges, and is more reproducible. The proposed method, termed ShrinkNet, is then applied to Glioblastoma to investigate the interactions between genes associated with patient survival.

Irrigation in agriculture mitigates the adverse effects of drought and improves crop production and yield. Still, water scarcity remains a persistent issue and water resources need to be used responsibly. To improve water use efficiency, precision irrigation is emerging as an approach where farmers can vary the application of water according to within field variation in soil and topographic conditions. As a precursor, methods to characterize spatial variation of soil hydraulic properties are needed. One such property is soil water holding capacity (WHC). This analysis develops a multivariate spatial model for predicting WHC across a field at various soil depths using sparse WHC observations and covariates such as soil electrical conductivity. To capture spatially varying cross-correlations in an efficient manner, we propose to extend the conditional specification of a multivariate Gaussian process by using spatially varying coefficients. Because data is already sparse, our analysis fully utilizes incomplete observations by imputing missing values that we treat as not missing at random. Additionally, due to the high cost of measuring WHC, we use a multivariate integrated mean square error criterion to choose a new observation location that, after sampling, will result in the least predictive uncertainty across the entire field.

Cohort studies in air pollution epidemiology aim to establish associations between health outcomes and air pollution exposures. Statistical analysis of such associations is complicated by the multivariate nature of the pollutant exposure data as well as the spatial misalignment that arises from the fact that exposure data are collected at regulatory monitoring network locations distinct from cohort locations. We present a novel clustering approach for addressing this challenge. Specifically, we present a method that uses geographic covariate information to cluster multi-pollutant observations and predict cluster membership at cohort locations. Our predictive $k$-means procedure identifies centers using a mixture model and is followed by multiclass spatial prediction. In simulations, we demonstrate that predictive $k$-means can reduce misclassification error by over 50% compared to ordinary $k$-means, with minimal loss in cluster representativeness. The improved prediction accuracy results in large gains of 30% or more in power for detecting effect modification by cluster in a simulated health analysis. In an analysis of the NIEHS Sister Study cohort using predictive $k$-means, we find that the association between systolic blood pressure (SBP) and long-term fine particulate matter (PM$_{2.5}$) exposure varies significantly between different clusters of PM$_{2.5}$ component profiles. Our cluster-based analysis shows that, for subjects assigned to a cluster located in the Midwestern U.S., a 10 $\mu$g/m$^{3}$ difference in exposure is associated with 4.37 mmHg (95% CI, 2.38, 6.35) higher SBP.

In mass spectrometry (MS) based quantitative proteomics research, the emerging iTRAQ (isobaric tag for relative and absolute quantitation) and TMT (tandem mass tags) techniques have been widely adopted for high throughput protein profiling. In a typical iTRAQ/TMT proteomics study, samples are grouped into batches, and each batch is processed by one multiplex experiment, in which the abundances of thousands of proteins/peptides in a batch of samples can be measured simultaneously. The multiplex labeling technique greatly enhances the throughput of protein quantification. However, the technical variation across different iTRAQ/TMT multiplex experiments is often large due to the dynamic nature of MS instruments. This leads to strong batch effects in the iTRAQ/TMT data. Moreover, the iTRAQ/TMT data often contain substantial batch-level nonignorable missing entries. Specifically, the abundance measures of a given protein/peptide are often either observed or missing altogether in all the samples from the same batch, with the missing probability depending on the combined batch-level abundances. We term this unique missing-data mechanism as the Batch-level Abundance-Dependent Missing-data Mechanism (BADMM). We introduce a new method—mixEMM—for analyzing iTRAQ/TMT data with batch effects and batch-level nonignorable missingness. The mixEMM method employs a linear mixed-effects model and explicitly models the batch effects and the BADMM. With simulation studies, we showed that, compared with existing approaches that utilize relative abundances and ignore the missing batches under the missing-completely-at-random assumption, the mixEMM method achieves more accurate parameter estimation and inference. We applied the method to an iTRAQ proteomics data from a breast cancer study and identified phosphopeptides differentially expressed between different breast cancer subtypes. The method can be applied to general clustered data with cluster-level nonignorable missing-data mechanisms.

Rapid technological advances have drastically improved the data collection capacity in occupational exposure assessment. However, advanced statistical methods for analyzing such data and drawing proper inference remain limited. The objectives of this paper are (1) to provide new spatio-temporal methodology that combines data from both roving and static sensors for data processing and hazard mapping across space and over time in an indoor environment, and (2) to compare the new method with the current industry practice, demonstrating the distinct advantages of the new method and the impact on occupational hazard assessment and future policy making in environmental health as well as occupational health. A novel spatio-temporal model with a continuous index in both space and time is proposed, and a profile likelihood-based model fitting procedure is developed that allows fusion of the two types of data. To account for potential differences between the static and roving sensors, we extend the model to have nonhomogenous measurement error variances. Our methodology is applied to a case study conducted in an engine test facility, and dynamic hazard maps are drawn to show features in the data that would have been missed by existing approaches, but are captured by the new method.

Recent advances in high-throughput biotechnologies have generated various types of genetic, genomic, epigenetic, transcriptomic and proteomic data across different biological conditions. It is likely that integrating data from diverse experiments may lead to a more unified and global view of biological systems and complex diseases. We present a coherent statistical framework for integrating various types of data from distinct but related biological conditions through graphical models. Specifically, our statistical framework is designed for modeling multiple networks with shared regulatory mechanisms from heterogeneous high-dimensional datasets. The performance of our approach is illustrated through simulations and its applications to cancer genomics.

In recent pharmacoepidemiology research, the increasing use of electronic medication dispensing data provides an unprecedented opportunity to examine various health outcomes associated with long-term medication usage. Often, patients may take multiple types of medications intended for the same medical condition and the medication exposure status and intensity may vary over time, posing challenges to the statistical modeling of such data. In this article, we propose a penalized Cox proportional hazards (PH) model with multiple functional covariates and potential interaction effects. We also consider constrained coefficient functions to ensure a diminishing medication effect over time. Hypothesis testing of interaction effect and main effect was discussed under the penalized Cox PH model setting. Our simulation studies demonstrate the adequate performance of the proposed methods for both parameter estimation and hypothesis testing. Application to a primary care depression cohort study was also illustrated to examine the effects of two common types of antidepressants on the risk of coronary artery disease.

Seasonal influenza is a serious public health and societal problem due to its consequences resulting from absenteeism, hospitalizations, and deaths. The overall burden of influenza is captured by the Centers for Disease Control and Prevention’s influenza-like illness network, which provides invaluable information about the current incidence. This information is used to provide decision support regarding prevention and response efforts. Despite the relatively rich surveillance data and the recurrent nature of seasonal influenza, forecasting the timing and intensity of seasonal influenza in the U.S. remains challenging because the form of the disease transmission process is uncertain, the disease dynamics are only partially observed, and the public health observations are noisy. Fitting a probabilistic state-space model motivated by a deterministic mathematical model [a susceptible-infectious-recovered (SIR) model] is a promising approach for forecasting seasonal influenza while simultaneously accounting for multiple sources of uncertainty. A significant finding of this work is the importance of thoughtfully specifying the prior, as results critically depend on its specification. Our conditionally specified prior allows us to exploit known relationships between latent SIR initial conditions and parameters and functions of surveillance data. We demonstrate advantages of our approach relative to alternatives via a forecasting comparison using several forecast accuracy metrics.

In the presence of treatment effect heterogeneity, the average treatment effect (ATE) in a randomized controlled trial (RCT) may differ from the average effect of the same treatment if applied to a target population of interest. If all treatment effect moderators are observed in the RCT and in a dataset representing the target population, then we can obtain an estimate for the target population ATE by adjusting for the difference in the distribution of the moderators between the two samples. This paper considers sensitivity analyses for two situations: (1) where we cannot adjust for a specific moderator $V$ observed in the RCT because we do not observe it in the target population; and (2) where we are concerned that the treatment effect may be moderated by factors not observed even in the RCT, which we represent as a composite moderator $U$. In both situations, the outcome is not observed in the target population. For situation (1), we offer three sensitivity analysis methods based on (i) an outcome model, (ii) full weighting adjustment and (iii) partial weighting combined with an outcome model. For situation (2), we offer two sensitivity analyses based on (iv) a bias formula and (v) partial weighting combined with a bias formula. We apply methods (i) and (iii) to an example where the interest is to generalize from a smoking cessation RCT conducted with participants of alcohol/illicit drug use treatment programs to the target population of people who seek treatment for alcohol/illicit drug use in the US who are also cigarette smokers. In this case a treatment effect moderator is observed in the RCT but not in the target population dataset.

The cost of electricity varies across the zones of the New York State electric system. While fair and open access to the electrical grid is sought, we show that residents currently do not equally benefit, or suffer, from price changes. Upcoming major investments in the grid offer an opportunity to rectify these inequalities, but only if we understand the price-change propagation dynamics for the current underlying infrastructure. We study these dynamics, estimating the partial correlations between changes in electricity prices in connected zones. We develop and investigate a robust exponentially weighted correlation estimator that performs well in the presence of electricity price spikes and can track a rapidly changing time-varying correlation. We show that price-change partial correlations are mostly positive, but can also be negative, and provide new insight into price-change dynamics within the grid that cannot be extracted from the price-setting algorithm or obtained from available transmission capability data.

Due to cost and time considerations, interest has focused on identifying surrogate markers that could be substituted for the clinical endpoint, time to an event of interest, in evaluation of treatment efficacy. Joint models are often used to assess the effect of surrogate markers and treatment. Motivated by recent works studying the AIDS Clinical Trial Group (ACTG) 175 data, we propose a partially time-varying coefficient proportional hazards model for modeling the relationship between the hazard of failure and time-dependent and time-independent covariates. The time-varying coefficients are approximated by polynomial splines, and the corrected score and conditional score approaches are adopted to estimate the regression coefficients. The proposed estimators are consistent, and the asymptotic normality is established for the constant coefficients, which enables us to construct confidence intervals and permits joint inference. The finite-sample performance of the proposed method is assessed by Monte Carlo simulation studies. The proposed model is applied to ACTG 175 data to assess the temporal dynamics of the effect of treatment and CD4 count on time to AIDS or death.

We propose Bayesian functional mixed effect time series models to explain the impact of engine idling on ultrafine particle (UFP) counts inside school buses. UFPs are toxic to humans and school engines emit particles primarily in the UFP size range. As school buses idle at bus stops, UFPs penetrate into cabins through cracks, doors, and windows. Counts increase over time at a size dependent rate once the engine turns on. How UFP counts inside buses vary by particle size over time and under different idling conditions is not yet well understood. We model UFP counts at a given time using a mixed effect model with a cubic B-spline basis as a function of size. The log residual variance over size is modeled using a quadratic B-spline basis to account for heterogeneity in error across size bin, and errors are autoregressive over time. Model predictions are communicated graphically. These methods provide information needed to quantify UFP counts by size and possibly minimize UFP exposure in the future.

Social contact patterns reveal with whom individuals tend to socialize, and therefore to whom they transmit respiratory infections. We infer highly detailed age-specific contact rates between the sexes using a hierarchical Bayesian model that smooths while simultaneously guaranteeing the inherent reciprocity of contact rates. Application of this approach to social contact data from a large prospective survey confirms a tendency that people, especially children and adolescents, mostly contact other people of their own age and sex, and reveals that women have more contact with children than men. These findings imply different exposure patterns between the two sexes for specific age groups, which agrees with available observations.

Prediction of aboveground biomass, particularly at large spatial scales, is necessary for estimating global-scale carbon sequestration. Since biomass can be measured only by sacrificing trees, total biomass on plots is never observed. Rather, allometric equations are used to convert individual tree diameter to individual biomass, perhaps with noise. The values for all trees on a plot are then summed to obtain a derived total biomass for the plot. Then, with derived total biomasses for a collection of plots, regression models, using appropriate environmental covariates, are employed to attempt explanation and prediction. Not surprisingly, when out-of-sample validation is examined, such a model will predict total biomass well for holdout data because it is obtained using exactly the same derived approach.

Apart from the somewhat circular nature of the regression approach, it also fails to employ the actual observed plot level response data. At each plot, we observe a random number of trees, each with an associated diameter, producing a sample of diameters. A model based on this random number of tree diameters provides understanding of how environmental regressors explain abundance of individuals, which in turn explains individual diameters.

We incorporate density dependence because the distribution of tree diameters over a plot of fixed size depends upon the number of trees on the plot. After fitting this model, we can obtain predictive distributions for individual-level biomass and plot-level total biomass. We show that predictive distributions for plot-level biomass obtained from a density-dependent model for diameters will be much different from predictive distributions using the regression approach. Moreover, they can be more informative for capturing uncertainty than those obtained from modeling derived plot-level biomass directly.

We develop a density-dependent diameter distribution model and illustrate with data from the national Forest Inventory and Analysis (FIA) database. We also describe how to scale predictions to larger spatial regions. Our predictions agree (in magnitude) with available wisdom on mean and variation in biomass at the hectare scale.

Characterization of multivariate time series of behaviour data from animal-borne sensors is challenging. Biologists require methods to objectively quantify baseline behaviour, and then assess behaviour changes in response to environmental stimuli. Here, we apply hidden Markov models (HMMs) to characterize blue whale movement and diving behaviour, identifying latent states corresponding to three main underlying behaviour states: shallow feeding, travelling, and deep feeding. The model formulation accounts for inter-whale differences via a computationally efficient discrete random effect, and measures potential effects of experimental acoustic disturbance on between-state transition probabilities. We identify clear differences in blue whale disturbance response depending on the behavioural context during exposure, with whales less likely to initiate deep foraging behaviour during exposure. Findings are consistent with earlier studies using smaller samples, but the HMM approach provides a more nuanced characterization of behaviour changes.

Discrete-time hidden Markov models are a broadly useful class of latent-variable models with applications in areas such as speech recognition, bioinformatics, and climate data analysis. It is common in practice to introduce temporal nonhomogeneity into such models by making the transition probabilities dependent on time-varying exogenous input variables via a multinomial logistic parametrization. We extend such models to introduce additional nonhomogeneity into the emission distribution using a generalized linear model (GLM), with data augmentation for sampling-based inference. However, the presence of the logistic function in the state transition model significantly complicates parameter inference for the overall model, particularly in a Bayesian context. To address this, we extend the recently-proposed Pólya-Gamma data augmentation approach to handle nonhomogeneous hidden Markov models (NHMMs), allowing the development of an efficient Markov chain Monte Carlo (MCMC) sampling scheme. We apply our model and inference scheme to 30 years of daily rainfall in India, leading to a number of insights into rainfall-related phenomena in the region. Our proposed approach allows for fully Bayesian analysis of relatively complex NHMMs on a scale that was not possible with previous methods. Software implementing the methods described in the paper is available via the R package NHMM.

Egocentric network sampling observes the network of interest from the point of view of a set of sampled actors, who provide information about themselves and anonymized information on their network neighbors. In survey research, this is often the most practical, and sometimes the only, way to observe certain classes of networks, with the sexual networks that underlie HIV transmission being the archetypal case. Although methods exist for recovering some descriptive network features, there is no rigorous and practical statistical foundation for estimation and inference for network models from such data. We identify a subclass of exponential-family random graph models (ERGMs) amenable to being estimated from egocentrically sampled network data, and apply pseudo-maximum-likelihood estimation to do so and to rigorously quantify the uncertainty of the estimates. For ERGMs parametrized to be invariant to network size, we describe a computationally tractable approach to this problem. We use this methodology to help understand persistent racial disparities in HIV prevalence in the US. We also discuss some extensions, including how our framework may be applied to triadic effects when data about ties among the respondent’s neighbors are also collected.

Roll call data are widely used to assess legislators’ preferences and ideology, as well as test theories of legislative behavior. In particular, roll call data is often used to determine whether the revealed preferences of legislators are affected by outside forces such as party pressure, minority status or procedural rules. This paper describes a Bayesian hierarchical model that extends existing spatial voting models to test sharp hypotheses about differences in preferences using posterior probabilities associated with such hypotheses. We use our model to investigate the effect of the change of party majority status during the 107th U.S. Senate on the revealed preferences of senators. This analysis provides evidence that change in party affiliation might affect the revealed preferences of legislators, but provides no evidence about the effect of majority status on the revealed preferences of legislators.