Adaptive sampling method to monitor low-risk pathways with limited surveillance resources.

The rise of globalization has led to a sharp increase in international trade with high volumes of containers, goods, and items moving across the world. Unfortunately, these trade pathways also facilitate the movement of unwanted pests, weeds, diseases, and pathogens. Each item could contain biosecurity risk material, but it is impractical to inspect every item. Instead, inspection efforts typically focus on high-risk items. However, low risk does not imply no risk. It is crucial to monitor the low-risk pathways to ensure that they are and remain low risk. To do so, many approaches would seek to estimate the risk to some precision, but increasingly lower risks require more samples. On a low-risk pathway that can be afforded only limited inspection resources, it makes more sense to assign fewer samples to the lower risk activities. We approach the problem by introducing two thresholds. Our method focuses on letting us know whether the risk is below certain thresholds, rather than estimating the risk precisely. This method also allows us to detect a significant change in risk. Our approach typically requires less sampling than previous methods, while still providing evidence to regulators to help them efficiently and effectively allocate inspection effort.

Multilevel joint frailty model for hierarchically clustered binary and survival data.

Hierarchical data arise when observations are clustered into groups. Multilevel models are practically useful in these settings, but these models are elusive in the context of hierarchical data with mixed multivariate outcomes. In this article, we consider binary and survival outcomes and assume the hierarchical structure is induced by clustering of both outcomes within patients and clustering of patients within hospitals which frequently occur in multicenter studies. We introduce a multilevel joint frailty model that analyzes the outcomes simultaneously to jointly estimate their regression parameters and explicitly model within-patient correlation between the outcomes and within-hospital correlation separately for each outcome. Estimation is facilitated by a computationally efficient residual maximum likelihood method that further predicts cluster-specific frailties for both outcomes and circumvents the formidable challenges induced by multidimensional integration that complicates the underlying likelihood. The performance of the model and estimation procedure is investigated via extensive simulation studies. The practical utility of the model is illustrated through simultaneous modeling of disease-free survival and binary endpoint of platelet recovery in a multicenter allogeneic bone marrow transplantation dataset that motivates this study.

In search of peak human athletic potential: A mathematical investigation.

This paper applies existing and new approaches to study trends in the performance of elite athletes over time. We study both track and field scores of men and women athletes on a yearly basis from 2001 to 2019, revealing several trends and findings. First, we perform a detailed regression study to reveal the existence of an "Olympic effect," where average performance improves during Olympic years. Next, we study the rate of change in athlete performance and fail to reject the notion that athlete scores are leveling off, at least among the top 100 annual scores. Third, we examine the relationship in performance trends among men and women's categories of the same event, revealing striking similarity, together with some anomalous events. Finally, we analyze the geographic composition of the world's top athletes, attempting to understand how the diversity by country and continent varies over time across events. We challenge a widely held conception of athletics that certain events are more geographically dominated than others. Our methods and findings could be applied more generally to identify evolutionary dynamics in group performance and highlight spatiotemporal trends in group composition.

Comparing the dynamics of COVID-19 infection and mortality in the United States, India, and Brazil.

This paper compares and contrasts the spread and impact of COVID-19 in the three countries most heavily impacted by the pandemic: the United States (US), India and Brazil. All three of these countries have a federal structure, in which the individual states have largely determined the response to the pandemic. Thus, we perform an extensive analysis of the individual states of these three countries to determine patterns of similarity within each. First, we analyse structural similarity and anomalies in the trajectories of cases and deaths as multivariate time series. Next, we study the lengths of the different waves of the virus outbreaks across the three countries and their states. Finally, we investigate suitable time offsets between cases and deaths as a function of the distinct outbreak waves. In all these analyses, we consistently reveal more characteristically distinct behaviour between US and Indian states, while Brazilian states exhibit less structure in their wave behaviour and changing progression between cases and deaths.

Optimal allocation of PCR tests to minimise disease transmission through contact tracing and quarantine.

PCR testing is a crucial capability for managing disease outbreaks, but it is also a limited resource and must be used carefully to ensure the information gain from testing is valuable. Testing has two broad uses for informing public health policy, namely to track epidemic dynamics and to reduce transmission by identifying and managing cases. In this work we develop a modelling framework to examine the effects of test allocation in an epidemic, with a focus on using testing to minimise transmission. Using the COVID-19 pandemic as an example, we examine how the number of tests conducted per day relates to reduction in disease transmission, in the context of logistical constraints on the testing system. We show that if daily testing is above the routine capacity of a testing system, which can cause delays, then those delays can undermine efforts to reduce transmission through contact tracing and quarantine. This work highlights that the two goals of aiming to reduce transmission and aiming to identify all cases are different, and it is possible that focusing on one may undermine achieving the other. To develop an effective strategy, the goals must be clear and performance metrics must match the goals of the testing strategy. If metrics do not match the objectives of the strategy, then those metrics may incentivise actions that undermine achieving the objectives.

On local intrinsic dimensionality of deformation in complex materials.

We propose a new metric called s-LID based on the concept of Local Intrinsic Dimensionality to identify and quantify hierarchies of kinematic patterns in heterogeneous media. s-LID measures how outlying a grain's motion is relative to its s nearest neighbors in displacement state space. To demonstrate the merits of s-LID over the conventional measure of strain, we apply it to data on individual grain motions in a set of deforming granular materials. Several new insights into the evolution of failure are uncovered. First, s-LID reveals a hierarchy of concurrent deformation bands that prevails throughout loading history. These structures vary not only in relative dominance but also spatial and kinematic scales. Second, in the nascent stages of the pre-failure regime, s-LID uncovers a set of system-spanning, criss-crossing bands: microbands for small s and embryonic-shearbands at large s, with the former being dominant. At the opposite extreme, in the failure regime, fully formed shearbands at large s dominate over the microbands. The novel patterns uncovered from s-LID contradict the common belief of a causal sequence where a subset of microbands coalesce and/or grow to form shearbands. Instead, s-LID suggests that the deformation of the sample in the lead-up to failure is governed by a complex symbiosis among these different coexisting structures, which amplifies and promotes the progressive dominance of the embryonic-shearbands over microbands. Third, we probed this transition from the microband-dominated regime to the shearband-dominated regime by systematically suppressing grain rotations. We found particle rotation to be an essential enabler of the transition to the shearband-dominated regime. When grain rotations are completely suppressed, this transition is prevented: microbands and shearbands coexist in relative parity.

Pupillary response to complex interdependent tasks: A cognitive-load theory perspective.

Pupil dilation is known to indicate cognitive load. In this study, we looked at the average pupillary responses of a cohort of 29 undergraduate students during graphical problem solving. Three questions were asked, based on the same graphical input. The questions were interdependent and comprised multiple steps. We propose a novel way of analyzing pupillometry data for such tasks on the basis of eye fixations, a commonly used eyetracking parameter. We found that pupil diameter increased during the solution process. However, pupil diameter did not always reflect the expected cognitive load. This result was studied within a cognitive-load theory model. Higher-performing students showed evidence of germane load and schema creation, indicating use of the interdependent nature of the tasks to inform their problem-solving process. However, lower-performing students did not recognize the interdependent nature of the tasks and solved each problem independently, which was expressed in a markedly different pupillary response pattern. We discuss the import of our findings for instructional design.

Spatial regression with covariate measurement error: A semiparametric approach.

Spatial data have become increasingly common in epidemiology and public health research thanks to advances in GIS (Geographic Information Systems) technology. In health research, for example, it is common for epidemiologists to incorporate geographically indexed data into their studies. In practice, however, the spatially defined covariates are often measured with error. Naive estimators of regression coefficients are attenuated if measurement error is ignored. Moreover, the classical measurement error theory is inapplicable in the context of spatial modeling because of the presence of spatial correlation among the observations. We propose a semiparametric regression approach to obtain bias-corrected estimates of regression parameters and derive their large sample properties. We evaluate the performance of the proposed method through simulation studies and illustrate using data on Ischemic Heart Disease (IHD). Both simulation and practical application demonstrate that the proposed method can be effective in practice.

A penalized likelihood approach for investigating gene-drug interactions in pharmacogenetic studies.

Pharmacogenetics investigates the relationship between heritable genetic variation and the variation in how individuals respond to drug therapies. Often, gene-drug interactions play a primary role in this response, and identifying these effects can aid in the development of individualized treatment regimes. Haplotypes can hold key information in understanding the association between genetic variation and drug response. However, the standard approach for haplotype-based association analysis does not directly address the research questions dictated by individualized medicine. A complementary post-hoc analysis is required, and this post-hoc analysis is usually under powered after adjusting for multiple comparisons and may lead to seemingly contradictory conclusions. In this work, we propose a penalized likelihood approach that is able to overcome the drawbacks of the standard approach and yield the desired personalized output. We demonstrate the utility of our method by applying it to the Scottish Randomized Trial in Ovarian Cancer. We also conducted simulation studies and showed that the proposed penalized method has comparable or more power than the standard approach and maintains low Type I error rates for both binary and quantitative drug responses. The largest performance gains are seen when the haplotype frequency is low, the difference in effect sizes are small, or the true relationship among the drugs is more complex.

Incorporating covariates in skewed functional data models.

We introduce a class of covariate-adjusted skewed functional models (cSFM) designed for functional data exhibiting location-dependent marginal distributions. We propose a semi-parametric copula model for the pointwise marginal distributions, which are allowed to depend on covariates, and the functional dependence, which is assumed covariate invariant. The proposed cSFM framework provides a unifying platform for pointwise quantile estimation and trajectory prediction. We consider a computationally feasible procedure that handles densely as well as sparsely observed functional data. The methods are examined numerically using simulations and is applied to a new tractography study of multiple sclerosis. Furthermore, the methodology is implemented in the R package cSFM, which is publicly available on CRAN.

Domain selection for the varying coefficient model via local polynomial regression.

In this article, we consider the varying coefficient model, which allows the relationship between the predictors and response to vary across the domain of interest, such as time. In applications, it is possible that certain predictors only affect the response in particular regions and not everywhere. This corresponds to identifying the domain where the varying coefficient is nonzero. Towards this goal, local polynomial smoothing and penalized regression are incorporated into one framework. Asymptotic properties of our penalized estimators are provided. Specifically, the estimators enjoy the oracle properties in the sense that they have the same bias and asymptotic variance as the local polynomial estimators as if the sparsity is known as a priori. The choice of appropriate bandwidth and computational algorithms are discussed. The proposed method is examined via simulations and a real data example.

Interquantile Shrinkage and Variable Selection in Quantile Regression.

Examination of multiple conditional quantile functions provides a comprehensive view of the relationship between the response and covariates. In situations where quantile slope coefficients share some common features, estimation efficiency and model interpretability can be improved by utilizing such commonality across quantiles. Furthermore, elimination of irrelevant predictors will also aid in estimation and interpretation. These motivations lead to the development of two penalization methods, which can identify the interquantile commonality and nonzero quantile coefficients simultaneously. The developed methods are based on a fused penalty that encourages sparsity of both quantile coefficients and interquantile slope differences. The oracle properties of the proposed penalization methods are established. Through numerical investigations, it is demonstrated that the proposed methods lead to simpler model structure and higher estimation efficiency than the traditional quantile regression estimation.

On the impact of covariate measurement error on spatial regression modelling.

Spatial regression models have grown in popularity in response to rapid advances in GIS (Geographic Information Systems) technology that allows epidemiologists to incorporate geographically indexed data into their studies. However, it turns out that there are some subtle pitfalls in the use of these models. We show that presence of covariate measurement error can lead to significant sensitivity of parameter estimation to the choice of spatial correlation structure. We quantify the effect of measurement error on parameter estimates, and then suggest two different ways to produce consistent estimates. We evaluate the methods through a simulation study. These methods are then applied to data on Ischemic Heart Disease (IHD).

Interquantile Shrinkage in Regression Models.

Conventional analysis using quantile regression typically focuses on fitting the regression model at different quantiles separately. However, in situations where the quantile coefficients share some common feature, joint modeling of multiple quantiles to accommodate the commonality often leads to more efficient estimation. One example of common features is that a predictor may have a constant effect over one region of quantile levels but varying effects in other regions. To automatically perform estimation and detection of the interquantile commonality, we develop two penalization methods. When the quantile slope coefficients indeed do not change across quantile levels, the proposed methods will shrink the slopes towards constant and thus improve the estimation efficiency. We establish the oracle properties of the two proposed penalization methods. Through numerical investigations, we demonstrate that the proposed methods lead to estimations with competitive or higher efficiency than the standard quantile regression estimation in finite samples. Supplemental materials for the article are available online.

A nonparametric spatial model for periodontal data with non-random missingness.

Periodontal disease progression is often quantified by clinical attachment level (CAL) defined as the distance down a tooth's root that is detached from the surrounding bone. Measured at 6 locations per tooth throughout the mouth (excluding the molars), it gives rise to a dependent data set-up. These data are often reduced to a one-number summary, such as the whole mouth average or the number of observations greater than a threshold, to be used as the response in a regression to identify important covariates related to the current state of a subject's periodontal health. Rather than a simple one-number summary, we set forward to analyze all available CAL data for each subject, exploiting the presence of spatial dependence, non-stationarity, and non-normality. Also, many subjects have a considerable proportion of missing teeth which cannot be considered missing at random because periodontal disease is the leading cause of adult tooth loss. Under a Bayesian paradigm, we propose a nonparametric flexible spatial (joint) model of observed CAL and the location of missing tooth via kernel convolution methods, incorporating the aforementioned features of CAL data under a unified framework. Application of this methodology to a data set recording the periodontal health of an African-American population, as well as simulation studies reveal the gain in model fit and inference, and provides a new perspective into unraveling covariate-response relationships in presence of complexities posed by these data.

Efficient Robust Regression via Two-Stage Generalized Empirical Likelihood.

Large- and finite-sample efficiency and resistance to outliers are the key goals of robust statistics. Although often not simultaneously attainable, we develop and study a linear regression estimator that comes close. Efficiency obtains from the estimator's close connection to generalized empirical likelihood, and its favorable robustness properties are obtained by constraining the associated sum of (weighted) squared residuals. We prove maximum attainable finite-sample replacement breakdown point, and full asymptotic efficiency for normal errors. Simulation evidence shows that compared to existing robust regression estimators, the new estimator has relatively high efficiency for small sample sizes, and comparable outlier resistance. The estimator is further illustrated and compared to existing methods via application to a real data set with purported outliers.

Consistent Group Identification and Variable Selection in Regression with Correlated Predictors.

Statistical procedures for variable selection have become integral elements in any analysis. Successful procedures are characterized by high predictive accuracy, yielding interpretable models while retaining computational efficiency. Penalized methods that perform coefficient shrinkage have been shown to be successful in many cases. Models with correlated predictors are particularly challenging to tackle. We propose a penalization procedure that performs variable selection while clustering groups of predictors automatically. The oracle properties of this procedure including consistency in group identification are also studied. The proposed method compares favorably with existing selection approaches in both prediction accuracy and model discovery, while retaining its computational efficiency. Supplemental material are available online.

Environmental, institutional, and demographic predictors of environmental literacy among middle school children.

Building environmental literacy (EL) in children and adolescents is critical to meeting current and emerging environmental challenges worldwide. Although environmental education (EE) efforts have begun to address this need, empirical research holistically evaluating drivers of EL is critical. This study begins to fill this gap with an examination of school-wide EE programs among middle schools in North Carolina, including the use of published EE curricula and time outdoors while controlling for teacher education level and experience, student attributes (age, gender, and ethnicity), and school attributes (socio-economic status, student-teacher ratio, and locale). Our sample included an EE group selected from schools with registered school-wide EE programs, and a control group randomly selected from NC middle schools that were not registered as EE schools. Students were given an EL survey at the beginning and end of the spring 2012 semester. Use of published EE curricula, time outdoors, and having teachers with advanced degrees and mid-level teaching experience (between 3 and 5 years) were positively related with EL whereas minority status (Hispanic and black) was negatively related with EL. Results suggest that school-wide EE programs were not associated with improved EL, but the use of published EE curricula paired with time outdoors represents a strategy that may improve all key components of student EL. Further, investments in teacher development and efforts to maintain enthusiasm for EE among teachers with more than 5 years of experience may help to boost student EL levels. Middle school represents a pivotal time for influencing EL, as improvement was slower among older students. Differences in EL levels based on gender suggest boys and girls may possess complementary skills sets when approaching environmental issues. Our findings suggest ethnicity related disparities in EL levels may be mitigated by time spent in nature, especially among black and Hispanic students.

Factor selection and structural identification in the interaction ANOVA model.

When faced with categorical predictors and a continuous response, the objective of an analysis often consists of two tasks: finding which factors are important and determining which levels of the factors differ significantly from one another. Often times, these tasks are done separately using Analysis of Variance (ANOVA) followed by a post hoc hypothesis testing procedure such as Tukey's Honestly Significant Difference test. When interactions between factors are included in the model the collapsing of levels of a factor becomes a more difficult problem. When testing for differences between two levels of a factor, claiming no difference would refer not only to equality of main effects, but also to equality of each interaction involving those levels. This structure between the main effects and interactions in a model is similar to the idea of heredity used in regression models. This article introduces a new method for accomplishing both of the common analysis tasks simultaneously in an interaction model while also adhering to the heredity-type constraint on the model. An appropriate penalization is constructed that encourages levels of factors to collapse and entire factors to be set to zero. It is shown that the procedure has the oracle property implying that asymptotically it performs as well as if the exact structure were known beforehand. We also discuss the application to estimating interactions in the unreplicated case. Simulation studies show the procedure outperforms post hoc hypothesis testing procedures as well as similar methods that do not include a structural constraint. The method is also illustrated using a real data example.

Variable Selection for Nonparametric Quantile Regression via Smoothing Spline AN OVA.

Quantile regression provides a more thorough view of the effect of covariates on a response. Nonparametric quantile regression has become a viable alternative to avoid restrictive parametric assumption. The problem of variable selection for quantile regression is challenging, since important variables can influence various quantiles in different ways. We tackle the problem via regularization in the context of smoothing spline ANOVA models. The proposed sparse nonparametric quantile regression (SNQR) can identify important variables and provide flexible estimates for quantiles. Our numerical study suggests the promising performance of the new procedure in variable selection and function estimation. Supplementary materials for this article are available online.