Empirical Bayes Methodology Research Articles

Crash modification factors for high friction surface treatment on horizontal curves of two-lane highways: A combined propensity scores matching and empirical Bayes before-after approach

Horizontal curves are locations that, as a result of the changing alignment, may be a contributing factor in roadway departure crashes. One low-cost countermeasure to mitigate crashes at these locations is the installation of the high friction surface treatment (HFST), which increases roadway friction and is intended to help keep drivers on the roadway when traversing a horizontal curve. This treatment has been implemented at numerous curves in Pennsylvania, but the overall safety effectiveness is not known. The purpose of this study is to estimate a suite of Crash Modification Factors (CMFs) for HFST applied to curve sections of undivided two-lane roadways. A novel combination of the empirical Bayes observational before-after study design and propensity score matching was used to estimate CMFs for multiple crash types, crash severities, and roadway settings (urban and rural). Propensity score matching was implemented to identify the most appropriate reference group to use within the empirical Bayes methodology. The results indicate that the installation of HFST is associated with a statistically significant decrease in all crash types and severities considered.

Safety Evaluation of Dual Left-Turn Lane Installations in North Carolina

Crash modification factors (CMFs) were calculated for the conversion of a single left-turn lane to a dual or double left-turn lane (DLTL). Despite their proliferation throughout urban and suburban traffic networks, the safety performance of intersection approaches with DLTLs has not been thoroughly investigated and documented within the library of transportation safety research. To date, no published research has been completed that recommends a CMF for DLTL installations. This research effort lays a foundation for the understanding of the before-after safety effect of this countermeasure. A sample of 36 signalized intersections in North Carolina were investigated that received DLTLs between 2004 and 2021. Of these intersections 18 received their DLTLs with no other accompanying geometric changes and were operating with protected left-turn phasing along the treated approaches before and after their DLTL installations. A before-after evaluation of these 18 sites using an empirical bayes methodology yielded the following CMFs: 0.974 (total crashes), 0.844 (fatal-and-injury crashes), 1.010 (property damage only crashes), 0.831 (frontal impact crashes), 0.951 (rear end crashes), and 1.241 (sideswipe crashes). This research recommends that the CMFs for fatal-and-injury crashes and property damage only crashes be used in future cost–benefit calculations when planning DLTL installations.

Safety Effectiveness of Rectangular Rapid Flashing Beacons Pedestrian Enhancement

A rectangular rapid flashing beacon (RRFB) is a pedestrian crosswalk countermeasure system that cautions drivers by providing them with real-time warning about the presence of pedestrians in an upcoming crosswalk. This paper investigated the safety effectiveness of existing RRFBs installed in the state of Florida between 2013 and 2018. Additionally, traffic volume, roadway characteristics, and land-use mix were included as explanatory variables. The study evaluated 154 treated sites with RRFB installations and 158 control sites with similar characteristics. Safety performance functions (SPF) were developed, and crash modification factors (CMF) were calculated using the empirical Bayes (EB) methodology for various crash types. A CMF of 0.31 for total pedestrian crashes was estimated, showing that RRFBs have the potential to reduce 69% of total pedestrian-involved crashes. CMF for total vehicular crashes and rear-end crashes were also investigated to ascertain whether RRFBs have adverse effects on rear-end crashes. CMF for total vehicular crashes was found to be 1.14, showing that RRFBs do not have positive effect in reducing total vehicular crashes. Similarly, it was observed that CMF for the rear-end crashes was 1.11, indicating RRFBs might have adverse effect on rear-end crashes because vehicles needs to slow down or stop due to the presence of pedestrians. CMFunctions for significant variables for pedestrian, rear-end, and total crash models were also estimated in this study. An economic analysis indicated that the implementation of RRFBs will yield a benefit to cost ratio (calculated over 3 years) of approximately 85.5 with a 4% discount rate.

Dynamic All-Red Extension: An Innovative Safety Countermeasure to Treat Red Light Running Crashes

The purpose of this project was to evaluate the safety effectiveness of Dynamic All-Red Extension (DARE) systems. North Carolina Department of Transportation has used DARE to combat red light running (RLR) crashes on major road approaches of selected rural, isolated traffic signals since 2011. Sixteen intersections were included in the before–after analysis. DARE systems in this study were implemented to target a specific crash type: frontal impact crashes (angle, left turn, right turn, head on) caused by vehicles traveling through the intersection and running the red light. Although there was some variability in the magnitude and significance of the results among treatment groups, there was a general reduction in the frequency of target RLR crashes. The crash modification factor (CMF) using empirical Bayes (EB) methodology was 0.93 (7% reduction in target RLR crashes) for all 16 treatment sites; for seven multilane at two-lane sites where DARE was the sole treatment, CMF was 0.65 (35% reduction in target RLR crashes), which was statistically significant at the 95% confidence level. The benefit–cost ratio of the treatment was 143:1, realized from low installation cost and the high cost of RLR crashes. The treatment appeared promising as a systemic safety treatment applied to isolated intersections with higher speed limits, especially for intersections with multilane major roads. Safety professionals should consider adding this safety countermeasure to the limited list of tools available to treat RLR crashes. DARE was inexpensive, demonstrated safety benefits, and caused minimal delays in rural applications without creating driver habituation.

Is eliciting dependency worth the effort? A study for the multivariate Poisson-Gamma probability model

We examine whether it is worthwhile eliciting subjective judgements to account for dependency in a multivariate Poisson-Gamma probability model. The challenge of estimating reliability during product design motivated the choice of model class. For the multivariate Poisson-Gamma model we adopt an empirical Bayes methodology to present an estimator with improved accuracy. A simulation study investigates the estimation error of this estimator for different degrees of dependency and examines the impact of dependency being mis-specified when assessed by subjective judgement. Our theoretical and simulation findings give analysts insights about the value of eliciting dependency.

Underperformance of Contemporary Phase III Oncology Trials and Strategies for Improvement.

Statistical testing in phase III clinical trials is subject to chance errors, which can lead to false conclusions with substantial clinical and economic consequences for patients and society. We collected summary data for the primary endpoints of overall survival (OS) and progression-related survival (PRS) (eg, time to other type of event) for industry-sponsored, randomized, phase III superiority oncology trials from 2008 through 2017. Using an empirical Bayes methodology, we estimated the number of false-positive and false-negative errors in these trials and the errors under alternative P value thresholds and/or sample sizes. We analyzed 187 OS and 216 PRS endpoints from 362 trials. Among 56 OS endpoints that achieved statistical significance, the true efficacy of experimental therapies failed to reach the projected effect size in 33 cases (58.4% false-positives). Among 131 OS endpoints that did not achieve statistical significance, the true efficacy of experimental therapies reached the projected effect size in 1 case (0.9% false-negatives). For PRS endpoints, there were 34 (24.5%) false-positives and 3 (4.2%) false-negatives. Applying an alternative P value threshold and/or sample size could reduce false-positive errors and slightly increase false-negative errors. Current statistical approaches detect almost all truly effective oncologic therapies studied in phase III trials, but they generate many false-positives. Adjusting testing procedures in phase III trials is numerically favorable but practically infeasible. The root of the problem is the large number of ineffective therapies being studied in phase III trials. Innovative strategies are needed to efficiently identify which new therapies merit phase III testing.

Evaluation of Sequential Dynamic Chevron Warning Systems on Rural Two-Lane Curves

Roadway departure crashes are a significant safety concern. The majority of these crashes occur on rural two-lane roadways, with a disproportionate number occurring on horizontal curves. The average crash rate for horizontal curves is about three times that of other highway segments. Curve-related crashes involve a number of roadway and driver causative factors, with speed being a preeminent factor. Implementing safety countermeasures on rural horizontal curves to address these crash types can improve the safety performance. Chevron alignment signs provide additional emphasis and guidance for drivers negotiating curves. To further emphasize the curve, some agencies have started using a sequential dynamic chevron warning system (SDCWS) which uses light emitting diode (LED) lights within each chevron sign to provide sequential lighted guidance through the curve. The research team evaluated 18 rural horizontal two-lane curves where a SDCWS had been implemented. Reference sites with similar characteristics were selected and included in the study. Models were developed using an empirical Bayes methodology for non-intersection (total) crashes and injury crashes. Additional countermeasures were present at some of the sites and were included in the model. Using these data, the study developed crash modification factors (CMFs) for SDCWS with a resulting CMF of 0.34 for total crashes (non-intersection) and 0.49 for injury crashes.

Bayes, Oracle Bayes and Empirical Bayes

This article concerns the Bayes and frequentist aspects of empirical Bayes inference. Some of the ideas explored go back to Robbins in the 1950s, while others are current. Several examples are discussed, real and artificial, illustrating the two faces of empirical Bayes methodology: “oracle Bayes” shows empirical Bayes in its most frequentist mode, while “finite Bayes inference” is a fundamentally Bayesian application. In either case, modern theory and computation allow us to present a sharp finite-sample picture of what is at stake in an empirical Bayes analysis.

Comparison of Bayesian techniques for the before–after evaluation of the safety effectiveness of short 2+1 road sections

In evaluating the effectiveness of a road safety treatment, the regression to the mean phenomenon is a cause for concern because of a possible overestimation of benefits. Therefore, Bayesian approaches are usually suggested as the most appropriate methodologies for before—after studies as they account for regression to the mean effects. The empirical Bayes (EB) methodology examines the estimation of the expected number of crashes that would have occurred without treatment and compares them with the crashes observed at the treated sites. Even if there is no significant regression to the mean bias, the EB technique requires a reliable and large dataset with sufficient years of observation and number of treated sites, adequate for estimating the safety effects of a treatment with acceptable standard errors. In this framework, a full Bayesian (FB) approach can mitigate the problem of using small datasets by providing more detailed causal inferences and more flexibility in selecting crash count distributions, acknowledging that a more complex methodology must be applied. With the aim of estimating the safety improvements of new, short 2 + 1 road sections in Poland limited by the existing road network, EB and FB estimations are compared and different safety performance function (SPF) model forms are used in order to evaluate the performance of the two methodologies. Results indicated that, even if crash modification factors (CMFs) resulted in similar average values, the EB trend is to underestimate CMFs compared with the more complex methodology, while overall the FB approach provided a lower standard deviation. The differences are more pronounced between the EB and FB approaches when a simple SPF model form is used for the analysed dataset. Moreover, for this specific dataset, the difference between the FB method and the EB method using a refined regression model with more variables was negligible.

Development of Crash Modification Factors for Continuous Flow Intersections

Innovative intersections are defined as any at-grade design concepts that are able to reduce the number of signal phases at the main intersection. The Continuous Flow Intersection (CFI) displaces the left turns from the main intersection approach using an additional upstream crossover, allowing the left turns to run concurrently with the through movements. This improves operations and increases the intersection capacity. It also benefits safety by reducing the number of conflict points. This paper presents a safety analysis and the development of Crash Modification Factors (CMF) for CFIs using the Empirical Bayes (EB) methodology. The methodology is applied to before and after crash data for eight treatment sites (conversion to CFI) and five sites in the comparison group. The results show that CFIs experience about 12% less total crashes after conversion. Further analysis needs to be conducted for different crash types and crash severity.

On the relation between the true and sample correlations under Bayesian modelling of gene expression datasets.

Abstract The prediction of cancer prognosis and metastatic potential immediately after the initial diagnoses is a major challenge in current clinical research. The relevance of such a signature is clear, as it will free many patients from the agony and toxic side-effects associated with the adjuvant chemotherapy automatically and sometimes carelessly subscribed to them. Motivated by this issue, several previous works presented a Bayesian model which led to the following conclusion: thousands of samples are needed to generate a robust gene list for predicting outcome. This conclusion is based on existence of some statistical assumptions including asymptotic independence of sample correlations. The current work makes two main contributions: (1) It shows that while the assumptions of the Bayesian model discussed by previous papers seem to be non-restrictive, they are quite strong. To demonstrate this point, it is shown that some standard sparse and Gaussian models are not included in the set of models which are mathematically consistent with these assumptions. (2) It is shown that the empirical Bayes methodology which was applied in order to test the relevant assumptions does not detect severe violations and consequently an overestimation of the required sample size might be incurred. Finally, we suggest that under some regularity conditions it is possible that the current theoretical results can be used for development of a new method to test the asymptotic independence assumption.

Empirical Bayes estimators in hierarchical models with mixture priors

ABSTRACTWe consider subgroup analyses within the framework of hierarchical modeling and empirical Bayes (EB) methodology for general priors, thereby generalizing the normal–normal model. By doing this one obtains greater flexibility in modeling. We focus on mixture priors, that is, on the situation where group effects are exchangeable within clusters of subgroups only. We establish theoretical results on accuracy, precision, shrinkage and selection bias of EB estimators under the general priors. The impact of model misspecification is investigated and the applicability of the methodology is illustrated with datasets from the (medical) literature.

State-space mark-recapture estimates reveal a recent decline in abundance of North Atlantic right whales.

North Atlantic right whales (Eubalaena glacialis Müller 1776) present an interesting problem for abundance and trend estimation in marine wildlife conservation. They are long lived, individually identifiable, highly mobile, and one of the rarest of cetaceans. Individuals are annually resighted at different rates, primarily due to varying stay durations among several principal habitats within a large geographic range. To date, characterizations of abundance have been produced that use simple accounting procedures with differing assumptions about mortality. To better characterize changing abundance of North Atlantic right whales between 1990 and 2015, we adapted a state–space formulation with Jolly‐Seber assumptions about population entry (birth and immigration) to individual resighting histories and fit it using empirical Bayes methodology. This hierarchical model included accommodation for the effect of the substantial individual capture heterogeneity. Estimates from this approach were only slightly higher than published accounting procedures, except for the most recent years (when recapture rates had declined substantially). North Atlantic right whales' abundance increased at about 2.8% per annum from median point estimates of 270 individuals in 1990 to 483 in 2010, and then declined to 2015, when the final estimate was 458 individuals (95% credible intervals 444–471). The probability that the population's trajectory post‐2010 was a decline was estimated at 99.99%. Of special concern was the finding that reduced survival rates of adult females relative to adult males have produced diverging abundance trends between sexes. Despite constraints in recent years, both biological (whales' distribution changing) and logistical (fewer resources available to collect individual photo‐identifications), it is still possible to detect this relatively recent, small change in the population's trajectory. This is thanks to the massive dataset of individual North Atlantic right whale identifications accrued over the past three decades. Photo‐identification data provide biological information that allows more informed inference on the status of this species.

Selection of Tuning Parameters, Solution Paths and Standard Errors for Bayesian Lassos

Penalized regression methods such as the lasso and elastic net (EN) have become popular for simultaneous variable selection and coefficient estimation. Implementation of these methods require selection of the penalty parameters. We propose an empirical Bayes (EB) methodology for selecting these tuning parameters as well as computation of the regularization path plots. The EB method does not suffer from the “double shrinkage problem” of frequentist EN. Also it avoids the difficulty of constructing an appropriate prior on the penalty parameters. The EB methodology is implemented by efficient importance sampling method based on multiple Gibbs sampler chains. Since the Markov chains underlying the Gibbs sampler are proved to be geometrically ergodic, Markov chain central limit theorem can be used to provide asymptotically valid confidence band for profiles of EN coefficients. The practical effectiveness of our method is illustrated by several simulation examples and two real life case studies. Although this article considers lasso and EN for brevity, the proposed EB method is general and can be used to select shrinkage parameters in other regularization methods.

Post‐selection point and interval estimation of signal sizes in Gaussian samples

AbstractWe tackle the problem of the estimation of a vector of underlying means (signal sizes) from a single vector‐valued observation y. Often one is interested in estimating only a subvector of signals corresponding to a set of selected, “interesting” sample elements. These “interesting” sample elements tend to have the largest absolute size, gleaned by applying some selection procedure like that of Benjamini & Hochberg (2015). Previous work on this estimation task proposes the reduction in size of the largest (absolute) sample elements either via shrinkage (like James–Stein) or by subtracting biases estimated using empirical Bayes methodology. We take a novel approach and adapt recent developments by Lee et al. (2016) in post‐selection inference. Adapting and applying their distributional results to our problem post‐selection point and interval estimators for underlying signal sizes are proposed. Simulations suggest that our estimator seems to perform quite well against competitors. Furthermore we prove an upper bound to the so‐called “worst case risk” of our estimator—when combined with the Benjamini–Hochberg selection procedure—and show that it is within a constant multiple of the minimax risk over a rich set of parameter spaces meant to evoke sparsity. The Canadian Journal of Statistics 45: 128–148; 2017 © 2017 Statistical Society of Canada

Australian-Arabic community attitudes to a shared model of accommodation for the 65+ year age group

PurposeThis paper aims to provide insights into Arabic-Australian community attitudes regarding social innovation of a new shared model of accommodation for the 65+ age group to facilitate independent behavior within a shared living environment.Design/methodology/approachA survey of 520 people of whom 65 per cent were Arabic speakers either by mother or second language. Survey responses were filtered to Arabic speakers and further analyzed to identify groups characterized by the latent attitudes underlying responses.FindingsThe results confirmed the presence of two small groups representing in aggregate 13 per cent of sample variance who have positive attitudes toward 65+ age group shared accommodation for either themselves or their parents. These respondents focused on companionship and cultural factors rather than potential financial or medical benefits from the new model.Research limitations/implicationsThe application of an empirical Bayes methodology to the limited data in this research implicitly restricts the interpretation of the results to the Australian-Arabic community that was investigated.Practical implicationsThe results of this research provide a sound basis for private sector interest in exploring differentiated architectures and business models that will facilitate choices of shared accommodation by the Australian-Arabic 65+ year age group.Social implicationsThis finding aligns with increasing health and mobility more widely among the rapidly growing 65+ year old segment of the Australian population and with recent Australian Government restructuring of age care to introduce greater personal accountability for self-care.Originality/valueThis research is original and important in setting future directions for expanding the richness of choice in Australian-Arabic community retirement living.

Bayesian Wavelet Analysis Using Nonlocal Priors with an Application to fMRI Analysis

We propose a Bayesian hierarchical wavelet methodology for nonparametric regression based on nonlocal priors. Our methodology assumes for the wavelet coefficients a prior that is a mixture of a point mass at zero and a Johnson-Rossell nonlocal prior. We consider two choices of Johnson-Rossell nonlocal priors: the moment prior and the inverse moment prior. To borrow strength across wavelet coefficients, in addition to more traditional specifications from the wavelet literature, we consider a logit specification for the mixture probability and a polynomial decay specification for the scale parameter. To estimate these specifications’ hyperparameters, we propose an empirical Bayes methodology based on Laplace approximation that allows fast analytic posterior inference for the wavelet coefficients. To assess performance, we perform a simulation study to compare our methodology to several other wavelet-based methods available in the literature. In terms of mean squared error, our methodology with the inverse moment prior yields superior results for cases of low signal-to-noise ratio, as well as for moderate to large sample sizes. Finally, we illustrate the flexibility of our novel methodology with an application to a functional magnetic resonance imaging (fMRI) dataset from a study of brain activations associated with working memory.

Projecting adverse event incidence rates using empirical Bayes methodology

Although there is considerable interest in adverse events observed in clinical trials, projecting adverse event incidence rates in an extended period can be of interest when the trial duration is limited compared to clinical practice. A naïve method for making projections might involve modeling the observed rates into the future for each adverse event. However, such an approach overlooks the information that can be borrowed across all the adverse event data. We propose a method that weights each projection using a shrinkage factor; the adverse event-specific shrinkage is a probability, based on empirical Bayes methodology, estimated from all the adverse event data, reflecting evidence in support of the null or non-null hypotheses. Also proposed is a technique to estimate the proportion of true nulls, called the common area under the density curves, which is a critical step in arriving at the shrinkage factor. The performance of the method is evaluated by projecting from interim data and then comparing the projected results with observed results. The method is illustrated on two data sets.

Empirical Bayes estimation for the stochastic blockmodel

Inference for the stochastic blockmodel is currently of burgeoning interest in the statistical community, as well as in various application domains as diverse as social networks, citation networks, brain connectivity networks (connectomics), etc. Recent theoretical developments have shown that spectral embedding of graphs yields tractable distributional results; in particular, a random dot product latent position graph formulation of the stochastic blockmodel informs a mixture of normal distributions for the adjacency spectral embedding. We employ this new theory to provide an empirical Bayes methodology for estimation of block memberships of vertices in a random graph drawn from the stochastic blockmodel, and demonstrate its practical utility. The posterior inference is conducted using a Metropolis-within-Gibbs algorithm. The theory and methods are illustrated through Monte Carlo simulation studies, both within the stochastic blockmodel and beyond, and experimental results on a Wikipedia graph are presented.

Efficient estimation and prediction for the Bayesian binary spatial model with flexible link functions.

Spatial generalized linear mixed models (SGLMMs) are popular models for spatial data with a non-Gaussian response. Binomial SGLMMs with logit or probit link functions are often used to model spatially dependent binomial random variables. It is known that for independent binomial data, the robit regression model provides a more robust (against extreme observations) alternative to the more popular logistic and probit models. In this article, we introduce a Bayesian spatial robit model for spatially dependent binomial data. Since constructing a meaningful prior on the link function parameter as well as the spatial correlation parameters in SGLMMs is difficult, we propose an empirical Bayes (EB) approach for the estimation of these parameters as well as for the prediction of the random effects. The EB methodology is implemented by efficient importance sampling methods based on Markov chain Monte Carlo (MCMC) algorithms. Our simulation study shows that the robit model is robust against model misspecification, and our EB method results in estimates with less bias than full Bayesian (FB) analysis. The methodology is applied to a Celastrus Orbiculatus data, and a Rhizoctonia root data. For the former, which is known to contain outlying observations, the robit model is shown to do better for predicting the spatial distribution of an invasive species. For the latter, our approach is doing as well as the classical models for predicting the disease severity for a root disease, as the probit link is shown to be appropriate. Though this article is written for Binomial SGLMMs for brevity, the EB methodology is more general and can be applied to other types of SGLMMs. In the accompanying R package geoBayes, implementations for other SGLMMs such as Poisson and Gamma SGLMMs are provided.