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A common problem seen in the ineffective execution of global multicenter trials is the frequent inability to recruit a sufficient number of patients. A myriad of barriers to recruiting enough patients timely exist and may include practical limits on the number of recruiting sites imposed by the various countries, as well as administrative, cost and unanticipated issues. The Poisson-gamma recruitment model is a widely accepted statistical tool used to predict and track recruitment at different levels of a trial and make inference. An optimal recruitment plan can be designed using mathematical optimization, however, the search is complicated with multiple nonlinear objectives and constraints that arise from regulatory and budgetary considerations. We review nature-inspired metaheuristic algorithms which are powerful, flexible, general purpose optimization tools and demonstrate their capability and utility in optimizing complex recruitment designs for global clinical trials using the Poisson-gamma model as an exemplary model. This research opens up new avenues for improving the efficiency and effectiveness of patient recruitment in clinical trials, thereby potentially accelerating the development of new medical treatments. [ABSTRACT FROM AUTHOR]

Background: When running a randomized controlled trial (RCT), a clinical site may face a situation when an eligible trial participant is to be randomized to the treatment that is not available at the site. In this case, there are two options: not to enroll the participant, or, without disclosing to the site, allocate the participant to a treatment arm with drug available at the site using a built-in feature of the interactive response technology (IRT). In the latter case, one has employed a "forced randomization" (FR). There seems to be an industry-wide consensus that using FR can be acceptable in confirmatory trials provided there are "not too many" instances of forcing. A better understanding of statistical properties of FR is warranted. Methods: We described four different IRT configurations with or without FR and illustrated them using a simple example. We discussed potential merits of FR and outlined some relevant theoretical risks and risk mitigation strategies. We performed a search using Cortellis Regulatory Intelligence database (IDRAC) (www.cortellis.com) to understand the prevalence of FR in clinical trial practice. We also proposed a structured template for development and evaluation of randomization designs featuring FR and showcased an application of this template for a hypothetical multi-center 1:1 RCT under three experimental settings ("base case", "slower recruitment", and "faster recruitment") to explore the effect of four different IRT configurations in combination with three different drug supply/re-supply strategies on some important operating characteristics of the trial. We also supplied the Julia code that can be used to reproduce our simulation results and generate additional results under user-specified experimental scenarios. Results: FR can eliminate refusals to randomize patients, which can cause frustration for patients and study site personnel, improve the study logistics, drug supply management, cost-efficiency, and recruitment time. Nevertheless, FR carries some potential risks that should be reviewed at the study planning stage and, ideally, prospectively addressed through risk mitigation planning. The Cortellis search identified only 9 submissions that have reported the use of FR; typically, the FR option was documented in IRT specifications. Our simulation evidence showed that under the considered realistic experimental settings, the percentage of FR is expected to be low. When FR with backfilling was used in combination with high re-supply strategy, the final treatment imbalance was negligibly small, the proportion of patients not randomized due to the lack of drug supply was close to zero, and the time to complete recruitment was shortened compared to the case when FR was not allowed. The drug overage was primarily determined by the intensity of the re-supply strategy and to a smaller extent by the presence or absence of the FR feature in IRT. Conclusion: FR with a carefully chosen drug supply/re-supply strategy can result in quantifiable improvements in the patients' and site personnel experience, trial logistics and efficiency while preventing an undesirable refusal to randomize a patient and a consequential unblinding at the site. FR is a useful design feature of multi-center RCTs provided it is properly planned for and carefully implemented. [ABSTRACT FROM AUTHOR]

Background: The design of a multi-center randomized controlled trial (RCT) involves multiple considerations, such as the choice of the sample size, the number of centers and their geographic location, the strategy for recruitment of study participants, amongst others. There are plenty of methods to sequentially randomize patients in a multi-center RCT, with or without considering stratification factors. The goal of this paper is to perform a systematic assessment of such randomization methods for a multi-center 1:1 RCT assuming a competitive policy for the patient recruitment process. Methods: We considered a Poisson-gamma model for the patient recruitment process with a uniform distribution of center activation times. We investigated 16 randomization methods (4 unstratified, 4 region-stratified, 4 center-stratified, 3 dynamic balancing randomization (DBR), and a complete randomization design) to sequentially randomize n = 500 patients. Statistical properties of the recruitment process and the randomization procedures were assessed using Monte Carlo simulations. The operating characteristics included time to complete recruitment, number of centers that recruited a given number of patients, several measures of treatment imbalance and estimation efficiency under a linear model for the response, the expected proportions of correct guesses under two different guessing strategies, and the expected proportion of deterministic assignments in the allocation sequence. Results: Maximum tolerated imbalance (MTI) randomization methods such as big stick design, Ehrenfest urn design, and block urn design result in a better balance–randomness tradeoff than the conventional permuted block design (PBD) with or without stratification. Unstratified randomization, region-stratified randomization, and center-stratified randomization provide control of imbalance at a chosen level (trial, region, or center) but may fail to achieve balance at the other two levels. By contrast, DBR does a very good job controlling imbalance at all 3 levels while maintaining the randomized nature of treatment allocation. Adding more centers into the study helps accelerate the recruitment process but at the expense of increasing the number of centers that recruit very few (or no) patients—which may increase center-level imbalances for center-stratified and DBR procedures. Increasing the block size or the MTI threshold(s) may help obtain designs with improved randomness–balance tradeoff. Conclusions: The choice of a randomization method is an important component of planning a multi-center RCT. Dynamic balancing randomization with carefully chosen MTI thresholds could be a very good strategy for trials with the competitive policy for patient recruitment. [ABSTRACT FROM AUTHOR]

Forecasting recruitments is a key component of the monitoring phase of multicenter studies. One of the most popular techniques in this field is the Poisson‐Gamma recruitment model, a Bayesian technique built on a doubly stochastic Poisson process. This approach is based on the modeling of enrollments as a Poisson process where the recruitment rates are assumed to be constant over time and to follow a common Gamma prior distribution. However, the constant‐rate assumption is a restrictive limitation that is rarely appropriate for applications in real studies. In this paper, we illustrate a flexible generalization of this methodology which allows the enrollment rates to vary over time by modeling them through B‐splines. We show the suitability of this approach for a wide range of recruitment behaviors in a simulation study and by estimating the recruitment progression of the Canadian Co‐infection Cohort. [ABSTRACT FROM AUTHOR]

The Poisson–Gamma model is obtained as a generalization of the Poisson model, when Gamma distributed block effects are assumed for Poisson count data. We show that optimal designs for estimating linear combinations of the model parameters coincide for the case of known and unknown parameters of the Gamma distribution. To obtain robust designs regarding parameter misspecification we determine standardized maximin D-optimal designs for a binary and a continuous design region. For standardized maximin c-optimality we show that the optimal designs for the Poisson–Gamma and Poisson model are equal and derive optimal designs for both models. [ABSTRACT FROM AUTHOR]

Tweedie's compound Poisson regression models have been introduced in recent years to model and predict daily, monthly and seasonal precipitation data. Tweedie's compound Poisson regression analysis of precipitation data captures the relationship between the mean structure of precipitation and covariates while accounting for its right‐skewness and zero‐inflation appropriately, and thus extends trend analysis stage of classical time series techniques to handle right‐skewed time series data with possible zero‐inflation. A distinctive advantage of Tweedie's compound Poisson modelling of precipitation data is that the occurrence and quantity of precipitation can be simultaneously modelled using a single distribution; however, this approach ignores serial correlation between precipitation data observed over time. In this study, we propose to accommodate complex correlation structures of time series precipitation data using the Autoregressive Integrated Moving Average (ARIMA) models at the next stage as done in the classical time series analysis. Our analyses of monthly precipitation data in Australia demonstrated the usefulness of our two‐stage approach to prediction of precipitation. [ABSTRACT FROM AUTHOR]

Despite a growing body of literature in the area of recruitment modeling for multicenter studies, in practice, statistical models to predict enrollments are rarely used and when they are, they often rely on unrealistic assumptions. The time-dependent Poisson-Gamma model (tPG) is a recently developed flexible methodology which allows analysts to predict recruitments in an ongoing multicenter trial, and its performance has been validated on data from a cohort study. In this article, we illustrate and further validate the tPG model on recruitment data from randomized controlled trials. Additionally, in the appendix, we provide a practical and easy to follow guide to its implementation via the tPG R package. To validate the model, we show the predictive performance of the proposed methodology in forecasting the recruitment process of two HIV vaccine trials conducted by the HIV Vaccine Trials Network in multiple Sub-Saharan countries. [ABSTRACT FROM AUTHOR]

We introduce a general framework for monitoring, modeling, and predicting the recruitment to multi-center clinical trials. The work is motivated by overly optimistic and narrow prediction intervals produced by existing time-homogeneous recruitment models for multi-center recruitment. We first present two tests for detection of decay in recruitment rates, together with a power study. We then introduce a model based on the inhomogeneous Poisson process with monotonically decaying intensity, motivated by recruitment trends observed in oncology trials. The general form of the model permits adaptation to any parametric curve-shape. A general method for constructing sensible parameter priors is provided and Bayesian model averaging is used for making predictions which account for the uncertainty in both the parameters and the model. The validity of the method and its robustness to misspecification are tested using simulated datasets. The new methodology is then applied to oncology trial data, where we make interim accrual predictions, comparing them to those obtained by existing methods, and indicate where unexpected changes in the accrual pattern occur. [ABSTRACT FROM AUTHOR]

The aim of this study was to propose a procedure for a prediction of the number of fragments generated by fire induced explosions of cylindrical pressure vessels. The prediction is carried out in terms of probabilities of individual fragment numbers. The prevailing numbers of two to four fragments are considered. The fragment number probabilities are estimated by applying data on vessel fragmentations acquired in investigations of past explosion accidents. The pressure vessel explosions known as BLEVEs are considered. The Bayesian analysis is used for the estimation of the fragment number probabilities. This analysis is carried out on the basis of Poisson-gamma model. An approach to developing a gamma prior distribution for the average number of fragments per explosion accident is proposed. The assessment of the fragment number probabilities is carried out by propagating uncertainty related to the average number of fragments to uncertainty in the fragment number probabilities. The stochastic (Monte Carlo) simulation is used for this propagation. Findings of this study are viewed as a possibility to improve the assessment of risk posed by pressure vessel explosions. [ABSTRACT FROM AUTHOR]

A novel analytic methodology for centralized statistical monitoring of the clinical trial interim enrollment performance is developed. The underlying technique uses a Poisson-gamma (PG) enrollment model developed by Anisimov and Fedorov in the previous publications. This technique is extended to modeling clinical centers performance and detecting outliers (low and high enrolling centers) using interim enrollment data and different approaches (P-values, 2D-classification). To analyze country/region performance, a new technique based on the approximation of the enrollment process in country/region by a PG process with aggregated parameters is developed. The developed methodology is applied to the analysis of the interim enrollment performance of a real clinical trial. The results support the efficiency of using this methodology in monitoring of various enrollment characteristics. [ABSTRACT FROM AUTHOR]

The Poisson–Gamma model is a generalization of the Poisson model, which can be used for modelling count data. We show that the D -optimality criterion for the Poisson–Gamma model is equivalent to a combined weighted optimality criterion of D -optimality and D s -optimality for the Poisson model. Moreover, we determine the D -optimal designs for the Poisson–Gamma model for multiple regression with an arbitrary number of covariates, obtaining the D s -optimal designs for the Poisson and Poisson–Gamma model as a special case. For linear optimality criteria like L - and c -optimality it is shown that the optimal designs in the Poisson and Poisson–Gamma model coincide. • D-optimality criterion for Poisson–Gamma model is equivalent to a combined weighted optimality criterion of D- and D s -optimality for the Poisson model. • D- and D s -optimal designs for multiple regression models are determined. • For linear optimality criteria the optimal designs for the Poisson and Poisson–Gamma model coincide. [ABSTRACT FROM AUTHOR]

Cancer is known to be one of the leading causes of mortality in the world. There were about 14.1 million incidences and 8.2 million deaths due to cancer globally. In terms of mouth cancer Age Standardized Rate is 4.0 per 100000 populations worldwide and 7.2 per 100000 populations in India. In Chennai, mouth cancer burden has significantly increased over the past decade irrespective of geographical region. In this paper, the mouth cancer incidence is used to analyze the spatial distribution for high risk and low risk areas of different zones in Chennai by gender for the period of 2004-2013. The aim of this study is to fit a Poisson Gamma model and to explore the Empirical Bayesian and frequentist approach for disease mapping of mouth cancer incidence for Chennai zones by sex. The results of the estimates reveal that the empirical Bayesian estimate is more stable than the conventional frequentist estimates. [ABSTRACT FROM AUTHOR]

Randomisation schemes are rules that assign patients to treatments in a clinical trial. Many of these schemes have the common aim of maintaining balance in the numbers of patients across treatment groups. The properties of imbalance that have been investigated in the literature are based on two treatment groups. In this paper, their properties for K > 2 treatments are studied for two randomisation schemes: centre-stratified permuted-block and complete randomisation. For both randomisation schemes, analytical approaches are investigated assuming that the patient recruitment process follows a Poisson-gamma model. When the number of centres involved in a trial is large, the imbalance for both schemes is approximated by a multivariate normal distribution. The accuracy of the approximations is assessed by simulation. A test for treatment differences is also considered for normal responses, and numerical values for its power are presented for centre-stratified permuted-block randomisation. To speed up the calculations, a combined analytical/approximate approach is used. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

ABSTRACT Generalized linear models ( GLMs) are used in understanding the impact of predictors on a dependent variable. The aim of this study is to fit GLMs to daily rainfall totals using potential predictors. First, the appropriate probability distributions within a specific family, the Tweedie family, were determined for daily rainfall totals from four stations of Peninsular Malaysia from 1983 to 2012. Within the Tweedie family, the Poisson Gamma ( PG) distribution was found appropriate to model both components: occurrence (dry/wet days) and amount (rainfall totals on wet days) of rainfall simultaneously. Then, the PG-GLMs were fitted to rainfall data with a sine term, a cosine term, lagged rainfall, NINO3.4 and Southern oscillation index ( SOI) as predictors. Finally, the models were compared using the Likelihood ratio test and the Akaike information criterion. Initially, considering the cyclic pattern of rainfall data, models with only sine and cosine terms (the base model) were fitted. Then the lagged rainfall and climatological variables were added each time to the base model. Diagnostic QQ plots indicate that the models fit the data well. The models were fitted using the first 60% of data and validated using the remainder. The models capture the various characteristics of observed datasets reasonably well. Including single climatological variables in the model significantly improves the fit compared to the base model with lagged rainfall (except for the south-east coastal station, Mersing), however, including both climatological predictors in the same model does not improve the model significantly. The model with SOI is only favoured for the east coastal station, Kuala Terengganu, and the model with NINO3.4 fits better to the inland and west coastal stations. The models are useful in understanding the impact of the studied climatological variables and to predict the amount and probability of rainfall. [ABSTRACT FROM AUTHOR]

Clinical testing accounts for almost 70% of the R &D expenditure in the pharmaceutical industry and most clinical trials experience considerable delays that result in extra costs. One of the major sources of these delays is the patient recruitment process. It is estimated that about 48% of the recruitment sites of a clinical trial fail to meet their deadlines due to slow recruitment rates and 11% do not recruit a single patient. Thus, determining the correct number of recruitment sites is paramount for more efficient supply chains in clinical trials. The calculation of the number of recruitment sites in clinical trials is based on factors such as the target number of patients, their estimated recruitment rates, and the associated operational costs. However, these calculations typically ignore the time needed for sites to be operational. In this paper, we analyze the impact of incorporating these site activation delays in determining the optimal number of clinical sites. Our study shows that ignoring these delays leads to overestimating the number of sites needed, thus resulting in an excess of expenditure. Consequently, the insights herein explained help quantify the impact of making better decisions in designing more efficient operations in clinical trials, both in terms of time and money. [ABSTRACT FROM AUTHOR]

We describe a class of random field models for geostatistical count data based on Gaussian copulas. Unlike hierarchical Poisson models often used to describe this type of data, Gaussian copula models allow a more direct modelling of the marginal distributions and association structure of the count data. We study in detail the correlation structure of these random fields when the family of marginal distributions is either negative binomial or zero-inflated Poisson; these represent two types of overdispersion often encountered in geostatistical count data. We also contrast the correlation structure of one of these Gaussian copula models with that of a hierarchical Poisson model having the same family of marginal distributions, and show that the former is more flexible than the latter in terms of range of feasible correlation, sensitivity to the mean function and modelling of isotropy. An exploratory analysis of a dataset of Japanese beetle larvae counts illustrate some of the findings. All of these investigations show that Gaussian copula models are useful alternatives to hierarchical Poisson models, specially for geostatistical count data that display substantial correlation and small overdispersion. [ABSTRACT FROM AUTHOR]

ABSTRACT Empirical Bayes (EB) estimates in general linear mixed models are useful for the small area estimation in the sense of increasing precision of estimation of small area means. However, one potential difficulty of EB is that the overall estimate for a larger geographical area based on a (weighted) sum of EB estimates is not necessarily identical to the corresponding direct estimate such as the overall sample mean. Another difficulty is that EB estimates yield over-shrinking, which results in the sampling variance smaller than the posterior variance. One way to fix these problems is the benchmarking approach based on the constrained empirical Bayes (CEB) estimators, which satisfy the constraints that the aggregated mean and variance are identical to the requested values of mean and variance. In this paper, we treat the general mixed models, derive asymptotic approximations of the mean squared error (MSE) of CEB and provide second-order unbiased estimators of MSE based on the parametric bootstrap method. These results are applied to natural exponential families with quadratic variance functions. As a specific example, the Poisson-gamma model is dealt with, and it is illustrated that the CEB estimates and their MSE estimates work well through real mortality data. [ABSTRACT FROM AUTHOR]

Abstract: This work proposes a class of hierarchical models for geostatistical count data that includes the model proposed by Diggle et al. (1998) [13] as a particular case. For this class of models the main second-order properties of the count variables are derived, and three models within this class are studied in some detail. It is shown that for this class of models there is a close connection between the correlation structure of the counts and their overdispersions, and this property can be used to explore the flexibility of the correlation structures of these models. It is suggested that the models in this class may not be adequate to represent data consisting mostly of small counts with substantial spatial correlation. Three geostatistical count datasets are used to illustrate these issues and suggest how the results might be used to guide the selection of a model within this class. [Copyright &y& Elsevier]

Statistical graphics are a fundamental, yet often overlooked, set of components in the repertoire of data analytic tools. Graphs are quick and efficient, yet simple instruments for preliminary exploration of a dataset to understand its structure and to provide insight into influential aspects of inference such as departures from assumptions and latent patterns. In this article, we present and assess a graphical device for choosing a method for estimating population size in capture–recapture studies of closed populations. The basic concept is derived from a homogeneous Poisson distribution where the ratios of neighboring Poisson probabilities multiplied by the value of the larger neighbor count are constant. This property extends to the zero-truncated Poisson distribution, which is of fundamental importance in capture–recapture studies. In practice, however, this distributional property is often violated. The graphical device developed here, the ratio plot, can be used for assessing specific departures from a Poisson distribution. For example, simple contaminations of an otherwise homogeneous Poisson model can be easily detected and a robust estimator for the population size can be suggested. Several robust estimators are developed and a simulation study is provided to give some guidance on which one should be used in practice. More systematic departures can also easily be detected using the ratio plot. In this article, the focus is on Gamma-mixtures of the Poisson distribution that leads to a linear pattern (called structured heterogeneity) in the ratio plot. More generally, the article shows that the ratio plot is monotone for arbitrary mixtures of power series densities. This article has online supplementary materials. [ABSTRACT FROM PUBLISHER]

Abstract: Online marketplace, taken the form of “open market” where a very large number of buyers and sellers participate, has occupied a rapid increasing position in e-commerce, which resulting in sellers’ increasing investment on online advertising. Hence, there is a growing need to identify the effectiveness of online advertising in the online marketplaces such as eBay.com. However, it is problematic to directly apply the existing online advertising effect models for click-through data of online marketplaces. Therefore, there is a need for developing a model to estimate the effectiveness of online advertising in online marketplace considering its characteristics. In this paper, we develop an analytical Bayesian approach to modeling click-though data by employing the Poisson–gamma distribution. Our results have implications for online advertising effect measurement, and may help guide advertisers in decision-making. [Copyright &y& Elsevier]

Abstract: This paper presents an application of the Bayesian Markov Chain Monte Carlo (MCMC) used to select cost-effective ad spots in online marketplaces. Due to the rise of electronic commerce, the online advertising industry which is highly complex undergoes rapid changes. And there are plenty of studies that keep coming up with the similar methodologies to predict click-through rates for ad spots. Previous research has mainly considered the following models: a logistic regression model and a binomial model connected by a linear link function. However, it is problematic to directly apply the existing online advertising effect models to the click-through data of online marketplaces. Because generally a click-through rate is fairly low so that a small change in its rate might give a somewhat larger prediction error in terms of click-throughs. We propose a Bayesian Poisson-gamma model to predict click-throughs instead of their rates and further extend to incorporate random effects in order to account for heterogeneity of variance between keywords. Our results may help guide online advertisers in decision-making. [Copyright &y& Elsevier]

Abstract: The online marketplace, in the form of an “open market” where a very large number of buyers and sellers participate, has occupied a rapidly increasing position in e-commerce, resulting in sellers’ increasing investment in online advertising. Hence, there is a growing need to identify the effectiveness of online advertising in online marketplaces such as eBay.com. However, it is problematic to directly apply the existing online advertising effect models to the click-through data of online marketplaces. Therefore, a model must be developed to estimate the effectiveness of online advertising in the online marketplace in terms of its characteristics. In this paper, we develop an analytical Bayesian approach to modeling click-through data by employing the Poisson-gamma distribution. Our results have implications for online advertising effect measurement, and may help guide advertisers in decision-making. [ABSTRACT FROM AUTHOR]

Abstract: Modelling rainfall is important for prediction and simulation purposes in many areas of planning, agriculture, forestry, meteorology and hydrology. Usually two different models are needed to understand the two important features of rainfall: the occurrence and the amount. Here we use a single model, a Tweedie generalized linear model, to model the occurrence and amount of rainfall simultaneously. Choosing a simple model with only sine and cosine terms as predictors, the model is fitted for 220 Australian stations, with 6 rainfall stations are taken as case studies. The model fits well to monthly rainfall data based on studying the probability of no rain each month, and mean monthly rainfall amounts. Using the model, simulating monthly rainfall data for the stations with inadequate rainfall records is possible. The model also allows for a disaggregation of monthly rainfall amounts into the number of rainfall events in each month and the mean amount of rainfall per event. This information can then be used in agriculture production system simulators for agricultural planning and management. [ABSTRACT FROM AUTHOR]

Objective: Nosocomial infection is one of the main causes of morbidity and mortality in patients admitted to hospital. One aim of this study is to determine its intrinsic and extrinsic risk factors. Nosocomial infection also increases the duration of hospital stay. We quantify, in relative terms, the increased duration of the hospital stay when a patient has the infection. Methods: We propose the use of logistic regression models with an asymmetric link to estimate the probability of a patient suffering a nosocomial infection. We use Poisson-Gamma regression models as a multivariate technique to detect the factors that really influence the average hospital stay of infected and noninfected patients. For both models, frequentist and Bayesian estimations were carried out and compared. Results: The models are applied to data from 1039 patients operated on in a Spanish hospital. Length of stay, the existance of a preoperative stay and obesity were found the main risk factors for a nosomial infection. The existence of a nosocomial infection multiplies the length of stay in the hospital by a factor of 2.87. Conclusion: The results show that the asymmetric logit improves the predictive capacity of conventional logistic regressions [ABSTRACT FROM AUTHOR]

Identifying regions with the highest and lowest mortality rates and producing the corresponding color-coded maps help epidemiologists identify promising areas for analytic etiological studies. Based on a two-stage Poisson–Gamma model with covariates, we use information on known risk factors, such as smoking prevalence, to adjust mortality rates and reveal residual variation in relative risks that may reflect previously masked etiological associations. In addition to covariate adjustment, we study rankings based on standardized mortality ratios (SMRs), empirical Bayes (EB) estimates, and a posterior percentile ranking (PPR) method and indicate circumstances that warrant the more complex procedures in order to obtain a high probability of correctly classifying the regions with the upper and lower of relative risks for , and 0.2. We also give analytic approximations to the probabilities of correctly classifying regions in the upper of relative risks for these three ranking methods. Using data on mortality from heart disease, we found that adjustment for smoking prevalence has an important impact on which regions are classified as high and low risk. With such a common disease, all three ranking methods performed comparably. However, for diseases with smaller event counts, such as cancers, and wide variation in event counts among regions, EB and PPR methods outperform ranking based on SMRs. [ABSTRACT FROM AUTHOR]

Abstract: This paper uses a semi-parametric Poisson-gamma model to estimate the relationships between crash counts and various roadway characteristics, including curvature, traffic levels, speed limit and surface width. A Bayesian nonparametric estimation procedure is employed for the model’s link function, substantially reducing the risk of a mis-specified model. It is shown via simulation that little is lost in terms of estimation quality if the nonparametric estimation procedure is used when standard parametric assumptions (e.g., linear functional forms) are satisfied, but there is significant gain if the parametric assumptions are violated. It is also shown that imposing appropriate monotonicity constraints on the relationships provides better function estimates. Results suggest that key factors for explaining crash rate variability across roadways are the amount and density of traffic, presence and degree of a horizontal curve, and road classification. Issues related to count forecasting on individual roadway segments and out-of-sample validation measures also are discussed. [Copyright &y& Elsevier]

The distribution of human capital is a recent addition to the list of fundamental determinants of growth. This paper addresses an important problem of how to utilize recently available data on the highest educational attainment of adults in the labor force to represent the human capital distribution of a country by a smooth probability density function. Using the data of Barro and Lee, over-dispersed Poisson and negative binomial distributions are selected to fit the distribution of the number of years of school. Our empirical investigations suggest that these standard discrete probability distributions are too smooth to account for properties of the data, i.e., schooling is more likely to be terminated at the completion of a level of attainment (e.g., primary, secondary, and higher education) than in the middle of one, an important feature contained in the frequency distribution of highest educational attainment. Future research should focus on more complex models which account for these spikes in the data. [Copyright &y& Elsevier]