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Within the past decade, there has been an increasing interest in the problem of joint analysis of clustered multiple outcome data, motivated by developmental toxicity applications. Typically, a toxic insult early in gestation may result in a resorbed fetus or a fetal death. If however the fetus survives the entire gestation period, growth reduction such as low birth weight may occur, or can exhibit a malformation. Ideally, a model should take the complete hierarchical structure of the data into account. So far, however, one has tackled the challenges in this setting only partly each time making different restricting assumptions (e.g., restriction to viable fetuses only). In addition, because of genetic similarity and the same treatment conditions, offsprings of the same mother behave more alike than those of another mother. Thus, responses on different fetuses within a cluster are likely to be correlated. The ultimate scientific question requires assessing the full effect of dose administration, not only in the malformation and weight outcome, but also in the death outcome. A hierarchical Bayesian method is proposed to this effect. Such a model can serve as a basis for quantitative risk assessment.

Summary In veterinary epidemiology, we are often confronted with hierarchical or clustered data. Typically animals are grouped within herds, and consequently we cannot ignore the possibility of animals within herds being more alike than between herds. Based on a serological survey of bovine herpes virus type 1 in cattle, we describe a method for the estimation of herd-specific rates at which susceptible animals acquire the infection at different ages. In contrast with the population-averaged force of infection, this method allows us to model the herd-specific force of infection, allowing investigation of the variability between herds. A random-effects approach is used to account for the correlation in the data, allowing us to study both population-averaged and herd-specific force of infection. In contrast, generalized estimating equations can be used when interest is only in the population-averaged force of infection. Further, a flexible predictor model is needed to describe the dependence of covariates appropriately. Fractional polynomials as proposed by Royston and Altman offer such flexibility. However, the flexibility of this model should be restricted, since only positive forces of infection have a meaningful interpretation.

Quantile regression is an alternative to OLS regression. In quantile regression, the sum of absolute deviations or the L1-norm is minimized, whereas the sum of squared deviations or the L2-norm is minimized in OLS regression. Quantile regression has the advantage over OLS-regression of being more robust to outlying observations. Furthermore, quantile regression provides information complementing the information provided by OLS-regression. In this study, a non-parametric approach to quantile regression is presented, which constrains the estimated-quantile function to be monotone increasing. In particular, P-splines with an additional asymmetric penalty enforcing monotonicity are used within an L1-framework. This can be translated into a linear programming problem, which will be solved using an interior point algorithm. As an illustration, the presented approach will be applied to estimate quantile growth curves and quantile antibody levels as a function of age.

Summary. In industrialized countries, transmission of hepatitis C occurs primarily through injecting drug use. Transmission of hepatitis C in injecting drug users is mainly associated with the sharing of contaminated syringes/needles, although evidence for risk of hepatitis C infection through sharing of other injecting paraphernalia is increasing. In this paper, the independent effects of sharing paraphernalia other than syringes/needles have been estimated. The prevalence and force of infection were modelled using three serological data sets from drug users in three centres in Belgium as a function of the sharing behaviour. It was found that sharing of materials other than syringes/needles indeed seemed to contribute substantially to the spread of hepatitis C among injecting drug users.

The Akaike information criterion, AIC, is one of the most frequently used methods to select one or a few good, optimal regression models from a set of candidate models. In case the sample is incomplete, the naive use of this criterion on the so-called complete cases can lead to the selection of poor or inappropriate models. A similar problem occurs when a sample based on a design with unequal selection probabilities, is treated as a simple random sample. In this paper, we consider a modification of AIC, based on reweighing the sample in analogy with the weighted Horvitz-Thompson estimates. It is shown that this weighted AIC-criterion provides better model choices for both incomplete and design-based samples. The use of the weighted AIC-criterion is illustrated on data from the Belgian Health Interview Survey, which motivated this research. Simulations show its performance in a variety of settings. Copyright (c) 2006 John Wiley & Sons, Ltd. Financial support from the IAP research network No. P5=24 of the Belgian Government (Belgian Science Policy) is gratefully acknowledged.

In this paper we present and discuss a novel, simple and easy to implement parametric modeling approach to assess synergy. An extended three parameter log-logistic model is used to analyse the data and calculate confidence intervals of the interaction indices. In addition the model corrects for the bias due to plate-location effects. The analysis is performed with PROC NLMIXED and SAS-code is provided. The approach is illustrated using data coming from an oncology study in which the inhibition effect of a combination of two compounds is studied using 96-well plates and a fixed-ratio design.

The aim of this paper is to gain a better understanding of the impact of simplification on a sequential model of activity-scheduling behavior which uses feature-selection methods. To that effect, the predictive performance of the Albatross model, which incorporates nine different facets of activity–travel behavior, based on the original full decision trees, is compared with the performance of the model based on trimmed decision trees. The results indicate that significantly smaller decision trees can be used for modeling the different choice facets of the sequential model system without losing much in predictive power. The performance of the models is compared at three levels: the choice-facet level, the activity-pattern level (comparing the observed and generated sequences of activities), and the trip-matrix level, comparing the correlation coefficients that determine the strength of the associations between the observed and the predicted origin–destination matrices. The results indicate that the model based on the trimmed decision trees predicts activity-diary schedules with a minimum loss of accuracy at the decision level. Moreover, the results indicate a slightly better performance at the activity-pattern and the trip-matrix level.

Measurements of both continuous and categorical outcomes appear in many statistical problems. One such example is the study of teratology and developmental toxicity, where both the probability that a live fetus is malformed (ordinal) or of low birth weight (continuous) are important measures in the context of teratogenicity. Although multivariate methods of the analysis of continuous outcomes are well understood, methods for jointly continuous and discrete outcomes are less familiar. We propose a likelihood-based method that is an extension of the Plackett-Dale approach. Specification of the full likelihood will be avoided using pseudo-likelihood methodology. The estimation of safe dose levels as part of quantitative risk assessment will be illustrated based on a developmental toxicity experiment of diethylene glycol dimethyl ether in mice.

Developmental toxicity studies are widely used to investigate the potential risk of environmental hazards. In dose–response experiments, subjects are randomly allocated to groups receiving various dose levels. Tests for trend are then often applied to assess possible dose effects. Recent techniques for risk assessment in this area are based on fitting dose–response models. The complexity of such studies implies a number of non-trivial challenges for model development and the construction of dose-related trend tests, including the hierarchical structure of the data, litter effects inducing extra variation, the functional form of the dose–response curve, the adverse event at dam or at fetus level, the inference paradigm, etc. The purpose of this paper is to propose a Bayesian trend test based on a non-linear power model for the dose effect and using an appropriate model for clustered binary data. Our work is motivated by the analysis of developmental toxicity studies, in which the offspring of exposed and control rodents are examined for defects. Simulations show the performance of the method over a number of samples generated under typical experimental conditions.

This study was aimed at the identification of location and household characteristics influencing the choice of keeping livestock or practising crop production in a post-conflict region in Central Africa. Two thousand eight hundred randomly selected families from Brazzaville (Congo) were surveyed. From these, 6% are both keeping livestock and producing crops, 3% are keeping livestock only, 24% are producing crops only and 67% are not producing crops nor keeping livestock. From these four groups, respectively, 135, 84, 246 and 245 households were interviewed to collect further data on household and location characteristics. Non-parametric and parametric techniques were compared as tools to analyse the groups. In the non-parametric classification tree method CART following variables were identified as being important for the engagement in keeping livestock or urban agriculture: keeping livestock before 1997, practising agriculture before 1997, property size, locality, income, availability of water, professional activity and level of instruction. Including surrogate variables resulted in extra variables: age, availability of electricity and sex. In the multinomial regression only the most important variables from the classification tree were withheld and other insights were obtained. The results of this research highlighted the shortcomings of multinomial regression. Fitting a full model containing all possible interactions becomes an impossible task with 20 explanatory variables. Using the classification tree information in a multinomial model appears the most appropriate solution, and this method is a useful tool for further work in the analysis of livestock and crop production systems. The importance of the historical component in the decision to practise crop production and keep livestock was demonstrated. Being involved in crop production develops roots, which cannot be destroyed by impediments such as periods of conflict. (C) 2003 Elsevier Ltd. All rights reserved.

Developmental toxicity studies are designed to assess the potential adverse effects of an exposure on developing fetuses. Safe dose levels can be determined using dose-response modelling. To this end, it is important to investigate the effect of misspecifying the dose-response model on the safe dose. Since classical polynomial predictors are often of poor quality, there is a clear need for alternative specifications of the predictors, such as fractional polynomials. By means of simulations, we will show how fractional polynomial predictors may resolve possible model misspecifications and may thus yield more reliable estimates of the benchmark doses.

Recently, a lot of concern has been raised about assumptions needed in order to fit statistical models to incomplete multivariate and longitudinal data. In response, research efforts are being devoted to the development of tools that assess the sensitivity of such models to often strong but always, at least in part, unverifiable assumptions. Many efforts have been devoted to longitudinal data, primarily in the selection model context, although some researchers have expressed interest in the pattern-mixture setting as well. A promising tool, proposed by Verbeke et al. (2001, Biometrics57, 43–50), is based on local influence (Cook, 1986, Journal of the Royal Statistical Society, Series B48, 133–169). These authors considered the Diggle and Kenward (1994, Applied Statistics43, 49–93) model, which is based on a selection model, integrating a linear mixed model for continuous outcomes with logistic regression for dropout. In this article, we show that a similar idea can be developed for multivariate and longitudinal binary data, subject to nonmonotone missingness. We focus on the model proposed by Baker, Rosenberger, and DerSimonian (1992, Statistics in Medicine11, 643–657). The original model is first extended to allow for (possibly continuous) covariates, whereafter a local influence strategy is developed to support the model-building process. The model is able to deal with nonmonotone missingness but has some limitations as well, stemming from the conditional nature of the model parameters. Some analytical insight is provided into the behavior of the local influence graphs. Récemment, beaucoup de soucis se sont manifestés à propos des hypothèses nécessaires pour ajuster des modèles statistiques à des données longitudinales multidimensionnelles incomplètes. En réponse, des recherches sont consacrés au développement d’outils évaluant la sensibilité de tels modèles à des hypothèses souvent fortes et toujours invérifiables, aumoins partiellement. Beaucoup d’efforts ont été consacrésaux données longitudinales principalement dans le contexte d’un modèle de sélection bien que quelques chercheurs aient montrée de l’intérêt pour le modèle de mélange de profils. Unoutil prometteur, proposé par Verbeke et coll.(2001), reposesur l’étude de l’influence locale. Ces auteurs considèrent le modèle de Diggle et Kenward(1994) qui repose sur un modèle de sélection et qui combine un modèle mixte linéaire pour descritères d’évaluation continus et une régression logistique pourles abandons de traitement. Dans ce papier, nous montrons qu’une idée similaire peut être développé pour des données binaires longitudinales multidimensionnelles, sujettes à un profil non-monotone de valeurs manquantes. Nous nous concentrons sur le modèle proposé par Baker, Rosenberger et Der Simonian(1992).Le modèle d’origine est d’abord étendu à la prise en compte de covariables, possiblement continues, puis une stratégie d’influence locale est développée à l’appui de la construction du modèle. Ce modèle peuttraiter un profil non-monotone de valeurs manquantes, mais présente certaines limitations liées à la nature conditionnelle des paramètres du modèle. Un apercu analytique est fourni pour le comportement des graphes d’influencelocale. We gratefully acknowledge support from FWO-VlaanderenResearch Project “Sensitivity Analysis for Incomplete andCoarse Data.” The fourth author gratefully acknowledgessupport from a research grant of Vlaams Instituut voor deBevordering van het Wetenschappelijk-Technologisch Onder-zoek in de Industrie. The fifth author wishes to thank theVlaamse Interuniversitaire Raad for granting support. We aregrateful for support from “Interuniversity Attraction PolesProgramme P5/24—Belgian State—Federal Office for Scien-tific, Technical and Cultural Affairs.”

Generalized additive models have become one of the most widely used modern statistical tools. Traditionally, they are fit through scatterplot smoothing and the backfitting algorithm. However, a more recent development is the direct fitting through the use of low-rank smoothers (Hastie, J. Roy. Statist. Soc. Ser. B 58 (1996) 379). A particularly attractive example of this is through use of penalized splines (Marx and Eilers, Comput. Statist. Data Anal. 28 (1998) 193). Such an approach has a number of advantages, particularly regarding computation. In this paper, we exploit the explicitness of penalized spline additive models to derive some useful and revealing theoretical approximations.

We investigate several methods commonly used to obtain a benchmark dose and show that those based on full likelihood or profile likelihood methods might have severe shortcomings. We propose two new profile likelihood-based approaches which overcome these problems. Another contribution is the extension of the benchmark dose determination to non full likelihood models, such as quasi-likelihood, generalized estimating equations, which are widely used in settings such as developmental toxicity where clustered data are encountered. This widening of the scope of application is possible by the use of (robust) score statistics. Benchmark dose methods are applied to a data set from a developmental toxicity study.

Background Meta-analyses have become an essential tool in synthesizing evidence on clinical and epidemiological questions derived from a multitude of similar studies assessing the particular issue. Appropriate and accessible statistical software is needed to produce the summary statistic of interest. Methods Metaprop is a statistical program implemented to perform meta-analyses of proportions in Stata. It builds further on the existing Stata procedure metan which is typically used to pool effects (risk ratios, odds ratios, differences of risks or means) but which is also used to pool proportions. Metaprop implements procedures which are specific to binomial data and allows computation of exact binomial and score test-based confidence intervals. It provides appropriate methods for dealing with proportions close to or at the margins where the normal approximation procedures often break down, by use of the binomial distribution to model the within-study variability or by allowing Freeman-Tukey double arcsine transformation to stabilize the variances. Metaprop was applied on two published meta-analyses: 1) prevalence of HPV-infection in women with a Pap smear showing ASC-US; 2) cure rate after treatment for cervical precancer using cold coagulation. Results The first meta-analysis showed a pooled HPV-prevalence of 43% (95% CI: 38%-48%). In the second meta-analysis, the pooled percentage of cured women was 94% (95% CI: 86%-97%). Conclusion By using metaprop, no studies with 0% or 100% proportions were excluded from the meta-analysis. Furthermore, study specific and pooled confidence intervals always were within admissible values, contrary to the original publication, where metan was used. Electronic supplementary material The online version of this article (doi:10.1186/2049-3258-72-39) contains supplementary material, which is available to authorized users.

The basic reproduction number R0 and the effective reproduction number R are pivotal parameters in infectious disease epidemiology, quantifying the transmission potential of an infection in a population. We estimate both parameters from 13 pre-vaccination serological data sets on varicella zoster virus (VZV) in 12 European countries and from population-based social contact surveys under the commonly made assumptions of endemic and demographic equilibrium. The fit to the serology is evaluated using the inferred effective reproduction number R as a model eligibility criterion combined with AIC as a model selection criterion. For only 2 out of 12 countries, the common choice of a constant proportionality factor is sufficient to provide a good fit to the seroprevalence data. For the other countries, an age-specific proportionality factor provides a better fit, assuming physical contacts lasting longer than 15 min are a good proxy for potential varicella transmission events. In all countries, primary infection with VZV most often occurs in early childhood, but there is substantial variation in transmission potential with R0 ranging from 2.8 in England and Wales to 7.6 in The Netherlands. Two non-parametric methods, the maximal information coefficient (MIC) and a random forest approach, are used to explain these differences in R0 in terms of relevant country-specific characteristics. Our results suggest an association with three general factors: inequality in wealth, infant vaccination coverage and child care attendance. This illustrates the need to consider fundamental differences between European countries when formulating and parameterizing infectious disease models. ES acknowledges support from a Methusalem research grant from the Flemish Government. NG is beneficiary of a postdoctoral grant from the AXA Research Fund. NH acknowledges support from the Antwerp University scientific chair in Evidence-Based Vaccinology, financed in 2009-2014 by an unrestricted gift from Pfizer. AM is currently receiving funding from the European Research Council under the European Union's Seventh Framework Program(FP7/2007-2013)/ERC Starting Grant [Agreement No. 283955]. Support from the IAP Research Network P7/06 of the Belgian State(Belgian Science Policy) is gratefully acknowledged. The computational resources and services used in this work were provided by the Hercules Foundation and the Flemish Government - department EWI. This study was initiated as part of POLYMOD, a European Commission project funded within the Sixth Framework Programme, Contract number: SSP22-CT-2004-502084.

In chemical risk assessment, it is important to determine the quantiles of the distribution of concentration data. The selection of an appropriate distribution and the estimation of particular quantiles of interest are largely hindered by the omnipresence of observations below the limit of detection, leading to left-censored data. The log-normal distribution is a common choice, but this distribution is not the only possibility and alternatives should be considered as well. Here, we focus on several distributions that are related to the log-normal distribution or that are seminonparametric extensions of the log-normal distribution. Whereas previous work focused on the estimation of the cumulative distribution function, our interest here goes to the estimation of quantiles, particularly in the left tail of the distribution where most of the left-censored data are located. Two different model averaged quantile estimators are defined and compared for different families of candidate models. The models and methods of selection and averaging are further investigated through simulations and illustrated on data of cadmium concentration in food products. The approach is extended to include covariates and to deal with uncertainty about the values of the limit of detection. These extensions are illustrated with (134) cesium measurements from Fukushima Prefecture, Japan. We can conclude that averaged models do achieve good performance characteristics in case no useful prior knowledge about the true distribution is available; that there is no structural difference in the performance of the direct and indirect method; and that, not surprisingly, only the true or closely approximating model can deal with extremely high percentages of censoring.

Antimicrobial resistance has become one of the main public health burdens of the last decades, and monitoring the development and spread of non-wild-type isolates has therefore gained increased interest. Monitoring is performed based on the minimum inhibitory concentration (MIC) values, which are collected through the application of dilution experiments. In order to account for the unobserved population heterogeneity of wild-type and non-wild-type isolates, mixture models are extremely useful. Instead of estimating the entire mixture globally, it was our major aim to provide an estimate for the wild-type first component only. The characteristics of this first component are not expected to change over time, once the wild-type population has been confidently identified for a given antimicrobial. With this purpose, we developed a new method based on the multinomial distribution, and we carry out a simulation study to study the properties of the new estimator. Because the new approach fits within the likelihood framework, we can compare distinct distributional assumptions in order to determine the most suitable distribution for the wild-type population. We determine the optimal parameters based on the AIC criterion, and attention is also paid to the model-averaged approach using the Akaike weights. The latter is thought to be very suitable to derive specific characteristics of the wild-type distribution and to determine limits for the wild-type MIC range. In this way, the new method provides an elegant means to compare distinct distributional assumptions and to quantify the wild-type MIC distribution of specific antibiotic-bacterium combinations.

Coenen, S (reprint author), Univ Antwerp, Vaccine & Infect Dis Inst VAXINFECTIO, Lab Med Microbiol, B-2020 Antwerp, Belgium. samuel.coenen@uantwerpen.be

When the data do not come from the assumed parametric model, the usual asymptotic chi-squared distribution under the null hypothesis, remains valid for “robustified” Wald and score test statistics. In this paper, we compare the performance of this chi-squared approximation to that of a semiparametric bootstrap method. The bootstrap approximation is based on a one-step bootstrap estimator reflecting the null hypothesis. One of the advantages of this one-step approach is that no bootstrap data have to be generated and no additional model fitting is required. Simulations on clustered binary data indicate that the robust score test is superior and that, in cases where the chi-squared type tests fail in reaching the prescribed significance level, the proposed bootstrap test succeeds in correcting this towards the nominal level. The different methods are also compared on real developmental toxicity data.

Local polynomial smoothers are used to estimate cell probabilities for sparse multinomial data. We give a full characterization in terms of the amount of smoothing of the Gaussian behavior of the sum of squared errrors of the local polynomial smoothers. From the discussion the beneficial effect of smoothing will become clear.

Core breakdown of ‘Conference’ pears (Pyrus communis L.) is characterised by softening and browning of tissue near the core and is associated with the development of cavities. The disorder causes large economic losses of ‘Conference’ pears in Belgium, stored under controlled atmospheres. Factors that influence development of the disorder, CO2 and O2 concentration, the size and weight of the pear, the picking date and the storage temperature, were investigated. Multiple logistic regression was used to establish prediction and classification models for both internal browning and cavity development. Over-mature fruit was more susceptible to core breakdown during storage. It was also found that pears with a large weight had a higher probability of developing brownheart. R 2 values from 0.7 to 0.92 were obtained between the predicted and measured percentages of brownheart and cavities. The models classified up to 86% of the pears correctly. In a final analysis, the time sequence of the symptoms occurring during core breakdown disorder development was modelled with a generalized logits model. © 2000 Elsevier Science B.V. All rights reserved.

SUMMARY We study lack-of-fit tests based on orthogonal series estimators. A common feature of these tests is that they are functions of score statistics that employ data-driven model dimensions. The criteria used to select the dimension are score-based versions of AIC and BIC. The tests can be applied in a wide variety of settings, including both continuous and discrete data. With two or more covariates, a model sequence, i.e. a path in the alternative models space, has to be chosen. Critical points and p-values of the lack-of-fit tests can be obtained via asymptotic distribution theory or by use of the bootstrap. Data examples and a simulation study illustrate the applicability of the tests.

The local likelihood estimator and a semiparametric bootstrap method are studied under weaker conditions than usual; it is not assumed that the true probability distribution underlying the observations is known and hence the local likelihood estimator might be based on an incorrect likelihood. Moreover, results are generalized to pseudolikelihood, which is based on a product of conditional densities. Strong consistency and asymptotic normality are derived under suitable regularity conditions and a study of the derivatives of the estimators is performed. It is shown that the bootstrap method leads to consistent estimators which can be used for constructing confidence regions. As an illustration, the local likelihood smoother and the bootstrap procedure are implemented for a selection of probability models for clustered binary data. A data example shows the method's applicability.

Developmental toxicity experiments are designed to assess potential adverse effects of drugs and other exposures on developing fetuses from pregnant dams. Extrapolation to humans is a very difficult problem. An important issue here is whether risk assessment should be based on the fetus or the litter level. In this paper, fetus and litter-based risks that properly account for cluster size are defined and compared for the beta-binomial model and a conditional model for clustered binary data. It is shown how the hierarchical structure of non-viable implants and viable but malformed offspring can be incorporated. Risks based on a joint model for death/resorption and malformation are contrasted with risks based on an adverse event defined as either death/resorption or malformation. The estimation of safe exposure levels for all risk types is discussed and it is shown how estimation of the cluster size distribution affects variance estimation. The methods are applied to data collected under the National Toxicology Program and in large sample simulations.

General methods for testing the fit of a parametric function are proposed. The idea underlying each method is to “accept” the prescribed parametric model if and only if it is chosen by a model selection criterion. Several different selection criteria are considered, including one based on a modified version of the Akaike information criterion and others based on various score statistics. The tests have a connection with nonparametric smoothing because they use orthogonal series estimators to detect departures from a parametric model. An important aspect of the tests is that they can be applied in a wide variety of settings, including generalized linear models, spectral analysis, the goodness-of-fit problem, and longitudinal data analysis. Implementation using standard statistical software is straightforward. Asymptotic distribution theory for several test statistics is described, and the tests are shown to be consistent against essentially any alternative hypothesis. Simulations and a data exampl...

Asymptotic properties of the parametric bootstrap procedure for maximum pseudolikelihood estimators and hypothesis tests are studied in the general framework of associated populations. The technique is applied to the analysis of toxicological experiments which, based on pseudolikelihood inference for clustered binary data, fits into this framework. It is shown that the bootstrap approximation can be used as an interesting alternative to the classical asymptotic distribution of estimators and test statistics. Finite sample simulations for clustered binary data models confirm the asymptotic theory and indicate some substantial improvements.

Bahadur proposed a now well-known although not very frequently used model for correlated binary data. In its general form, it combines marginallogits with pairwise and higher order correlations, to describe the joint response distribution. In many applications, the third and higher order correlations are set equal to zero. We show that this simplification leads to a considerably inflated likelihood ratio test statistic. This phenomenon is intimately related to the constraints on the parameter space. Clustered data from developmental toxicity studies further illustrate the implications of this issue.

The nonparametric regression technique of local polynomial fitting is extended to multiparameter likelihood models. Some well-known appealing features of local polynomial smoothers, such as the behavior at the boundary, are shown to carry over to the multiparameter case. Asymptotic consistency and normality of the resulting estimators are derived under suitable regularity conditions. This work is motivated by the need for a nonparametric alternative to parametric dose-response models for clustered binary data. Probability models for clustered binary response data include a success probability parameter and one or more correlation parameters. The proposed local polynomial estimators can play an important role as a diagnostic tool or to suggest the form of the functional relationships in parametric likelihood models. As an illustration, it is shown how the local likelihood estimation procedure can be implemented for fitting a dose-response curve based on the beta-binomial model. A data example and ...

For sparse multinomial data we study sparse consistency rates for frequency estimators and for local polynomial cell probability estimators. Our results illustrate the beneficial effect of nonparametric smoothing. Compared to sparse consistency properties for maximum penalized likelihood cell probability estimators our results require less stringent conditions and allow more flexible sparseness conditions.

To estimate cell probabilities for sparse multinomial data several smoothing techniques have been investigated. Here we propose local polynomial smoothers as estimators for the cell probabilities and we study their performance. For the mean sum of squared errors we obtain the optimal rate of convergence and we establish a central limit theorem. We show that local polynomial smoothers provide a nice alternative for already existing nonparametric estimators and we discuss interrelations. Some illustrations are also included.

Objectives: The aim of this study was to measure differences in safety culture perceptions within Belgian acute hospitals and to examine variability based on language, work area, staff position, and work experience. Methods: The Hospital Survey on Patient Safety Culture was distributed to hospitals participating in the national quality and safety program (2007-2009). Hospitals were invited to participate in a comparative study. Data of 47,136 respondents from 89 acute hospitals were used for quantitative analysis. Percentages of positive response were calculated on 12 dimensions. Generalized estimating equations models were fitted to explore differences in safety culture. Results: Handoffs and transitions, staffing, and management support for patient safety were considered as major problem areas. Dutch-speaking hospitals had higher odds of positive perceptions for most dimensions in comparison with French-speaking hospitals. Safety culture scores were more positive for respondents working in pediatrics, psychiatry, and rehabilitation compared with the emergency department, operating theater, and multiple hospital units. We found an important gap in safety culture perceptions between leaders and assistants within disciplines. Administration and middle management had lower perceptions toward patient safety. Respondents working less than 1 year in the current hospital had more positive safety culture perceptions in comparison with all other respondents. Conclusions: Large comparative databases provide the opportunity to identify distinct high and low scoring groups. In our study, language, work area, and profession were identified as important safety culture predictors. Years of experience in the hospital had only a small effect on safety culture perceptions.

Movement of animals from one farm to another is a potential risk and can lead to the spreading of livestock diseases. Therefore, in order to implement effective control measures, it is important to understand the movement network in a given area. Using the SANITEL data from 2005 to 2009, around 2 million cattle movements in Belgium were traced. Exploratory analysis revealed different spatial structures for the movement of different cattle types: fattening calves are mostly moved to the Antwerp region, adult cattle are moved to different parts in Belgium. Based on these differences, movement of cattle would more likely cause a spread of disease to a larger number of areas in Belgium as compared to the fattening calves. A closer inspection of the spatial and temporal patterns of cattle movement using a weighted negative binomial model, revealed a significant short-distance movement of bovine which could be an important factor contributing to the local spreading of a disease. The model however revealed hot spot areas of movement in Belgium; four areas in the Walloon region (Luxembourg, Hainaut, Namur and Liege) were found as hot spot areas while East and West Flanders are important "receivers" of movement. This implies that an introduction of a disease to these Walloon regions could result in a spread toward the East and West Flanders regions, as what happened in the case of Bluetongue BTV-8 outbreak in 2006. The temporal component in the model also revealed a linear trend and short- and long-term seasonality in the cattle movement with a peak around spring and autumn. The result of this explorative analysis enabled the identification of "hot spots" in time and space which is important in enhancing any existing monitoring and surveillance system.

Background: Accurate estimates of the size of the drug-using populations are essential for evidence-based policy making. However, drug users form a ‘hidden’ population, necessitating the use of indirect methods to estimate population sizes. Methods: The benchmark-multiplier method was applied to estimate the population size of ever injecting drug users (ever-IDUs), aged 18–64 years, in Belgium using data from the national HIV/AIDS register and from a sero-behavioral study among injecting drug users. However, missing risk factor information and absence of follow-up of the HIV+/AIDS– cases, limits the usefulness of the Belgian HIV/AIDS register as benchmark. To overcome these limitations, statistical corrections were required. In particular, Imputation by Chained Equations was used to correct for the missing risk factor information whereas stochastic mortality modelling was applied to account for the mortality among the HIV+/AIDS– cases. Monte Carlo simulation was used to obtain confidence intervals, properly reflecting the uncertainty due to random error as well as the uncertainty associated with the two statistical corrections mentioned above. Results: In 2010, the prevalence (/1000) of ever-IDUs was estimated to be 3.5 with 95% confidence interval [2.5;4.8]. No significant time trends were observed for the period 2000–2010. Conclusions: To be able to estimate the ever-IDU population size using the Belgian HIV/AIDS register as benchmark, statistical corrections were required without which seriously biased estimates would result. By developing the improved methodology, Belgium is again able to provide ever-IDU population estimates, which are essential to assess the coverage of treatment and to forecast health care needs and costs.

Background Evidence on the influence of comorbidity and comedication on clinical outcomes in patients with type 2 diabetes mellitus is scarce. Aim To ascertain the effect of five chronic diseases (joint disorder, respiratory disease, anaemia, malignancy, depression) and three chronically used drugs (non-steroid anti-inflammatory drugs [NSAIDs], corticosteroids, antidepressants) on treatment for hypoglycaemia in patients with type 2 diabetes. Design and setting Retrospective cohort study in a variety of practices across Flanders, Belgium. Method A retrospective cohort study was conducted, based on data from Intego, a general practice-based continuous morbidity registry. Multiple logistic regression analysis was used to predict the change in glycosylated haemoglobin (HbA1c) levels related to comorbidity, comedication, and a combination of both in 3416 patients with type 2 diabetes. Adjustments were made for age, sex, and diabetes-treatment group (diet, oral antidiabetic drugs, combination treatment, insulin). Results Concomitant joint and respiratory disorders, as well as the chronic use of NSAIDs and corticosteroids, either separately or in combination, were significantly associated with the worsening of HbA1c levels. Anaemia, depression, malignancy, and antidepressants had no statistically significant influence on the efficacy of treatment for hypoglycaemia. Conclusion The presence of some comorbid diseases or drug use can impede the efficacy of treatment for type 2 diabetes. This finding supports the need to develop treatment recommendations, taking into account the presence of both chronic comorbidity and comedication. Further research must be undertaken to ascertain the effect other combinations of chronic diseases have on the efficacy of treatment of this and other diseases.

When Bluetongue Virus Serotype 8 (BTV-8) was first detected in Northern Europe in 2006, several guidelines were immediately put into place with the goal to protect farms and stop the spreading of the disease. This however did not prevent further rapid spread of BTV-8 across Northern Europe. Using information on the 2006 Bluetongue outbreak in cattle farms in Belgium, a spatio-temporal transmission model was formulated. The model quantifies the local transmission of the disease between farms within a municipality, the short-distance transmission between farms across neighbouring municipalities and the transmission as a result of cattle movement. Different municipality-level covariates such as farm density, land composition variables, temperature and precipitation, were assessed as possibly influencing each component of the transmission process. Results showed a significant influence of the different covariates in each model component, particularly the significant effect of temperature and precipitation values in the number of infected farms. The model which allowed us to predict the dynamic spreading of BTV for different movement restriction scenarios, also affirmed the significant impact of cattle movement in the 2006 BTV outbreak pattern. Simulation results further showed the importance of considering the size of restriction zones in the formulation of guidelines for animal infectious diseases. Support from the IAP Research Network P7/06 of the Belgian State (Belgian Science Policy) and the Flemish Research Council (G064710). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Conducting dietary exposure assessment (E) consists in combining deterministically or probabilistically food consumption figures (Q) with concentrations (C) of a given chemical substance in a number of foods or food categories. Occurrence data can be obtained either from control and monitoring programs or from a total diet Study (TDS). In both cases, data reported to be below the limit of detection (LOD), called “non-detects” or “left-censored data”, are likely to have a critical influence on the results of the assessment. Both the LOD and the limit of quantification (LOQ) are of special importance for exposure estimations in risk assessments as they determine the minimum value that can be detected and quantified, respectively.

The hepatitis C virus (HCV) and the human immunodeficiency virus (HIV) are a clear threat for public health, with high prevalences especially in high risk groups such as injecting drug users. People with HIV infection who are also infected by HCV suffer from a more rapid progression to HCV-related liver disease and have an increased risk for cirrhosis and liver cancer. Quantifying the impact of HIV and HCV co-infection is therefore of great importance. We propose a new joint mathematical model accounting for co-infection with the two viruses in the context of injecting drug users (IDUs). Statistical concepts and methods are used to assess the model from a statistical perspective, in order to get further insights in: (i) the comparison and selection of optional model components, (ii) the unknown values of the numerous model parameters, (iii) the parameters to which the model is most 'sensitive' and (iv) the combinations or patterns of values in the high-dimensional parameter space which are most supported by the data. Data from a longitudinal study of heroin users in Italy are used to illustrate the application of the proposed joint model and its statistical assessment. The parameters associated with contact rates (sharing syringes) and the transmission rates per syringe-sharing event are shown to play a major role. (C) 2013 Elsevier B.V. All rights reserved.

A weighted bootstrap version is defined for U-quantiles. Our main result shows that the (conditional) distribution of the weighted bootstrapped U-quantile provides a strongly consistent estimator for the unknown distribution for the U-quantile under consideration. For the proof we rely on a rank statistic approach.

The transmission of pathogens to susceptible hosts is dependent on the vector population dynamics. In Europe, bank voles (Myodes glareolus) carry Puumala hantavirus, which causes nephropathia epidemica (NE) in humans. Fluctuations in bank vole populations and epidemics in humans are correlated but the main factors influencing this relationship remain unclear. In Belgium, more NE cases are reported in spring than in autumn. There is also a higher incidence of human infections during years of large vole populations. This study aimed to better understand the link between virus prevalence in the vector, vole demography, habitat quality, and human infections. Three rodent populations in different habitats bordering Brussels city, Belgium, were studied for two years. The seroprevalence in voles was influenced first by season (higher in spring), then by vole density, vole weight (a proxy for age), and capture site but not by year or sex. Moreover, voles with large maximal distance between two captures had a high probability for Puumala seropositivity. Additionally, the local vole density showed similar temporal variations as the number of NE cases in Belgium. These results showed that, while season was the main factor influencing vole seroprevalence, it was not sufficient to explain human risks. Indeed, vole density and weight, as well as the local habitat, were essential to understanding the interactions in these host-pathogen dynamics. This can, in turn, be of importance for assessing the human risks. We are grateful to the members of the Unit of Social Ecology in the Universite Libre de Bruxelles for their support. Thanks are also due to the field assistants for their help in capturing rodents. We would like to thank Dr. S. Godefroid for her help with the botanical information. We are grateful to Sara Van der Heyden for her suggestions. We also thank two anonymous referees for their important remarks. This research was supported by the Institute for the encouragement of Scientific Research and Innovation of Brussels (ISRIB) and the Veterinary and Agrochemical Research Centre (VAR).

Background: Chest pain is a common complaint in primary care, with coronary heart disease (CHD) being the most concerning of many potential causes. Systematic reviews on the sensitivity and specificity of symptoms and signs summarize the evidence about which of them are most useful in making a diagnosis. Previous meta-analyses are dominated by studies of patients referred to specialists. Moreover, as the analysis is typically based on study-level data, the statistical analyses in these reviews are limited while meta-analyses based on individual patient data can provide additional information. Our patient-level meta-analysis has three unique aims. First, we strive to determine the diagnostic accuracy of symptoms and signs for myocardial ischemia in primary care. Second, we investigate associations between study-or patient-level characteristics and measures of diagnostic accuracy. Third, we aim to validate existing clinical prediction rules for diagnosing myocardial ischemia in primary care. This article describes the methods of our study and six prospective studies of primary care patients with chest pain. Later articles will describe the main results. less thanbrgreater than less thanbrgreater thanMethods/Design: We will conduct a systematic review and IPD meta-analysis of studies evaluating the diagnostic accuracy of symptoms and signs for diagnosing coronary heart disease in primary care. We will perform bivariate analyses to determine the sensitivity, specificity and likelihood ratios of individual symptoms and signs and multivariate analyses to explore the diagnostic value of an optimal combination of all symptoms and signs based on all data of all studies. We will validate existing clinical prediction rules from each of the included studies by calculating measures of diagnostic accuracy separately by study. less thanbrgreater than less thanbrgreater thanDiscussion: Our study will face several methodological challenges. First, the number of studies will be limited. Second, the investigators of original studies defined some outcomes and predictors differently. Third, the studies did not collect the same standard clinical data set. Fourth, missing data, varying from partly missing to fully missing, will have to be dealt with. Despite these limitations, we aim to summarize the available evidence regarding the diagnostic accuracy of symptoms and signs for diagnosing CHD in patients presenting with chest pain in primary care. less thanbrgreater than less thanbrgreater thanReview registration: Centre for Reviews and Dissemination (University of York): CRD42011001170 Funding Agencies|Federal Ministry of Education and Research (BMBF)|FKZ 01GK0920

Missing data often occur in regression analysis. Imputation, weighting, direct likelihood, and Bayesian inference are typical approaches for missing data analysis. The focus is on missing covariate data, a common complication in the analysis of sample surveys and clinical trials. A key quantity when applying weighted estimators is the mean score contribution of observations with missing covariate(s), conditional on the observed covariates. This mean score can be estimated parametrically or nonparametrically by its empirical average using the complete case data in case of repeated values of the observed covariates, typically assuming categorical or categorized covariates. A nonparametric kernel based estimator is proposed for this mean score, allowing the full exploitation of the continuous nature of the covariates. The performance of the kernel based method is compared to that of a complete case analysis, inverse probability weighting, doubly robust estimators and multiple imputation, through simulations. (C) 2011 Elsevier B.V. All rights reserved. This work has been funded by the IAP research network nr P6/03 of the Belgian Government (Belgian Science Policy). The computational resources and services used in this work were provided by the VSC (Flemish Supercomputer Center), funded by the Research Foundation - Flanders (FWO) and the Flemish Government – department EWI.

In the previous chapter we have shown how the basic reproduction number can be estimated using serological data and an assumed social contact pattern in the population (either discrete or continuous). Such an approach does not take into account the underlying contact mixing pattern in the population but assumes that the configuration of contact patterns is known and estimated the transmission parameters under a specific configuration. In this chapter, we present an alternative approach in which transmission parameters can be estimated from serological data augmented with social contact data when dealing with airborne infections.

As discussed in previous chapters and illustrated by different methods, prevalence and force of infection (FOI) (and, as we will show in Chaps. 14 and 15, indirectly other parameters such as the basic reproduction number) are estimated from so-called seroprevalence data. Seroprevalence data are obtained by dichotomizing or trichotomizing disease-specific antibody levels using one or two threshold values, often provided by the test manufacturer. In particular, individuals are diagnosed as infected (left-censored age at infection, its value somewhere before the age at the time of the test) if their test result exceeds a certain threshold value τ s u and as being susceptible (right-censored age at infection) if their result falls below a possibly different threshold τ s l ≤τ s u . In case two different threshold values are used (τ s l

In this chapter, we introduce the basic SIR model and its properties. In this first section, we introduce the SIR model and review its dynamic properties assuming homogeneous mixing. In Sect. 3.2 the SIR model in endemic equilibrium is discussed whereas the link to serological data is made in Sect. 3.3. A short description of additional compartments often added to the SIR model is given in Sect. 3.4. The extension of the SIR model for populations consisting of subpopulations (for instance by age) is discussed in Sect.3.5. We end this chapter with a discussion in Sect.3.6.

In Chaps. 6–8, (flexible) parametric, nonlinear, nonparametric, and semi-parametric models to estimate the force of infection from seroprevalence data have been introduced. All these methods rely on the steady-state assumption of which the plausibility is untestable in case of one cross-sectional sample (Keiding 1991; Nagelkerke et al. 1999).

The dynamics, prevention, and control of infectious diseases can be simulated by means of mathematical models. Many options have been described to formulate such models (for an overview see e.g. Capasso 2008). In general, a set of partial differential equations (PDEs) can be used to describe the mathematics of the model. Consider for instance the basic SIR model (Sect. 3.1.1)