Geert Molenberghs

Universiteit Hasselt, Hasselt, Flanders, Belgium

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Publications (413)628.89 Total impact

  • Thomas Neyens, Christel Faes, Geert Molenberghs
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    ABSTRACT: Modern disease mapping commonly uses hierarchical Bayesian methods to model overdispersion and spatial correlation. Classical random-effects based solutions include the Poisson-gamma model, which uses the conjugacy between the Poisson and gamma distributions, but which does not model spatial correlation, on the one hand, and the more advanced CAR model, which also introduces a spatial autocorrelation term but without a closed-form posterior distribution on the other. In this paper, a combined model is proposed: an alternative convolution model accounting for both overdispersion and spatial correlation in the data by combining the Poisson-gamma model with a spatially-structured normal CAR random effect. The Limburg Cancer Registry data on kidney and prostate cancer in Limburg were used to compare the conventional and new models. A simulation study confirmed results and interpretations coming from the real datasets. Relative risk maps showed that the combined model provides an intermediate between the non-patterned negative binomial and the sometimes oversmoothed CAR convolution model.
    Spatial and spatio-temporal epidemiology. 09/2012; 3(3):185-94.
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    ABSTRACT: Introduction Reflex responses of cardiac cycle time intervals (CCTI) can be measured by echocardiography, and are reported to differ between uneventful pregnancy (UP) and pre-eclampsia (PE). It is unknown whether impedance cardiography (ICG) is a useful method to measure CCTI during pregnancy. Objectives ICG measurements of CCTI before and after orthostatic challenge are evaluated in UP and in the clinical phase of PE. Methods Examinations were performed twice in 16 UP (30–36 weeks), and once in 30 early PE (EPE, <34 weeks) and in 32 late PE (LPE, ⩾34 weeks). A 3rd generation ICG device using a 4 electrode arrangement (NICCOMO, Medis, Germany) was used to measure CCTI in supine position and after moving to upright position. The pre-ejection period (PEP) is the time-interval between ventricular depolarisation and start of aortic flow. The left ventricular ejection time (LVET) is the time-interval between opening and closing of the aortic valve. Diastolic time (DT) is heart period duration – (PEP+LVET). Orthostatic-induced changes from supine to upright position (cardiac reflex response or CRR) were evaluated using One-sample Wilcoxon Signed Rank Tests. All CRRs in EPE and LPE were compared to UP using Mann-Whitney U tests. Data are represented as medians (interquartile ranges). Results Maternal age was comparable between all groups [29 (26–32) years; p ⩾ 0.47]. Gestational age was comparable between both early [31 (28–32) vs 31 (27–33) weeks] and late [37 (36–39) vs 38 (36–39) weeks] third trimester UP and PE [p ⩾ 0.38]. Pre-gestational BMI was higher in EPE compared to UP [26 (24–32) vs 23 (21–24); p < 0.01]. This was not true for LPE [25 (23–28); p = 0.06]. Birth weight percentiles were lower in both EPE and LPE compared to UP [UP: 44 (38–78), EPE: 18 (5–28), LPE: 31 (18–59); p < 0.05], and also lower in EPE compared to LPE [p = 0.03]. CRRs within each group are shown in Table 1. The CRRs of PEP were significantly different between UP and both EPE and LPE [p ⩽ 0.01], due to orthostatic-induced increase in PE but not in UP . Conclusion Our study confirms that orthostasis does not change PEP in UP but induces a significant increase of PEP in PE. The increased reflex-induced duration of isovolumetric contraction time can be explained by a decreased left ventricular performance in the clinical phase of PE as compared to UP. ICG turns out to be a straightforward and useful method to evaluate these hemodynamic features.
    Pregnancy Hypertension: An International Journal of Women's Cardiovascular Health. 07/2012; 2(3):230.
  • Samuel Iddi, Geert Molenberghs
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    ABSTRACT: Overdispersion and correlation are two features often encountered when modeling non-Gaussian dependent data, usually as a function of known covariates. Methods that ignore the presence of these phenomena are often in jeopardy of leading to biased assessment of covariate effects. The beta-binomial and negative binomial models are well known in dealing with overdispersed data for binary and count data, respectively. Similarly, generalized estimating equations (GEE) and the generalized linear mixed models (GLMM) are popular choices when analyzing correlated data. A so-called combined model simultaneously acknowledges the presence of dependency and overdispersion by way of two separate sets of random effects. A marginally specified logistic-normal model for longitudinal binary data which combines the strength of the marginal and hierarchical models has been previously proposed. These two are brought together to produce a marginalized longitudinal model which brings together the comfort of marginally meaningful parameters and the ease of allowing for overdispersion and correlation. Apart from model formulation, estimation methods are discussed. The proposed model is applied to two clinical studies and compared to the existing approach. It turns out that by explicitly allowing for overdispersion random effect, the model significantly improves.
    Computational Statistics & Data Analysis. 06/2012; 56(6).
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    ABSTRACT: We report the discovery of low-amplitude gravity-mode oscillations in the massive binary star V380 Cyg, from 180 d of Kepler custom-aperture space photometry and 5 months of high-resolution high signal-to-noise spectroscopy. The new data are of unprecedented quality and allowed to improve the orbital and fundamental parameters for this binary. The orbital solution was subtracted from the photometric data and led to the detection of periodic intrinsic variability with frequencies of which some are multiples of the orbital frequency and others are not. Spectral disentangling allowed the detection of line-profile variability in the primary. With our discovery of intrinsic variability interpreted as gravity mode oscillations, V380 Cyg becomes an important laboratory for future seismic tuning of the near-core physics in massive B-type stars.
    Monthly Notices of the Royal Astronomical Society 05/2012; · 5.52 Impact Factor
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    ABSTRACT: Improving proof-of-concept (PoC) studies is a primary lever for improving drug development. Since drug development is often done by institutions that work on multiple drugs simultaneously, the present work focused on optimum choices for rates of false positive (α) and false negative (β) results across a portfolio of PoC studies. Simple examples and a newly derived equation provided conceptual understanding of basic principles regarding optimum choices of α and β in PoC trials. In examples that incorporated realistic development costs and constraints, the levels of α and β that maximized the number of approved drugs and portfolio value varied by scenario. Optimum choices were sensitive to the probability the drug was effective and to the proportion of total investment cost prior to establishing PoC. Results of the present investigation agree with previous research in that it is important to assess optimum levels of α and β. However, the present work also highlighted the need to consider cost structure using realistic input parameters relevant to the question of interest.
    Journal of Biopharmaceutical Statistics 05/2012; 22(3):596-607. · 0.73 Impact Factor
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    ABSTRACT: Longitudinal experiments often involve multiple outcomes measured repeatedly within a set of study participants. While many questions can be answered by modeling the various outcomes separately, some questions can only be answered in a joint analysis of all of them. In this article, we will present a review of the many approaches proposed in the statistical literature. Four main model families will be presented, discussed and compared. Focus will be on presenting advantages and disadvantages of the different models rather than on the mathematical or computational details.
    Statistical Methods in Medical Research 04/2012; · 2.36 Impact Factor
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    ABSTRACT: The vast majority of settings for which frequentist statistical properties are derived assume a fixed, a priori known sample size. Familiar properties then follow, such as, for example, the consistency, asymptotic normality, and efficiency of the sample average for the mean parameter, under a wide range of conditions. We are concerned here with the alternative situation in which the sample size is itself a random variable which may depend on the data being collected. Further, the rule governing this may be deterministic or probabilistic. There are many important practical examples of such settings, including missing data, sequential trials, and informative cluster size. It is well known that special issues can arise when evaluating the properties of statistical procedures under such sampling schemes, and much has been written about specific areas (Grambsch P. Sequential sampling based on the observed Fisher information to guarantee the accuracy of the maximum likelihood estimator. Ann Stat 1983; 11: 68-77; Barndorff-Nielsen O and Cox DR. The effect of sampling rules on likelihood statistics. Int Stat Rev 1984; 52: 309-326). Our aim is to place these various related examples into a single framework derived from the joint modeling of the outcomes and sampling process and so derive generic results that in turn provide insight, and in some cases practical consequences, for different settings. It is shown that, even in the simplest case of estimating a mean, some of the results appear counterintuitive. In many examples, the sample average may exhibit small sample bias and, even when it is unbiased, may not be optimal. Indeed, there may be no minimum variance unbiased estimator for the mean. Such results follow directly from key attributes such as non-ancillarity of the sample size and incompleteness of the minimal sufficient statistic of the sample size and sample sum. Although our results have direct and obvious implications for estimation following group sequential trials, there are also ramifications for a range of other settings, such as random cluster sizes, censored time-to-event data, and the joint modeling of longitudinal and time-to-event data. Here, we use the simplest group sequential setting to develop and explicate the main results. Some implications for random sample sizes and missing data are also considered. Consequences for other related settings will be considered elsewhere.
    Statistical Methods in Medical Research 04/2012; · 2.36 Impact Factor
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    ABSTRACT: BACKGROUND: In medical and biomedical areas, binary and binomial outcomes are very common. Such data are often collected longitudinally from a given subject repeatedly overtime, which result in clustering of the observations within subjects, leading to correlation, on the one hand. The repeated binary outcomes from a given subject, on the other hand, constitute a binomial outcome, where the prescribed mean-variance relationship is often violated, leading to the so-called overdispersion. METHODS: Two longitudinal binary data sets, collected in south western Ethiopia: the Jimma infant growth study, where the child's early growth is studied, and the Jimma longitudinal family survey of youth where the adolescent's school attendance is studied over time, are considered. A new model which combines both overdispersion, and correlation simultaneously, also known as the combined model is applied. In addition, the commonly used methods for binary and binomial data, such as the simple logistic, which accounts neither for the overdispersion nor the correlation, the beta-binomial model, and the logistic-normal model, which accommodate only for the overdispersion, and correlation, respectively, are also considered for comparison purpose. As an alternative estimation technique, a Bayesian implementation of the combined model is also presented. RESULTS: The combined model results in model improvement in fit, and hence the preferred one, based on likelihood comparison, and DIC criterion. Further, the two estimation approaches result in fairly similar parameter estimates and inferences in both of our case studies. Early initiation of breastfeeding has a protective effect against the risk of overweight in late infancy (p = 0.001), while proportion of overweight seems to be invariant among males and females overtime (p = 0.66). Gender is significantly associated with school attendance, where girls have a lower rate of attendance (p = 0.001) as compared to boys. CONCLUSION: We applied a flexible modeling framework to analyze binary and binomial longitudinal data. Instead of accounting for overdispersion, and correlation separately, both can be accommodated simultaneously, by allowing two separate sets of the beta, and the normal random effects at once.
    Archives of public health = Archives belges de sante publique. 04/2012; 70(1):7.
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    ABSTRACT: Age is associated with immune dysregulation, which results in an increased infection rate and reduced effectiveness of vaccination. We assessed whether an intervention with Lactobacillus casei Shirota (LcS) in elderly nursing home residents reduced their susceptibility to respiratory symptoms and improved their immune response to influenza vaccination. Between October 2007 and April 2008, a randomized, double-blind, placebo-controlled trial was conducted in 737 healthy people aged ≥ 65 y in 53 nursing homes in Antwerp, Belgium. Volunteers were randomly assigned to receive a probiotic (n = 375; 2 bottles of fermented milk that contained ≥ 6.5 × 10(9) live LcS/bottle) or a placebo (n = 362; similar drink with no bacteria) for 176 d. After 21 d, all subjects received an influenza vaccination. Primary outcome parameters were the number of days with respiratory symptoms, the probability of respiratory symptoms, and antiinfluenza antibody titer by hemagglutination inhibition after vaccination. Univariate and multivariate modeling showed no effect of the probiotic on clinical outcome parameters. Generalized linear mixed modeling showed no effect of the probiotic itself on the probability of respiratory symptoms [OR of probiotic: 0.8715; 95% CI: 0.6168, 1.2887). No significant difference regarding the influenza-vaccination immune response was shown. The results of this study show that daily consumption of a fermented milk drink that contains LcS has no statistically or clinically significant effect on the protection against respiratory symptoms. This trial was registered at as NCT00849277.
    American Journal of Clinical Nutrition 03/2012; 95(5):1165-71. · 6.50 Impact Factor
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    ABSTRACT: Uncomplicated pregnancies (n = 16) were evaluated longitudinally and compared to early- (n = 12) and late-onset (n = 14) preeclampsia patients, assessed once at diagnosis. Pulse transit time (PTT), equivalent to pulse wave velocity, was measured as the time interval between corresponding characteristics of electrocardiography and Doppler waves, corrected for heart rate, at the level of renal interlobar veins, hepatic veins, and arcuate branches of uterine arteries. Impedance cardiography was used to measure PTT at the level of the thoracic aorta. In normal pregnancy, all PTT increased gradually (P ≤ .01). Pulse transit time was shorter in late-onset preeclampsia (P < .05) and also in early-onset preeclampsia, with exception for hepatic veins and thoracic aorta (P > .05). Our results indicate that PTT is an easy and highly accessible measure for vascular reactivity at both arterial and venous sites of the circulation. Our observations correlate well with known gestational cardiovascular adaptation mechanisms. This suggests that PTT could be used as a new parameter in the evaluation and prediction of preeclampsia.
    Reproductive sciences (Thousand Oaks, Calif.) 02/2012; 19(4):431-6. · 2.31 Impact Factor
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    Elasma Milanzi, Ariel Alonso, Geert Molenberghs
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    ABSTRACT: Poisson data frequently exhibit overdispersion; and, for univariate models, many options exist to circumvent this problem. Nonetheless, in complex scenarios, for example, in longitudinal studies, accounting for overdispersion is a more challenging task. Recently, Molenberghs, presented a model that accounts for overdispersion by combining two sets of random effects. However, introducing a new set of random effects implies additional distributional assumptions for intrinsically unobservable variables, which has not been considered before. Using the combined model as a framework, we explored the impact of ignoring overdispersion in complex longitudinal settings via simulations. Furthermore, we evaluated the effect of misspecifying the random-effects distribution on both the combined model and the classical Poisson hierarchical model. Our results indicate that even though inferences may be affected by ignored overdispersion, the combined model is a promising tool in this scenario.
    Statistics in Medicine 02/2012; 31(14):1475-82. · 2.04 Impact Factor
  • Statistics in Biopharmaceutical Research 01/2012; 4(2):205-215. · 0.51 Impact Factor
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    ABSTRACT: A mixed effects least squares support vector machine (LS-SVM) classifier is introduced to extend the standard LS-SVM classifier for handling longitudinal data. The mixed effects LS-SVM model contains a random intercept and allows to classify highly unbalanced data, in the sense that there is an unequal number of observations for each case at non-fixed time points. The methodology consists of a regression modeling and a classification step based on the obtained regression estimates. Regression and classification of new cases are performed in a straightforward manner by solving a linear system. It is demonstrated that the methodology can be generalized to deal with multi-class problems and can be extended to incorporate multiple random effects. The technique is illustrated on simulated data sets and real-life problems concerning human growth.
    Computational Statistics & Data Analysis. 01/2012; 56:611-628.
  • An Creemers, Marc Aerts, Niel Hens, Geert Molenberghs
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    ABSTRACT: 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.
    Computational Statistics & Data Analysis. 01/2012; 56:100-113.
  • Samuel Iddi, Geert Molenberghs
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    ABSTRACT: The shared-parameter model and its so-called hierarchical or random-effects extension are widely used joint modeling approaches for a combination of longitudinal continuous, binary, count, missing, and survival outcomes that naturally occurs in many clinical and other studies. A random effect is introduced and shared or allowed to differ between two or more repeated measures or longitudinal outcomes, thereby acting as a vehicle to capture association between the outcomes in these joint models. It is generally known that parameter estimates in a linear mixed model (LMM) for continuous repeated measures or longitudinal outcomes allow for a marginal interpretation, even though a hierarchical formulation is employed. This is not the case for the generalized linear mixed model (GLMM), that is, for non-Gaussian outcomes. The aforementioned joint models formulated for continuous and binary or two longitudinal binomial outcomes, using the LMM and GLMM, will naturally have marginal interpretation for parameters associated with the continuous outcome but a subject-specific interpretation for the fixed effects parameters relating covariates to binary outcomes. To derive marginally meaningful parameters for the binary models in a joint model, we adopt the marginal multilevel model (MMM) due to Heagerty [13] and Heagerty and Zeger [14] and formulate a joint MMM for two longitudinal responses. This enables to (1) capture association between the two responses and (2) obtain parameter estimates that have a population-averaged interpretation for both outcomes. The model is applied to two sets of data. The results are compared with those obtained from the existing approaches such as generalized estimating equations, GLMM, and the model of Heagerty [13]. Estimates were found to be very close to those from single analysis per outcome but the joint model yields higher precision and allows for quantifying the association between outcomes. Parameters were estimated using maximum likelihood. The model is easy to fit using available tools such as the SAS NLMIXED procedure.
    Journal of Applied Statistics 01/2012; · 0.45 Impact Factor
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    ABSTRACT: To describe total outpatient systemic antibiotic use in Europe from 1997 to 2009 and to analyse statistically trends of total use and composition of use over time. For the period 1997-2009, data on outpatient use of systemic antibiotics aggregated at the level of the active substance were collected and expressed in defined daily doses (WHO, version 2011) and packages per 1000 inhabitants per day (DID and PID, respectively). Outpatient antibiotic (ATC J01) use in DID in the 33 European countries able to deliver valid data was analysed using longitudinal and compositional data analyses. Total outpatient antibiotic use in 2009 varied by a factor of 3.8 between the countries with the highest (38.6 DID in Greece) and lowest (10.2 DID in Romania) use. For Europe, a significant increase was found in total outpatient antibiotic use, as well as a significant seasonal variation, which decreased over time from 1997 to 2009. Relative use of penicillins and quinolones significantly increased over time with respect to sulphonamides and trimethoprim, and relative use of quinolones increased with respect to macrolide/lincosamide/streptogramin as well. More detailed analyses of these major antibiotic subgroups will be described in separate papers. Outpatient antibiotic use in Europe measured as DID has increased since 1997, whereas seasonal variation has decreased over time. European Surveillance of Antimicrobial Consumption (ESAC) data on outpatient antibiotic use in Europe enable countries to audit their antibiotic use. Complemented by longitudinal and compositional data analyses, these data provide a tool for assessing public health strategies aimed at reducing antibiotic resistance and optimizing antibiotic prescribing.
    Journal of Antimicrobial Chemotherapy 12/2011; 66 Suppl 6:vi3-12. · 5.34 Impact Factor
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    ABSTRACT: Data on more than a decade of outpatient macrolide, lincosamide and streptogramin (MLS) use in Europe were collected from 33 countries within the European Surveillance of Antimicrobial Consumption (ESAC) project, funded by the European Centre for Disease Prevention and Control (ECDC), using the WHO Anatomical Therapeutic Chemical (ATC)/defined daily dose (DDD) methodology. For the period 1997-2009, data on outpatient use of systemic MLS aggregated at the level of the active substance were collected and expressed in DDD (WHO, version 2011) per 1000 inhabitants per day (DID). Using a classification based on mean plasma elimination half-life, macrolide use was analysed for trends over time, seasonal variation and composition. Total outpatient MLS use in 2009 varied by a factor of 18 between the countries with highest (11.5 DID in Greece) and lowest (0.6 DID in Sweden) use. MLS use showed high seasonal variation. Short-, intermediate- and long-acting macrolides were the most commonly used agents in 2, 25 and 5 countries, respectively (mainly erythromycin, clarithromycin and azithromycin, respectively). In Sweden, mainly lincosamides (clindamycin) were used. Lincosamide use was observed in all countries, while substantial use of a streptogramin was only seen in France (pristinamycin). For Europe, a significant increase in outpatient MLS use was found, as well as a significant seasonal variation, which increased over time from 1997 to 2009. Relative use of long-acting macrolides and lincosamides significantly increased over time with respect to intermediate-acting macrolides, and relative use of the latter increased with respect to short-acting macrolides. The observed differences between European countries in the levels of MLS use and the extreme seasonal variations in their use suggest that this subgroup of antibiotics is still prescribed inappropriately in many countries.
    Journal of Antimicrobial Chemotherapy 12/2011; 66 Suppl 6:vi37-45. · 5.34 Impact Factor
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    ABSTRACT: Resistance to antibiotics is a major public health problem and antibiotic use is being increasingly recognized as the main selective pressure driving this resistance. Yearly and quarterly data on outpatient antibiotic use were collected by the European Surveillance of Antimicrobial Consumption (ESAC) project for the period 1997-2009 from 33 and 27 European countries, respectively, and expressed in defined daily doses per 1000 inhabitants per day. Since repeated measures were taken for the countries, correlation has to be taken into account when analysing the data. This paper illustrates the application of mixed-effects models to the study of country-specific outpatient antibiotic use in Europe. Mixed models are useful in a wide variety of disciplines in the biomedical, physical and social sciences. In this application for outpatient antibiotic use, the linear mixed model is extended to a non-linear mixed model, allowing analysis of seasonal variation on top of a global trend, with country-specific effects for global mean use and amplitude, and trends over time in use and in amplitude.
    Journal of Antimicrobial Chemotherapy 12/2011; 66 Suppl 6:vi79-87. · 5.34 Impact Factor
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    ABSTRACT: In this tutorial, statistical methods for studying outpatient use of antibiotics in Europe are described, using data provided by IMS Health. The methods are applied to two related research questions, namely the assessment of changes in the relative volume of use of different antibiotic subclasses over time and changes in the absolute volume of antibiotic use.
    Journal of Antimicrobial Chemotherapy 12/2011; 66 Suppl 6:vi89-94. · 5.34 Impact Factor
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    ABSTRACT: Data on 13 years of outpatient cephalosporin use were collected from 33 European countries within the European Surveillance of Antimicrobial Consumption (ESAC) project, funded by the European Centre for Disease Prevention and Control (ECDC), and analysed in detail. For the period 1997-2009, data on outpatient use of systemic cephalosporins aggregated at the level of the active substance were collected using the Anatomical Therapeutic Chemical (ATC)/defined daily dose (DDD) method (WHO, version 2011) and expressed in DDD per 1000 inhabitants per day (DID). For detailed analysis of trends over time, seasonal variation and composition of outpatient cephalosporin use in 33 European countries, we distinguished between first-generation (J01DB), second-generation (J01DC), third-generation (J01DD) and fourth-generation (J01DE) cephalosporins. Total outpatient cephalosporin use in 2009 varied from 8.7 DID in Greece to 0.03 DID in Denmark. In general, use was higher in Southern and Eastern European countries than in Northern European countries. Total outpatient cephalosporin use increased over time by 0.364 (SD 0.473) DID between 1997 and 2009. Cephalosporin use increased for half of the countries. Low-consuming Northern European countries and the UK further decreased their use. Second-generation cephalosporins increased by >20% in seven countries (mainly cefuroxime), coinciding with a decrease in first-generation cephalosporins. Substantial parenteral use of third-generation substances (mainly ceftriaxone) was observed in France, Italy and the Russian Federation. Since 1997, the use of the older (narrow-spectrum) cephalosporins decreased in favour of the newer (i.e. broad-spectrum) cephalosporins in most countries. Extreme variations between European countries in cephalosporin use over time suggest that they are to a large extent inappropriately used.
    Journal of Antimicrobial Chemotherapy 12/2011; 66 Suppl 6:vi25-35. · 5.34 Impact Factor

Publication Stats

7k Citations
628.89 Total Impact Points


  • 2006–2014
    • Universiteit Hasselt
      • • Interuniversity Institute for Biostatistics and statistical Bioinformatics (I-BioStat)
      • • Faculty of Medicine and Life Sciences
      Hasselt, Flanders, Belgium
  • 1994–2014
    • University of Leuven
      Louvain, Flanders, Belgium
  • 2013
    • Vertex Pharmaceuticals
      Cambridge, Massachusetts, United States
  • 2011–2013
    • University of KwaZulu-Natal
      Port Natal, KwaZulu-Natal, South Africa
    • Case Western Reserve University
      • Department of Epidemiology and Biostatistics
      Cleveland, OH, United States
  • 2008–2013
    • Ziekenhuis Oost Limburg
      • Department of Radiology
      Genck, Flanders, Belgium
  • 1997–2011
    • University of Antwerp
      • Vaccine & infectious disease institute
      Antwerpen, VLG, Belgium
  • 2010
    • Duke-NUS Graduate Medical School Singapore
      Tumasik, Singapore
    • Hospital of the University of Pennsylvania
      • Department of Biostatistics and Epidemiology
      Philadelphia, Pennsylvania, United States
  • 2009
    • University of Florida
      • Department of Small Animal Clinical Sciences
      Gainesville, FL, United States
    • University of the Philippines Diliman
      Кесон-Сити, National Capital Region, Philippines
    • PMB
      Provence-Alpes-Côte d'Azur, France
    • National Institute Of Oncology And Radiobiology
      La Habana, Ciudad de La Habana, Cuba
    • Maastricht University
      • Department of Methodology and Statistics
      Maastricht, Provincie Limburg, Netherlands
    • Erasmus MC
      • Department of Bioinformatics
      Rotterdam, South Holland, Netherlands
  • 2003–2009
    • Transnationale Universiteit Limburg
      University Center, Virginia, United States
  • 2001–2009
    • London School of Hygiene and Tropical Medicine
      • Department of Medical Statistics
      London, ENG, United Kingdom
    • University of Michigan
      Ann Arbor, Michigan, United States
    • Utah State University
      • Department of Mathematics and Statistics
      Logan, OH, United States
  • 2004–2008
    • Johnson & Johnson
      New Brunswick, New Jersey, United States
    • Clinical Research Ireland
      Dublin, Leinster, Ireland
    • McLean Hospital
      Cambridge, Massachusetts, United States
  • 2007
    • Ghent University
      • Department of Applied Mathematics and Computer Science
      Gent, VLG, Belgium
  • 2004–2006
    • Eli Lilly
      • Lilly Research Laboratories
      Indianapolis, Indiana, United States
  • 2002
    • Texas A&M University
      • Department of Statistics
      College Station, TX, United States
    • Università Telematica "E-Campus"
      Campobasso, Molise, Italy
  • 1999
    • University of Kent
      Cantorbery, England, United Kingdom
  • 1998–1999
    • Harvard University
      • Department of Biostatistics
      Boston, MA, United States
    • International Drug Development Institute
      Walloon Region, Belgium