Paul H C Eilers

Max Planck Institute for Demographic Research, Rostock, Mecklenburg-Vorpommern, Germany

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Publications (214)

  • [Show abstract] [Hide abstract] ABSTRACT: An important aim of the analysis of agricultural field trials is to obtain good predictions for genotypic performance, by correcting for spatial effects. In practice these corrections turn out to be complicated, since there can be different types of spatial effects; those due to management interventions applied to the field plots and those due to various kinds of erratic spatial trends. This paper presents models for field trials in which the random spatial component consists of tensor product Penalized splines (P-splines). A special ANOVA-type reformulation leads to five smooth additive spatial components, which form the basis of a mixed model with five unknown variance components. On top of this spatial field, effects of genotypes, blocks, replicates, and/or other sources of spatial variation are described by a mixed model in a standard way. We show the relation between several definitions of heritability and the effective dimension or the effective degrees of freedom associated to the genetic component. The approach is illustrated with large-scale field trial experiments. An R-package is provided.
    Article · Jul 2016
  • Diego Ayma · María Durbán · Dae-Jin Lee · Paul H.C. Eilers
    [Show abstract] [Hide abstract] ABSTRACT: Mortality data provide valuable information for the study of the spatial distribution of mortality risk, in disciplines such as spatial epidemiology and public health. However, they are frequently available in an aggregated form over irregular geographical units, hindering the visualization of the underlying mortality risk. Also, it can be of interest to obtain mortality risk estimates on a finer spatial resolution, such that they can be linked to potential risk factors that are usually measured in a different spatial resolution. In this paper, we propose the use of the penalized composite link model and its mixed model representation. This model considers the nature of mortality rates by incorporating the population size at the finest resolution, and allows the creation of mortality maps at a finer scale, thus reducing the visual bias resulting from the spatial aggregation within original units. We also extend the model by considering individual random effects at the aggregated scale, in order to take into account the overdispersion. We illustrate our novel proposal using two datasets: female deaths by lung cancer in Indiana, USA, and male lip cancer incidence in Scotland counties. We also compare the performance of our proposal with the area-to-point Poisson kriging approach.
    Article · Jul 2016 · Spatial Statistics
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    Full-text Article · May 2016 · Scientific Reports
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    [Show abstract] [Hide abstract] ABSTRACT: In wide-field super-resolution microscopy, investigating the nanoscale structure of cellular processes, and resolving fast dynamics and morphological changes in cells requires algorithms capable of working with a high-density of emissive fluorophores. Current deconvolution algorithms estimate fluorophore density by using representations of the signal that promote sparsity of the super-resolution images via an L1-norm penalty. This penalty imposes a restriction on the sum of absolute values of the estimates of emitter brightness. By implementing an L0-norm penalty – on the number of fluorophores rather than on their overall brightness – we present a penalized regression approach that can work at high-density and allows fast super-resolution imaging. We validated our approach on simulated images with densities up to 15 emitters per μm-2 and investigated total internal reflection fluorescence (TIRF) data of mitochondria in a HEK293-T cell labeled with DAKAP-Dronpa. We demonstrated super-resolution imaging of the dynamics with a resolution down to 55 nm and a 0.5 s time sampling.
    Full-text Article · Mar 2016 · Scientific Reports
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    [Show abstract] [Hide abstract] ABSTRACT: We investigated the rainfall patterns and associated fluctuations of wild large herbivore species in the Great Limpopo Transfrontier Conservation Area (GLTFCA), southern Africa. The study objectives were to: (i) establish the synchrony in rainfall and drought occurrence patterns in Gonarezhou National Park, Zimbabwe, and four adjacent areas, and (ii) determine the responses of different large herbivore species’ populations to droughts. We used annual rainfall data collected from the five sites within the GLTFCA and large herbivore population data collected from multispecies aerial surveys in Gonarezhou and Kruger National Park, South Africa. Our results showed that between 1970 and 2009, Gonarezhou recorded three wet years (1977, 1978 and 2000) and six drought years (1973, 1983, 1989, 1992, 1994 and 2005). However, there were some variations in the drought occurrences between Gonarezhou and the four adjacent areas indicating a weak synchrony in rainfall patterns. Furthermore, seven large herbivore species showed dips in their populations associated with the 1992 severe drought, with most of the species’ populations recovering thereafter. Our study suggests that rainfall does have a strong influence on large herbivore population dynamics especially in really dry years in African savanna ecosystems. Our findings underscore the need for further detailed studies on bottom-up processes influencing large herbivore population trends in savanna ecosystems with high rainfall variability.
    Full-text Article · Jan 2016 · Tropical Ecology
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    [Show abstract] [Hide abstract] ABSTRACT: Deleterious effects of prenatal tobacco smoking on fetal growth and newborn weight are well-established. One of the proposed mechanisms underlying this relationship is alterations in epigenetic programming. We selected 506 newborns from a population-based prospective birth cohort in the Netherlands. Prenatal parental tobacco smoking was assessed using self-reporting questionnaires. Information on birth outcomes was obtained from medical records. The deoxyribonucleic acid (DNA) methylation of the growth genes IGF2DMR and H19 was measured in newborn umbilical cord white blood cells. Associations were assessed between parental tobacco smoking and DNA methylation using linear mixed models and adjusted for potential confounders. The DNA methylation levels of IGF2DMR and H19 in the non-smoking group were median (90 % range), 54.0 % (44.6-62.0), and 30.0 % (25.5-34.0), in the first trimester only smoking group 52.2 % (44.5-61.1) and 30.8 % (27.1-34.1), and in the continued smoking group 51.6 % (43.9-61.3) and 30.2 % (23.7-34.8), respectively. Continued prenatal maternal smoking was inversely associated with IGF2DMR methylation (β = -1.03, 95 % CI -1.76; -0.30) in a dose-dependent manner (P-trend = 0.030). This association seemed to be slightly more profound among newborn girls (β = -1.38, 95 % CI -2.63; -0.14) than boys (β = -0.72, 95 % CI -1.68; 0.24). H19 methylation was also inversely associated continued smoking <5 cigarettes/day (β = -0.96, 95 % CI -1.78; -0.14). Moreover, the association between maternal smoking and newborns small for gestational age seems to be partially explained by IGF2DMR methylation (β = -0.095, 95 % CI -0.249; -0.018). Among non-smoking mothers, paternal tobacco smoking was not associated with IGF2DMR or H19 methylation. Maternal smoking is inversely associated with IGF2DMR methylation in newborns, which can be one of the underlying mechanisms through which smoking affects fetal growth.
    Full-text Article · Dec 2015
  • [Show abstract] [Hide abstract] ABSTRACT: A fast and stable algorithm for estimating multidimensional adaptive P-spline models is presented. We call it as Separation of Overlapping Penalties (SOP) as it is an extension of the Separation of Anisotropic Penalties (SAP) algorithm. SAP was originally derived for the estimation of the smoothing parameters of a multidimensional tensor product P-spline model with anisotropic penalties.
    Conference Paper · Jul 2015
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    P. X. Hurtado-Lopez · B. B. Tessema · S. K. Schnabel · [...] · R. G. F. Visser
    [Show abstract] [Hide abstract] ABSTRACT: Understanding the genetic basis of plant development in potato requires a proper characterization of plant morphology over time. Parameters related to different aging stages can be used to describe the developmental processes. It is attractive to map these traits simultaneously in a QTL analysis; because the power to detect a QTL will often be improved and it will be easier to identify pleiotropic QTLs. We included complex, agronomic traits together with plant development parameters in a multi-trait QTL analysis. First, the results of our analysis led to coherent insight into the genetic architecture of complex traits in potato. Secondly, QTL for parameters related to plant development were identified. Thirdly, pleiotropic regions for various types of traits were identified. Emergence, number of main stems, number of tubers and yield were explained by 9, 5, 4 and 6 QTL, respectively. These traits were measured once during the growing season. The genetic control of flowering, senescence and plant height, which were measured at regular time intervals, was explained by 9, 10 and 12 QTL, respectively. Genetic relationships between aboveground and belowground traits in potato were observed in 14 pleiotropic QTL. Some of our results suggest the presence of QTL-by-Environment interactions. Therefore, additional studies comparing development under different photoperiods are required to investigate the plasticity of the crop.
    Full-text Article · Jul 2015 · Euphytica
  • Susan R Bryan · Paul H C Eilers · Emmanuel M E H Lesaffre · [...] · Koenraad A Vermeer
    [Show abstract] [Hide abstract] ABSTRACT: One of the difficulties in modeling visual field (VF) data is the sometimes large and correlated measurement errors in the point-wise sensitivity estimates. As these errors affect all locations of the same VF, we propose to model them as global visit effects (GVE). We evaluate this model and show the effect it has on progression estimation and prediction. Visual field series (24-2 Full Threshold; 15 biannual VFs per patient) of 125 patients with primary glaucoma were included in the analysis. The contribution of the GVE was evaluated by comparing the fitting and predictive ability of a conventional model, which does not contain GVE, to such a model that incorporates the GVE. Moreover, the GVE's effect on the estimated slopes was evaluated by determining the absolute difference between the slopes of the models. Finally, the magnitude of the GVE was compared with that of other measurement errors. The GVE model showed a significant improvement in both the model fit and predictive ability over the conventional model, especially when the number of VFs in a series is limited. The average absolute difference in slopes between the models was 0.13 dB/y. Lastly, the magnitude of the GVE was more than three times larger than the measureable factors combined. By incorporating the GVE in the longitudinal modeling of VF data, better estimates may be obtained of the rate of progression as well as of predicted future sensitivities.
    Article · Jul 2015 · Investigative ophthalmology & visual science
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    Silvia Rizzi · Jutta Gampe · Paul H C Eilers
    [Show abstract] [Hide abstract] ABSTRACT: Ungrouping binned data can be desirable for many reasons: Bins can be too coarse to allow for accurate analysis; comparisons can be hindered when different grouping approaches are used in different histograms; and the last interval is often wide and open-ended and, thus, covers a lot of information in the tail area. Age group-specific disease incidence rates and abridged life tables are examples of binned data. We propose a versatile method for ungrouping histograms that assumes that only the underlying distribution is smooth. Because of this modest assumption, the approach is suitable for most applications. The method is based on the composite link model, with a penalty added to ensure the smoothness of the target distribution. Estimates are obtained by maximizing a penalized likelihood. This maximization is performed efficiently by a version of the iteratively reweighted least-squares algorithm. Optimal values of the smoothing parameter are chosen by minimizing Akaike's Information Criterion. We demonstrate the performance of this method in a simulation study and provide several examples that illustrate the approach. Wide, open-ended intervals can be handled properly. The method can be extended to the estimation of rates when both the event counts and the exposures to risk are grouped. © The Author 2015. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health.
    Full-text Article · Jun 2015 · American journal of epidemiology
  • Conference Paper · Jun 2015
  • Ron Wehrens · Tom G Bloemberg · Paul H C Eilers
    [Show abstract] [Hide abstract] ABSTRACT: Alignment of peaks across samples is a difficult but unavoidable step in the data analysis for all analytical techniques containing a separation step like chromatography. Important application examples are the fields of metabolomics and proteomics. Parametric time warping (PTW) has already shown to be very useful in these fields because of the highly restricted form of the warping functions, avoiding overfitting. Here, we describe a new formulation of PTW, working on peak-picked features rather than on complete profiles. Not only does this allow for a much more smooth integration in existing pipelines, it also speeds up the (already among the fastest) algorithm by orders of magnitude. Using two publicly available data sets we show the potential of the new approach. The first set is a LC-DAD data set of grape samples, and the second an LC-MS data set of apple extracts. Parametric time warping of peak lists is implemented in the ptw package, version 1.9.1 and onwards, available from Github ( and CRAN ( The package also contains a vignette, providing more theoretical details and scripts to reproduce the results below. © The Author (2015). Published by Oxford University Press. All rights reserved. For Permissions, please email:
    Article · May 2015 · Bioinformatics
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    Abdelmajid Djennad · Robert Rigby · Dimitrios Stasinopoulos · [...] · Paul H C Eilers
    [Show abstract] [Hide abstract] ABSTRACT: In many settings of empirical interest, time variation in the distribution parameters is important for capturing the dynamic behaviour of time series processes. Although the fitting of heavy tail distributions has become easier due to computational advances, the joint and explicit modelling of time-varying conditional skewness and kurtosis is a challenging task. We propose a class of parameter-driven time series models referred to as the generalized structural time series (GEST) model. The GEST model extends Gaussian structural time series models by a) allowing the distribution of the dependent variable to come from any parametric distribution, including highly skewed and kurtotic distributions (and mixed distributions) and b) expanding the systematic part of parameter-driven time series models to allow the joint and explicit modelling of all the distribution parameters as structural terms and (smoothed) functions of independent variables. The paper makes an applied contribution in the development of a fast local estimation algorithm for the evaluation of a penalised likelihood function to update the distribution parameters over time without the need for evaluation of a high-dimensional integral based on simulation methods.
    Full-text Technical Report · Mar 2015
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    S. R. Bryan · P. H. C. Eilers · B. Li · [...] · E. M. E. H. Lesaffre
    [Show abstract] [Hide abstract] ABSTRACT: The Bayesian approach has become increasingly popular because it allows to model quite complex models via Markov chain Monte Carlo (MCMC) sampling. However, it is also recognized nowadays that MCMC sampling can become computationally prohibitive when a complex model needs to be fit to a large data set. To overcome this problem, we applied and extended a recently proposed two-stage approach to model a complex hierarchical data structure of glaucoma patients who participate in an ongoing Dutch study. Glaucoma is one of the leading causes of blindness in the world. In order to detect deterioration at an early stage, a model for predicting visual fields (VF) in time is needed. Hence, the true underlying VF progression can be determined, and treatment strategies can then be optimized to prevent further VF loss. Since we were unable to fit these data with the classical one-stage approach upon which the current popular Bayesian software is based, we made use of the two-stage Bayesian approach. The considered hierarchical longitudinal model involves estimating a large number of random effects and deals with censoring and high measurement variability. In addition, we extended the approach with tools for model evaluation
    Full-text Article · Feb 2015
  • [Show abstract] [Hide abstract] ABSTRACT: Most longitudinal growth curve models evaluate the evolution of each of the anthropometric measurements separately. When applied to a 'reference population', this exercise leads to univariate reference curves against which new individuals can be evaluated. However, growth should be evaluated in totality, that is, by evaluating all body characteristics jointly. Recently, Cole et al. suggested the Superimposition by Translation and Rotation (SITAR) model, which expresses individual growth curves by three subject-specific parameters indicating their deviation from a flexible overall growth curve. This model allows the characterization of normal growth in a flexible though compact manner. In this paper, we generalize the SITAR model in a Bayesian way to multiple dimensions. The multivariate SITAR model allows us to create multivariate reference regions, which is advantageous for prediction. The usefulness of the model is illustrated on longitudinal measurements of embryonic growth obtained in the first semester of pregnancy, collected in the ongoing Rotterdam Predict study. Further, we demonstrate how the model can be used to find determinants of embryonic growth. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.
    Article · Jan 2015 · Statistics in Medicine
  • Paul Eilers · Brian Marx · Maria Durban
    [Show abstract] [Hide abstract] ABSTRACT: P-splines first appeared in the limelight twenty years ago. Since then they have become popular in applications and in theoretical work. The combination of a rich B-spline basis and a simple difference penalty lends itself well to a variety of generalizations, because it is based on regression. In effect, P-splines allow the building of a "backbone" for the "mixing and matching" of a variety of additive smooth structure components, while inviting all sorts of extensions: varying-coefficient effects, signal (functional) regressors, two-dimensional surfaces, non-normal responses, quantile (expectile) modelling, among others. Strong connections with mixed models and Bayesian analysis have been established. We give an overview of many of the central developments during the first two decades of P-splines.
    Article · Jan 2015 · SORT (Statistics and Operations Research Transactions)
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    [Show abstract] [Hide abstract] ABSTRACT: The beneficial health effects of fruits and vegetables have been attributed to their polyphenol content. These compounds undergo many bioconversions in the body. Modeling polyphenol exposure of humans upon intake is a prerequisite for understanding the modulating effect of the food matrix and the colonic microbiome. This modeling is not a trivial task and requires a careful integration of measuring techniques, modeling methods and experimental design. Moreover, both at the population level as well as the individual level polyphenol exposure has to be quantified and assessed. We developed a strategy to quantify polyphenol exposure based on the concept of nutrikinetics in combination with population-based modeling. The key idea of the strategy is to derive nutrikinetic model parameters that summarize all information of the polyphenol exposure at both individual and population level. This is illustrated by a placebo-controlled crossover study in which an extract of wine/grapes and black tea solids was administered to twenty subjects. We show that urinary and plasma nutrikinetic time-response curves can be used for phenotyping the gut microbial bioconversion capacity of individuals. Each individual harbours an intrinsic microbiota composition converting similar polyphenols from both test products in the same manner and stable over time. We demonstrate that this is a novel approach for associating the production of two gut-mediated γ-valerolactones to specific gut phylotypes. The large inter-individual variation in nutrikinetics and γ-valerolactones production indicated that gut microbial metabolism is an essential factor in polyphenol exposure and related potential health benefits.
    Full-text Article · Dec 2014 · Metabolomics
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    [Show abstract] [Hide abstract] ABSTRACT: Maternal one-carbon (1-C) metabolism provides methylgroups for fetal development and programing by DNA methylation as one of the underlying epigenetic mechanisms. We aimed to investigate maternal 1-C biomarkers, folic acid supplement use, and MTHFR C677T genotype as determinants of 1-C metabolism in early pregnancy in association with newborn DNA methylation levels of fetal growth and neurodevelopment candidate genes. The participants were 463 mother-child pairs of Dutch national origin from a large population-based birth cohort in Rotterdam, The Netherlands. In early pregnancy (median 13.0 weeks, 90% range 10.4-17.1), we assessed the maternal folate and homocysteine blood concentrations, folic acid supplement use, and the MTHFR C677T genotype in mothers and newborns. In newborns, DNA methylation was measured in umbilical cord blood white blood cells at 11 regions of the seven genes: NR3C1, DRD4, 5-HTT, IGF2DMR, H19, KCNQ1OT1, and MTHFR. The associations between the 1-C determinants and DNA methylation were examined using linear mixed models. An association was observed between maternal folate deficiency and lower newborn DNA methylation, which attenuated after adjustment for potential confounders. The maternal MTHFR TT genotype was significantly associated with lower DNA methylation. However, maternal homocysteine and folate concentrations, folic acid supplement use, and the MTHFR genotype in the newborn were not associated with newborn DNA methylation. The maternal MTHFR C677T genotype, as a determinant of folate status and 1-C metabolism, is associated with variations in the epigenome of a selection of genes in newborns. Research on the implications of these variations in methylation on gene expression and health is recommended.
    Full-text Article · Dec 2014 · Reproduction (Cambridge, England)
  • [Show abstract] [Hide abstract] ABSTRACT: The superficial branch of the radial nerve (SBRN) is known for developing neuropathic pain syndromes after trauma. These pain syndromes can be hard to treat due to the involvement of other nerves in the forearm. When a nerve is cut, the Schwann cells, and also other cells in the distal segment of the transected nerve, produce the nerve growth factor (NGF) in the entire distal segment. If two nerves overlap anatomically, similar to the lateral antebrachial cutaneous nerve (LACN) and SBRN, the increase in secretion of NGF, which is mediated by the injured nerve, results in binding to the high-affinity NGF receptor, tyrosine kinase A (TrkA). This in turn leads to possible sprouting and morphological changes of uninjured fibers, which ultimately causes neuropathic pain. The aim of this study was to map the level of overlap between the SBRN and LACN. Twenty arms (five left and 15 right) were thoroughly dissected. Using a new analysis tool called CASAM (Computer Assisted Surgical Anatomy Mapping), the course of the SBRN and LACN could be compared visually. The distance between both nerves was measured at 5-mm increments, and the number of times they intersected was documented. In 81% of measurements, the distance between the nerves was >10 mm, and in 49% the distance was even <5 mm. In 95% of the dissected arms, the SBRN and LACN intersected. On average, they intersected 2.25 times. The close (anatomical) relationship between the LACN and the SBRN can be seen as a factor in the explanation of persistent neuropathic pain in patients with traumatic or iatrogenic lesion of the SBRN or the LACN. Copyright © 2014 British Association of Plastic, Reconstructive and Aesthetic Surgeons. Published by Elsevier Ltd. All rights reserved.
    Article · Oct 2014 · Journal of Plastic Reconstructive & Aesthetic Surgery
  • [Show abstract] [Hide abstract] ABSTRACT: STUDY QUESTION Is in vitro fertilization treatment with or without intracytoplasmatic sperm injection (IVF/ICSI) associated with changes in first and second trimester embryonic and fetal growth trajectories and birthweight in singleton pregnancies?
    Article · Oct 2014 · Human Reproduction

Publication Stats

7k Citations


  • 2015
    • Max Planck Institute for Demographic Research
      Rostock, Mecklenburg-Vorpommern, Germany
  • 2014-2015
    • Erasmus University Rotterdam
      Rotterdam, South Holland, Netherlands
  • 2009-2015
    • Erasmus MC
      • Department of Biostatistics
      Rotterdam, South Holland, Netherlands
    • Leiden University
      Leyden, South Holland, Netherlands
  • 2011-2012
    • Wageningen University
      Wageningen, Gelderland, Netherlands
  • 2006
    • Louisiana State University
      • Department of Experimental Statistics
      Baton Rouge, Louisiana, United States