Paul H C Eilers

Erasmus MC, Rotterdam, South Holland, Netherlands

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Publications (223)

  • [Show abstract] [Hide abstract] ABSTRACT: Offspring exposed to preeclampsia (PE) show an increased risk of cardiovascular disease in adulthood. We hypothesize that this is mediated by a disturbed vascular development of the placenta, umbilical cord and fetus. Therefore, we investigated associations between early-onset PE (EOPE), late-onset PE (LOPE) and features of placental and newborn vascular health.
    Article · Nov 2016 · Placenta
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    Gianluca Frasso · Paul H. C. Eilers
    [Show abstract] [Hide abstract] ABSTRACT: We present a direct semi-parametric approach for the estimation of the State Price Density (SPD) implied in quoted option prices. We treat the observed prices as expected values of possible pay-offs at maturity weighted by the unknown probability density function. We model the logarithm of the latter as a smooth function while matching the expected values of the potential pay-offs with the observed prices. This leads to a special case of the penalized composite link model. Our estimates do not rely on any parametric assumption on the underlying asset price dynamics and are consistent with no-arbitrage conditions.
    Full-text available · Article · Oct 2016
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    [Show abstract] [Hide abstract] ABSTRACT: Data analysed here derive from experiments conducted to study neurons' activity in the visual cortex of behaving monkeys. We consider a spatio-temporal adaptive penalized spline (P-spline) approach for modelling the firing rate of visual neurons. To the best of our knowledge, this is the first attempt in the statistical literature for locally adaptive smoothing in three dimensions. Estimation is based on the Separation of Overlapping Penalties (SOP) algorithm, which provides the stability and speed we look for.
    Full-text available · Article · Oct 2016
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    [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 \textit{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.
    Full-text available · Article · Oct 2016
  • S. Hugelier · P. H. C. Eilers · O. Devos · C. Ruckebusch
    [Show abstract] [Hide abstract] ABSTRACT: Penalized regression with a combination of sparseness and an interframe penalty is explored for image deconvolution in wide-field single-molecule fluorescence microscopy. The aim is to reconstruct superresolution images, which can be achieved by averaging the positions and intensities of individual fluorophores obtained from the analysis of successive frames. Sparsity of the fluorophore distribution in the spatial domain is obtained with an L0-norm penalty on estimated fluorophore intensities, effectively constraining the number of fluorophores per frame. Simultaneously, continuity of the fluorophore localizations in the time mode is obtained by penalizing the total numbers of pixel status changes between successive frames. We implemented the interframe penalty in a sparse deconvolution algorithm (sparse image deconvolution and reconstruction) for improved imaging of densely labeled biological samples. For simulated and real biological data, we show that more accurate estimates of the final superresolution images of cellular structures can be obtained.
    Article · Oct 2016 · Journal of Chemometrics
  • [Show abstract] [Hide abstract] ABSTRACT: In the field of cardio-thoracic surgery, valve function is monitored over time after surgery. The motivation for our research comes from a study which includes patients who received a human tissue valve in the aortic position. These patients are followed prospectively over time by standardized echocardiographic assessment of valve function. Loss of follow-up could be caused by valve intervention or the death of the patient. One of the main characteristics of the human valve is that its durability is limited. Therefore, it is of interest to obtain a prognostic model in order for the physicians to scan trends in valve function over time and plan their next intervention, accounting for the characteristics of the data. Several authors have focused on deriving predictions under the standard joint modeling of longitudinal and survival data framework that assumes a constant effect for the coefficient that links the longitudinal and survival outcomes. However, in our case this may be a restrictive assumption. Since the valve degenerates, the association between the biomarker with survival may change over time. To improve dynamic predictions we propose a Bayesian joint model that allows a time-varying coefficient to link the longitudinal and the survival processes, using P-splines. We evaluate the performance of the model in terms of discrimination and calibration, while accounting for censoring.
    Article · Sep 2016
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    [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.
    Full-text available · Article · Jul 2016
  • [Show abstract] [Hide abstract] ABSTRACT: Data analysed here derive from experiments conducted to study neurons' activity in the visual cortex of behaving monkeys. We consider a spatio-temporal adaptive penalized spline (P-spline) approach for modelling the firing rate of visual neurons. To the best of our knowledge, this is the first attempt in the statistical literature for locally adaptive smoothing in three dimensions. Estimation is based on the Separation of Overlapping Penalties (SOP) algorithm, which provides the stability and speed we look for
    Conference Paper · 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 available · 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 available · 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 available · 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 available · 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 available · 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
  • Silvia Rizzi · Jutta Gampe · Paul H. C. Eilers
    File available · Data · Jun 2015
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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 available · 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

Publication Stats

7k Citations


  • 2015
    • Erasmus MC
      Rotterdam, South Holland, Netherlands
    • Erasmus University Rotterdam
      Rotterdam, South Holland, Netherlands
  • 2011
    • Wageningen University
      Wageningen, Gelderland, Netherlands
  • 2009
    • Leiden University
      Leyden, South Holland, Netherlands
  • 2006
    • Louisiana State University
      • Department of Experimental Statistics
      Baton Rouge, Louisiana, United States