Multidimensional adaptive P-splines with application to neurons' activity studies.

The receptive field (RF) of a visual neuron is the region of the space that elicits neuronal responses. It can be mapped using different techniques that allow inferring its spatial and temporal properties. Raw RF maps (RFmaps) are usually noisy, making it difficult to obtain and study important features of the RF. A possible solution is to smooth them using P-splines. Yet, raw RFmaps are characterized by sharp transitions in both space and time. Their analysis thus asks for spatiotemporal adaptive P-spline models, where smoothness can be locally adapted to the data. However, the literature lacks proposals for adaptive P-splines in more than two dimensions. Furthermore, the extra flexibility afforded by adaptive P-spline models is obtained at the cost of a high computational burden, especially in a multidimensional setting. To fill these gaps, this work presents a novel anisotropic locally adaptive P-spline model in two (e.g., space) and three (space and time) dimensions. Estimation is based on the recently proposed SOP (Separation of Overlapping Precision matrices) method, which provides the speed we look for. Besides the spatiotemporal analysis of the neuronal activity data that motivated this work, the practical performance of the proposal is evaluated through simulations, and comparisons with alternative methods are reported.

Nowcasting the Number of New Symptomatic Cases During Infectious Disease Outbreaks Using Constrained P-spline Smoothing.

During an infectious disease outbreak, timely information on the number of new symptomatic cases is crucial. However, the reporting of new cases is usually subject to delay due to the incubation period, time to seek care, and diagnosis. This results in a downward bias in the numbers of new cases by the times of symptoms onset towards the current day. The real-time assessment of the current situation while correcting for underreporting is called nowcasting. We present a nowcasting method based on bivariate P-spline smoothing of the number of reported cases by time of symptoms onset and delay. Our objective is to predict the number of symptomatic-but-not-yet-reported cases and combine these with the already reported symptomatic cases into a nowcast. We assume the underlying two-dimensional reporting intensity surface to be smooth. We include prior information on the reporting process as additional constraints: the smooth surface is unimodal in the reporting delay dimension, is (almost) zero at a predefined maximum delay and has a prescribed shape at the beginning of the outbreak. Parameter estimation is done efficiently by penalized iterative weighted least squares. We illustrate our method on a large measles outbreak in the Netherlands. We show that even with very limited information the method is able to accurately predict the number of symptomatic-but-not-yet-reported cases. This results in substantially improved monitoring of new symptomatic cases in real time.

Human embryonic curvature studied with 3D ultrasound in ongoing pregnancies and miscarriages.

Embryonic growth is often impaired in miscarriages. It is postulated that derangements in embryonic growth result in abnormalities of the embryonic curvature. This study aims to create first trimester reference charts of the human embryonic curvature and investigate differences between ongoing pregnancies and miscarriages. Weekly ultrasonographic scans from ongoing pregnancies and miscarriages were used from the Rotterdam periconceptional cohort and a cohort of recurrent miscarriages. In 202 ongoing pregnancies and 33 miscarriages, first trimester crown rump length and total arch length were measured to assess the embryonic curvature. The results show that the total arch length increases and shows more variation with advanced gestation. The crown rump length/total arch length ratio shows a strong increase from 8+0 to 10+0 weeks and flattening thereafter. No significant difference was observed between the curvature of embryos of ongoing pregnancies and miscarriages. The majority of miscarried embryos could not be measured. Therefore, this technique is too limited to recommend the measurement of the embryonic curvature in clinical practice.

Improved dynamic predictions from joint models of longitudinal and survival data with time-varying effects using P-splines.

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.

Modelling spatial trends in sorghum breeding field trials using a two-dimensional P-spline mixed model.

KEY MESSAGE: A flexible and user-friendly spatial method called SpATS performed comparably to more elaborate and trial-specific spatial models in a series of sorghum breeding trials. Adjustment for spatial trends in plant breeding field trials is essential for efficient evaluation and selection of genotypes. Current mixed model methods of spatial analysis are based on a multi-step modelling process where global and local trends are fitted after trying several candidate spatial models. This paper reports the application of a novel spatial method that accounts for all types of continuous field variation in a single modelling step by fitting a smooth surface. The method uses two-dimensional P-splines with anisotropic smoothing formulated in the mixed model framework, referred to as SpATS model. We applied this methodology to a series of large and partially replicated sorghum breeding trials. The new model was assessed in comparison with the more elaborate standard spatial models that use autoregressive correlation of residuals. The improvements in precision and the predictions of genotypic values produced by the SpATS model were equivalent to those obtained using the best fitting standard spatial models for each trial. One advantage of the approach with SpATS is that all patterns of spatial trend and genetic effects were modelled simultaneously by fitting a single model. Furthermore, we used a flexible model to adequately adjust for field trends. This strategy reduces potential parameter identification problems and simplifies the model selection process. Therefore, the new method should be considered as an efficient and easy-to-use alternative for routine analyses of plant breeding trials.

Bayesian hierarchical modeling of longitudinal glaucomatous visual fields using a two-stage approach.

The Bayesian approach has become increasingly popular because it allows to fit quite complex models to data via Markov chain Monte Carlo sampling. However, it is also recognized nowadays that Markov chain Monte Carlo sampling can become computationally prohibitive when applied to a large data set. We encountered serious computational difficulties when fitting an hierarchical model to longitudinal glaucoma data of patients who participate in an ongoing Dutch study. To overcome this problem, we applied and extended a recently proposed two-stage approach to model these data. 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 (VFs) 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. Because 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. Copyright © 2017 John Wiley & Sons, Ltd.

Fast parametric time warping of peak lists.

UNLABELLED: 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 datasets we show the potential of the new approach. The first set is a LC-DAD dataset of grape samples, and the second an LC-MS dataset of apple extracts. AVAILABILITY AND IMPLEMENTATION: Parametric time warping of peak lists is implemented in the ptw package, version 1.9.1 and onwards, available from Github (https://github.com/rwehrens/ptw) and CRAN (http://cran.r-project.org). The package also contains a vignette, providing more theoretical details and scripts to reproduce the results below. CONTACT: ron.wehrens@wur.nl.

Efficient estimation of smooth distributions from coarsely grouped data.

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.

A multivariate Bayesian model for embryonic growth.

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.

Sparse deconvolution in one and two dimensions: applications in endocrinology and single-molecule fluorescence imaging.

Deconvolution of noisy signals is an important task in analytical chemistry, examples being spectral deconvolution or deconvolution in microscopy. When the number of spectral peaks or single emitters in imaging is limited, the solution of the deconvolution is required to be sparse, and desirable results are obtained using a penalized estimation techniques. We impose sparseness by using penalized regression with a penalty based on the L0-norm, as discussed in earlier work. Several extensions to this approach are presented. Results are demonstrated on pulse identification in endocrine data where the aim is to model the secretion pattern as a sparse series of spikes. An application in single-molecule fluorescence imaging demonstrates the algorithm when applied to two-dimensional data.

Determinants of maternal pregnancy one-carbon metabolism and newborn human DNA methylation profiles.

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.

Risk factors and consequences of maternal anaemia and elevated haemoglobin levels during pregnancy: a population-based prospective cohort study.

BACKGROUND: To determine sociodemographic and life style-related risk factors and trimester specific maternal, placental, and fetal consequences of maternal anaemia and elevated haemoglobin levels in pregnancy. METHODS: In a population-based prospective cohort study of 7317 mothers, we measured haemoglobin levels in early pregnancy [gestational age median 14.4 weeks (inter-quartile-range 12.5-17.5)]. Anaemia (haemoglobin ≤11 g/dl) and elevated haemoglobin levels (haemoglobin ≥13.2 g/dl) were defined according to the WHO criteria. Maternal blood pressure, placental function and fetal growth were measured in each trimester. Data on gestational hypertensive disorders and birth outcomes was collected from hospitals. RESULTS: Older maternal age, higher body mass index, primiparity and European descent were associated with higher haemoglobin levels (P < 0.05). Elevated haemoglobin levels were associated with increased systolic and diastolic blood pressure throughout pregnancy (mean differences 5.1 mmHg, 95% confidence interval [CI] 3.8, 6.5 and 4.1 mmHg, 95% CI 3.0, 5.2, respectively) and with a higher risk of third trimester uterine artery notching (RR 1.3, 95% CI 1.0, 1.7). As compared with maternal normal haemoglobin levels, not anaemia, but elevated haemoglobin levels were associated with fetal head circumference, length, and weight growth restriction from third trimester onwards (P < 0.05). Elevated haemoglobin levels were associated with increased risks of gestational hypertensive disorders (RR 1.4, 95% CI 1.1, 1.8) and adverse birth outcomes (RR 1.4, 95% CI 1.1, 1.7). CONCLUSIONS: In a low-risk population, various sociodemographic and life style factors affect haemoglobin levels during pregnancy. Elevated haemoglobin levels are associated with increased risks of maternal, placental, and fetal complications.

Secular trend of dental development in Dutch children.

Many studies have established dental age standards for different populations; however, very few studies have investigated whether dental development is stable over time on a population level. Therefore, the aim of this study was to analyze changes in dental maturity in Dutch children born between 1961 and 2004. We used 2,655 dental panoramic radiographs of 2- to 16-year-old Dutch children from studies performed in three major cities in the Netherlands. Based on a trend in children born between 1961 and 1994, we predicted that a child of a certain age and gender born in 1963 achieved the same dental maturity on average, 1.5 years later than a child of the same age born 40 years later. After adjusting for the birth year of a child in the analysis, the regression coefficient of the city variable was reduced by 56.6% and it remained statistically significant. The observed trend from 1961 to 1994 was extrapolated to 9- to 10-year-old children born in 2002-2004, and validation with the other samples of children with the same characteristics showed that 95.9%-96.8% of the children had dental maturity within the 95% of the predicted range. Dental maturity score was significantly and positively associated with the year of birth, gender, and age in Dutch children, indicating a trend in earlier dental development during the observation period, 1961-2004. These findings highlight the necessity of taking the year of birth into account when assessing dental development within a population with a wider time span.

Molecular subtypes of glioma identified by genome-wide methylation profiling.

Recent studies have indicated a prognostic role for genome-wide methylation in gliomas: Tumors that show an overall increase in DNA methylation at CpG sites (CIMP+; CpG island methylator phenotype) have a more favorable prognosis than CIMP- gliomas. Here, we have determined whether methylation profiling can identify more and clinically relevant molecular subtypes of glioma by performing genome-wide methylation profiling on 138 glial brain tumors of all histological diagnosis. Hopach (Hierarchical ordered partitioning and collapsing hybrid) clustering using the 1,000 most variable CpGs identified three distinct glioma subtypes (C+(1p19q), C+(wt), and C-) and one adult brain subtype. All "C+(1p19q) " and "C+(wt)" tumors were CIMP+ whereas most (50/54) "C-" tumors were CIMP-. The C- subtype gliomas contained many glioblastomas and all pilocytic astrocytomas. 1p19q LOH was frequent in the C+(1p19q) subtype. Other genetic changes (IDH1 mutation and EGFR amplification) and gene-expression based molecular subtypes also segregated in distinct methylation subtypes, demonstrating that these subtypes are also genetically distinct. Each subtype was associated with its own prognosis: median survival for C-, C+(1p19q), and C+(wt) tumors was 1.18, 5.00, and 2.62 years, respectively. The prognostic value of these methylation subtypes was validated on an external dataset from the TCGA. Analysis of recurrences of 14 primary tumors samples indicates that shifts between some C+(wt) and C+(1p/19q) tumors can occur between the primary and recurrent tumor, but CIMP status remained stable. Our data demonstrate that methylation profiling identifies at least three prognostically relevant subtypes of glioma that can aid diagnosis and potentially guide treatment for patients.

Smooth deconvolution of low-field NMR signals.

BACKGROUND: Low resolution nuclear magnetic resonance (LR-NMR) is a common technique to identify the constituents of complex materials (such as food and biological samples). The output of LR-NMR experiments is a relaxation signal which can be modelled as a type of convolution of an unknown density of relaxation times with decaying exponential functions, plus random Gaussian noise. The challenge is to estimate that density, a severely ill-posed problem. A complication is that non-negativity constraints need to be imposed in order to obtain valid results. SIGNIFICANCE AND NOVELTY: We present a smooth deconvolution model for solution of the inverse estimation problem in LR-NMR relaxometry experiments. We model the logarithm of the relaxation time density as a smooth function using (adaptive) P-splines while matching the expected residual magnetisations with the observed ones. The roughness penalty removes the singularity of the deconvolution problem, and the estimated density is positive by design (since we model its logarithm). The model is non-linear, but it can be linearized easily. The penalty has to be tuned for each given sample. We describe an efficient EM-type algorithm to optimize the smoothing parameter(s). RESULTS: We analyze a set of food samples (potato tubers). The relaxation spectra extracted using our method are similar to the ones described in the previous experiments but present sharper peaks. Using penalized signal regression we are able to accurately predict dry matter content of the samples using the estimated spectra as covariates.

GWAS on your notebook: fast semi-parallel linear and logistic regression for genome-wide association studies.

BACKGROUND: Genome-wide association studies have become very popular in identifying genetic contributions to phenotypes. Millions of SNPs are being tested for their association with diseases and traits using linear or logistic regression models. This conceptually simple strategy encounters the following computational issues: a large number of tests and very large genotype files (many Gigabytes) which cannot be directly loaded into the software memory. One of the solutions applied on a grand scale is cluster computing involving large-scale resources. We show how to speed up the computations using matrix operations in pure R code. RESULTS: We improve speed: computation time from 6 hours is reduced to 10-15 minutes. Our approach can handle essentially an unlimited amount of covariates efficiently, using projections. Data files in GWAS are vast and reading them into computer memory becomes an important issue. However, much improvement can be made if the data is structured beforehand in a way allowing for easy access to blocks of SNPs. We propose several solutions based on the R packages ff and ncdf.We adapted the semi-parallel computations for logistic regression. We show that in a typical GWAS setting, where SNP effects are very small, we do not lose any precision and our computations are few hundreds times faster than standard procedures. CONCLUSIONS: We provide very fast algorithms for GWAS written in pure R code. We also show how to rearrange SNP data for fast access.

Human embryonic growth trajectories and associations with fetal growth and birthweight.

STUDY QUESTION: How do human embryonic growth trajectories evolve in the first trimester, and is first-trimester embryonic growth associated with fetal growth and birthweight (BW)? SUMMARY ANSWER: Human embryonic growth rates increase between 9 and 10 weeks of gestation and are associated with mid-pregnancy fetal growth and BW. WHAT IS KNOWN ALREADY: Fetal growth is associated with health and disease risks in later life. Until recently, prenatal care and research have been focused predominantly on fetal growth in the second and third trimesters of pregnancy. Longitudinal first-trimester data remain scarce. STUDY DESIGN, SIZE, DURATION: We recruited 201 pregnancies before 8 weeks of gestation in a prospective periconception cohort study conducted in a tertiary center. PARTICIPANTS/MATERIALS, SETTING, METHODS: We performed weekly 3D ultrasound scans from enrollment up to 13 weeks of gestation. To create embryonic growth trajectories, serial crown-rump length (CRL) measurements were performed using the V-Scope software in the BARCO I-Space. Mid-pregnancy fetal growth parameters and BW were obtained from medical records. Z-scores were calculated for CRL, mid-pregnancy estimated fetal weight (EFW) and BW. Associations between embryonic and fetal growth parameters were investigated using Pearson's correlation coefficients. MAIN RESULTS AND THE ROLE OF CHANCE: During the early first trimester (up to 9 weeks of gestation), we observed a constant absolute mean embryonic CRL growth rate of 0.99 mm/day (SD 0.10), while the relative growth rate decreased. Between 9 and 10 weeks of gestation, the absolute growth rate increased, and during late first trimester (from 10 weeks of gestation onward), we observed a constant mean relative growth rate of 4.1% (SD 0.006) per day. Overall, early and late first-trimester median CRL Z-scores were strongly correlated with mid-pregnancy EFW (r overall/early/late = 0.57/0.57/0.54, P < 0.001) but only overall and late CRL Z-scores were correlated with BW (r overall = 0.15, P = 0.04; r early = 0.10, P = 0.17; r late = 0.17, P = 0.02). LIMITATIONS, REASONS FOR CAUTION: This study was conducted in a tertiary hospital. Therefore, future studies in other populations are warranted to confirm our results. WIDER IMPLICATIONS OF THE FINDINGS: This study shows differences between early and late first-trimester embryonic growth coinciding with changes in intrauterine nourishment. The established associations between first-trimester embryonic growth and fetal size in mid-pregnancy and at birth emphasize that more research is warranted to establish the importance of these results for preconceptional and early pregnancy care.

Duration of breastfeeding and gender are associated with methylation of the LEPTIN gene in very young children.

BACKGROUND: Perinatal environmental factors have been associated with the metabolic programming of children and consequent disease risks in later life. Epigenetic modifications that lead to altered gene expression may be involved. Here, we study early life environmental and constitutional factors in association with the DNA methylation of leptin (LEP), a non-imprinted gene implicated in appetite regulation and fat metabolism. METHODS: We investigated maternal education, breastfeeding, and constitutional factors of the child at 17 mo of age. We measured the DNA methylation of LEP in whole blood and the concentration of leptin in serum. RESULTS: Duration of breastfeeding was negatively associated with LEP methylation. Low education (≤12 y of education) was associated with higher LEP methylation. Boys had higher birth weight and lower LEP methylation than girls. An inverse association was established between birth weight per SD increase (+584 g) and LEP methylation. High BMI and leptin concentration were associated with lower methylation of LEP. CONCLUSION: The early life environment and constitutional factors of the child are associated with epigenetic variations in LEP. Future studies must reveal whether breastfeeding and the associated decrease in LEP methylation is an epigenetic mechanism contributing to the protective effect of breastfeeding against obesity.

Fast linear mixed model computations for genome-wide association studies with longitudinal data.

Genome-wide association studies are characterized by a huge number of statistical tests performed to discover new disease-related genetic variants [in the form of single-nucleotide polymorphisms (SNPs)] in human DNA. Many SNPs have been identified for cross-sectionally measured phenotypes. However, there is a growing interest in genetic determinants of the evolution of traits over time. Dealing with correlated observations from the same individual, we need to apply advanced statistical techniques. The linear mixed model is popular but also much more computationally demanding than fitting a linear regression model to independent observations. We propose a conditional two-step approach as an approximate method to explore the longitudinal relationship between the trait and the SNP. In a simulation study, we compare several fast methods with respect to their accuracy and speed. The conditional two-step approach is applied to relate SNPs to longitudinal bone mineral density responses collected in the Rotterdam Study.

Alternative normalization and analysis pipeline to address systematic bias in NanoString GeoMx Digital Spatial Profiling data.

Spatial transcriptomics is a novel technique that provides RNA-expression data with tissue-contextual annotations. Quality assessments of such techniques using end-user generated data are often lacking. Here, we evaluated data from the NanoString GeoMx Digital Spatial Profiling (DSP) platform and standard processing pipelines. We queried 72 ROIs from 12 glioma samples, performed replicate experiments of eight samples for validation, and evaluated five external datasets. The data consistently showed vastly different signal intensities between samples and experimental conditions that resulted in biased analysis. We evaluated the performance of alternative normalization strategies and show that quantile normalization can adequately address the technical issues related to the differences in data distributions. Compared to bulk RNA sequencing, NanoString DSP data show a limited dynamic range which underestimates differences between conditions. Weighted gene co-expression network analysis allowed extraction of gene signatures associated with tissue phenotypes from ROI annotations. Nanostring GeoMx DSP data therefore require alternative normalization methods and analysis pipelines.