Varying Coefficient Tensor Models for Brain Imaging

We revisit a multidimensional varying-coefficient model (VCM), by allowing regressor coefficients to vary smoothly in more than one dimension, thereby extending the VCM of Hastie and Tibshirani. The motivating example is 3-dimensional, involving a special type of nuclear magnetic resonance measurement technique that is being used to estimate the diffusion tensor at each point in the human brain. We aim to improve the current state of the art, which is to apply a multiple regression model for each voxel separately using information from six or more volume images. We present a model, based on P-spline tensor products, to introduce spatial smoothness of the estimated diffusion tensor. Since the regression design matrix is space-invariant, a 4-dimensional tensor product model results, allowing more efficient computation with penalized array regression

Space-Varying Coefficient Models for Brain Imaging

The methodological development and the application in this paper originate from diffusion tensor imaging (DTI), a powerful nuclear magnetic resonance technique enabling diagnosis and monitoring of several diseases as well as reconstruction of neural pathways. We reformulate the current analysis framework of separate voxelwise regressions as a 3d space-varying coefficient model (VCM) for the entire set of DTI images recorded on a 3d grid of voxels. Hence by allowing to borrow strength from spatially adjacent voxels, to smooth noisy observations, and to estimate diffusion tensors at any location within the brain, the three-step cascade of standard data processing is overcome simultaneously. We conceptualize two VCM variants based on B-spline basis functions: a full tensor product approach and a sequential approximation, rendering the VCM numerically and computationally feasible even for the huge dimension of the joint model in a realistic setup. A simulation study shows that both approaches outperform the standard method of voxelwise regressions with subsequent regularization. Due to major efficacy, we apply the sequential method to a clinical DTI data set and demonstrate the inherent ability of increasing the rigid grid resolution by evaluating the incorporated basis functions at intermediate points. In conclusion, the suggested fitting methods clearly improve the current state-of-the-art, but ameloriation of local adaptivity remains desirable

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

Bilinear modulation models for seasonal tables of counts

We propose generalized linear models for time or age-time tables of seasonal counts, with the goal of better understanding seasonal patterns in the data. The linear predictor contains a smooth component for the trend and the product of a smooth component (the modulation) and a periodic time series of arbitrary shape (the carrier wave). To model rates, a population offset is added. Two-dimensional trends and modulation are estimated using a tensor product B-spline basis of moderate dimension. Further smoothness is ensured using difference penalties on the rows and columns of the tensor product coefficients. The optimal penalty tuning parameters are chosen based on minimization of a quasi-information criterion. Computationally efficient estimation is achieved using array regression techniques, avoiding excessively large matrices. The model is applied to female death rate in the US due to cerebrovascular diseases and respiratory diseases

On the estimation of variance parameters in non-standard generalised linear mixed models: application to penalised smoothing

We present a novel method for the estimation of variance parameters in generalised linear mixed models. The method has its roots in Harville (J Am Stat Assoc 72(358):320-338, 1977)'s work, but it is able to deal with models that have a precision matrix for the random effect vector that is linear in the inverse of the variance parameters (i.e., the precision parameters). We call the method SOP (separation of overlapping precision matrices). SOP is based on applying the method of successive approximations to easy-to-compute estimate updates of the variance parameters. These estimate updates have an appealing form: they are the ratio of a (weighted) sum of squares to a quantity related to effective degrees of freedom. We provide the sufficient and necessary conditions for these estimates to be strictly positive. An important application field of SOP is penalised regression estimation of models where multiple quadratic penalties act on the same regression coefficients. We discuss in detail two of those models: penalised splines for locally adaptive smoothness and for hierarchical curve data. Several data examples in these settings are presented.This research was supported by the Basque Government through the BERC 2018-2021 program and by Spanish Ministry of Economy and Competitiveness MINECO through BCAM Severo Ochoa excellence accreditation SEV-2013-0323 and through projects MTM2017-82379-R funded by (AEI/FEDER, UE) and acronym “AFTERAM”, MTM2014-52184-P and MTM2014-55966-P. The MRI/DTI data were collected at Johns Hopkins University and the Kennedy-Krieger Institute. We are grateful to Pedro Caro and Iain Currie for useful discussions, to Martin Boer and Cajo ter Braak for the detailed reading of the paper and their many suggestions, and to Bas Engel for sharing with us his knowledge. We are also grateful to the two peer referees for their constructive comments of the paper

Multidimensional Adaptive Penalised Splines with Application to Neurons' Activity Studies

P-spline models have achieved great popularity both in statistical and in applied research. A possible drawback of P-spline is that they assume a smooth transition of the covariate effect across its whole domain. In some practical applications, however, it is desirable and needed to adapt smoothness locally to the data, and adaptive P-splines have been suggested. Yet, the extra flexibility afforded by adaptive P-spline models is obtained at the cost of a high computational burden, especially in a multidimensional setting. Furthermore, to the best of our knowledge, the literature lacks proposals for adaptive P-splines in more than two dimensions. Motivated by the need for analysing data derived from experiments conducted to study neurons' activity in the visual cortex, this work presents a novel locally adaptive anisotropic 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. The practical performance of the proposal is evaluated through simulations, and comparisons with alternative methods are reported. In addition to the spatio-temporal analysis of the data that motivated this work, we also discuss an application in two dimensions on the absenteeism of workers

Visualization of Genomic Changes by Segmented Smoothing Using an L0 Penalty

Copy number variations (CNV) and allelic imbalance in tumor tissue can show strong segmentation. Their graphical presentation can be enhanced by appropriate smoothing. Existing signal and scatterplot smoothers do not respect segmentation well. We present novel algorithms that use a penalty on the norm of differences of neighboring values. Visualization is our main goal, but we compare classification performance to that of VEGA

Risk factors and outcomes associated with first-trimester fetal growth restriction

Context: Adverse environmental exposures lead to developmental adaptations in fetal life. The influences of maternal physical characteristics and lifestyle habits on first-trimester fetal adaptations and the postnatal consequences are not known. Objective: To determine the risk factors and outcomes associated with firsttrimester growth restriction. Design, Setting, and Participants: Prospective evaluation of the associations of maternal physical characteristics and lifestyle habits with first-trimester fetal crown to rump length in 1631 mothers with a known and reliable first day of their last menstrual period and a regular menstrual cycle. Subsequently, we assessed the associations of first-trimester fetal growth restriction with the risks of adverse birth outcomes and postnatal growth acceleration until the age of 2 years. The study was based in Rotterdam, the Netherlands. Mothers were enrolled between 2001 and 2005. Main Outcome Measures: First-trimester fetal growth was measured as fetal crown to rump length by ultrasound between the gestational age of 10 weeks 0 days and 13 weeks 6 days. Main birth outcomes were preterm birth (gestational age <37 weeks), low birth weight (<2500 g), and small size for gestational age (lowest fifth birth centile). Postnatal growth was measured until the age of 2 years. Results In the multivariate analysis, maternal age was positively associated with firsttrimester fetal crown to rump length (difference per maternal year of age, 0.79 mm; 95% confidence interval [CI], 0.41 to 1.18 per standard deviation score increase). Higher diastolic blood pressure and higher hematocrit levels were associated with a shorter crown to rump length (differences, -0.40 mm; 95% CI, -0.74 to -0.06 and -0.52 mm; 95% CI, -0.90 to -0.14 per standard deviation increase, respectively). Compared with mothers who were nonsmokers and optimal users of folic acid supplements, those who both smoked and did not use folic acid supplements had shorter fetal crown to rump lengths (difference, -3.84 mm; 95% CI, -5.71 to -1.98). Compared with normal first-trimester fetal growth, first-trimester growth restriction was associated with increased risks of preterm birth (4.0% vs 7.2%; adjusted odds ratio [OR], 2.12; 95% CI, 1.24 to 3.61), low birth weight (3.5% vs 7.5%; adjusted OR, 2.42; 95% CI, 1.41 to 4.16), and small size for gestational age at birth (4.0% vs 10.6%; adjusted OR, 2.64; 95% CI, 1.64 to 4.25). Each standard deviation decrease in firsttrimester fetal crown to rump length was associated with a postnatal growth acceleration until the age of 2 years (standard deviation score increase, 0.139 per 2 years; 95% CI, 0.097 to 0.181). Conclusions Maternal physical characteristics and lifestyle habits were independently associated with early fetal growth. First-trimester fetal growth restriction was associated with an increased risk of adverse birth outcomes and growth acceleration in early childhood

MLPAinter for MLPA interpretation: An integrated approach for the analysis, visualisation and data management of Multiplex Ligation-dependent Probe Amplification

Background: Multiplex Ligation-Dependent Probe Amplification (MLPA) is an application that can be used for the detection of multiple chromosomal aberrations in a single experiment. In one reaction, up to 50 different genomic sequences can be analysed. For a reliable work-flow, tools are needed for administrative support, data management, normalisation, visualisation, reporting and interpretation.Results: Here, we developed a data management system, MLPAInter for MLPA interpretation, that is windows executable and has a stand-alone database for monitoring and interpreting the MLPA data stream that is generated from the experimental setup to analysis, quality control and visualisation. A statistical approach is applied for the normalisation and analysis of large series of MLPA traces, making use of multiple control samples and internal controls.Conclusions: MLPAinter visualises MLPA data in plots with information about sample replicates, normalisation settings, and sample characteristics. This integrated approach helps in the automated handling of large series of MLPA data and guarantees a quick and streamlined dataflow from the beginning of an experiment to an authorised report