396 research outputs found
An analysis of life expectancy and economic production using expectile frontier zones
The wealth of a country is assumed to have a strong non-linear influence on the life expectancy of its inhabitants. We follow up on research by Preston and study the relationship with gross domestic product. Smooth curves for the average but also for (upper) frontiers are constructed by a combination of least asymmetrically weighted squares and P-splines. Guidelines are given for optimizing the amount of smoothing and the definition of frontiers. The model is applied to a large set of countries in different years. It is also used to estimate life expectancy performance for individual countries and to show how it changed over time.frontier estimation, gross domestic product, least asymmetrically weighted squares, life expectancy, production frontier, smoothing
League tables for literacy survey data based on random effect models.
Data from the International Adult Literacy Survey are used to illustrate how league tables can be obtained from summary data, consisting of
percentages and their standard errors, using random effects models estimated by
nonparametric maximum likelihood
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
League tables for literacy survey data based on random effect models
Data from the International Adult Literacy Survey are used to illustrate how league tables can be obtained from summary data, consisting of percentages and their standard errors, using random effects models estimated by nonparametric maximum likelihood
Twenty years of P-splines
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 âbackboneâ for the âmixing and matchingâ 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.Peer Reviewe
Twenty years of P-splines
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 âbackboneâ for the âmixing and matchingâ 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
Improved dynamic predictions from joint models of longitudinal and survival data with time-varying effects using P-splines
Improved dynamic predictions from joint models of longitudinal and survival data with time-varying effects using P-splines
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