315 research outputs found
A D-vine copula mixed model for joint meta-analysis and comparison of diagnostic tests
For a particular disease, there may be two diagnostic tests developed, where each of the tests is subject to several studies. A quadrivariate generalised linear mixed model (GLMM) has been recently proposed to joint meta-analyse and compare two diagnostic tests. We propose a D-vine copula mixed model for joint meta-analysis and comparison of two diagnostic tests. Our general model includes the quadrivariate GLMM as a special case and can also operate on the original scale of sensitivities and specificities. The method allows the direct calculation of sensitivity and specificity for each test, as well as the parameters of the summary receiver operator characteristic (SROC) curve, along with a comparison between the SROCs of each test. Our methodology is demonstrated with an extensive simulation study and illustrated by meta-analysing two examples where two tests for the diagnosis of a particular disease are compared. Our study suggests that there can be an improvement on GLMM in fit to data since our model can also provide tail dependencies and asymmetries
Hybrid copula mixed models for combining case-control and cohort studies in meta-analysis of diagnostic tests
Copula mixed models for trivariate (or bivariate) meta-analysis of diagnostic test accuracy studies accounting (or not) for disease prevalence have been proposed in the biostatistics literature to synthesize information. However, many systematic reviews often include case-control and cohort studies, so one can either focus on the bivariate meta-analysis of the case-control studies or the trivariate meta-analysis of the cohort studies, as only the latter contains information on disease prevalence. In order to remedy this situation of wasting data we propose a hybrid copula mixed model via a combination of the bivariate and trivariate copula mixed model for the data from the case-control studies and cohort studies, respectively. Hence, this hybrid model can account for study design and also due to its generality can deal with dependence in the joint tails. We apply the proposed hybrid copula mixed model to a review of the performance of contemporary diagnostic imaging modalities for detecting metastases in patients with melanoma
Copula Eigenfaces with Attributes: Semiparametric Principal Component Analysis for a Combined Color, Shape and Attribute Model
Principal component analysis is a ubiquitous method in parametric appearance modeling for describing dependency and variance in datasets. The method requires the observed data to be Gaussian-distributed. We show that this requirement is not fulfilled in the context of analysis and synthesis of facial appearance. The model mismatch leads to unnatural artifacts which are severe to human perception. As a remedy, we use a semiparametric Gaussian copula model, where dependency and variance are modeled separately. This model enables us to use arbitrary Gaussian and non-Gaussian marginal distributions. Moreover, facial color, shape and continuous or categorical attributes can be analyzed in an unified way. Accounting for the joint dependency between all modalities leads to a more specific face model. In practice, the proposed model can enhance performance of principal component analysis in existing pipelines: The steps for analysis and synthesis can be implemented as convenient pre- and post-processing steps
A vine copula mixed effect model for trivariate meta-analysis of diagnostic test accuracy studies accounting for disease prevalence
A bivariate copula mixed model has been recently proposed to synthesize diagnostic test accuracy studies and it has been shown that it is superior to the standard generalized linear mixed model in this context. Here, we call trivariate vine copulas to extend the bivariate meta-analysis of diagnostic test accuracy studies by accounting for disease prevalence. Our vine copula mixed model includes the trivariate generalized linear mixed model as a special case and can also operate on the original scale of sensitivity, specificity, and disease prevalence. Our general methodology is illustrated by re-analyzing the data of two published meta-analyses. Our study suggests that there can be an improvement on trivariate generalized linear mixed model in fit to data and makes the argument for moving to vine copula random effects models especially because of their richness, including reflection asymmetric tail dependence, and computational feasibility despite their three dimensionality
Fast uncertainty quantification of tracer distribution in the brain interstitial fluid with multilevel and quasi Monte Carlo
Efficient uncertainty quantification algorithms are key to understand the
propagation of uncertainty -- from uncertain input parameters to uncertain
output quantities -- in high resolution mathematical models of brain
physiology. Advanced Monte Carlo methods such as quasi Monte Carlo (QMC) and
multilevel Monte Carlo (MLMC) have the potential to dramatically improve upon
standard Monte Carlo (MC) methods, but their applicability and performance in
biomedical applications is underexplored. In this paper, we design and apply
QMC and MLMC methods to quantify uncertainty in a convection-diffusion model of
tracer transport within the brain. We show that QMC outperforms standard MC
simulations when the number of random inputs is small. MLMC considerably
outperforms both QMC and standard MC methods and should therefore be preferred
for brain transport models.Comment: Multilevel Monte Carlo, quasi Monte Carlo, brain simulation, brain
fluids, finite element method, biomedical computing, random fields,
diffusion-convectio
Variable order Mittag-Leffler fractional operators on isolated time scales and application to the calculus of variations
We introduce new fractional operators of variable order on isolated time
scales with Mittag-Leffler kernels. This allows a general formulation of a
class of fractional variational problems involving variable-order difference
operators. Main results give fractional integration by parts formulas and
necessary optimality conditions of Euler-Lagrange type.Comment: This is a preprint of a paper whose final and definite form is with
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