Elicitation of multivariate prior distributions: A nonparametric Bayesian approach

In the context of Bayesian statistical analysis, elicitation is the process of formulating a prior density f(.) about one or more uncertain quantities to represent a person's knowledge and beliefs. Several different methods of eliciting prior distributions for one unknown parameter have been proposed. However, there are relatively few methods for specifying a multivariate prior distribution and most are just applicable to specific classes of problems and/or based on restrictive conditions, such as independence of variables. Besides, many of these procedures require the elicitation of variances and correlations, and sometimes elicitation of hyperparameters which are difficult for experts to specify in practice. Garthwaite et al. (2005) discuss the different methods proposed in the literature and the difficulties of eliciting multivariate prior distributions. We describe a flexible method of eliciting multivariate prior distributions applicable to a wide class of practical problems. Our approach does not assume a parametric form for the unknown prior density f(.), instead we use nonparametric Bayesian inference, modelling f(.) by a Gaussian process prior distribution. The expert is then asked to specify certain summaries of his/her distribution, such as the mean, mode, marginal quantiles and a small number of joint probabilities. The analyst receives that information, treating it as a data set D with which to update his/her prior beliefs to obtain the posterior distribution for f(.). Theoretical properties of joint and marginal priors are derived and numerical illustrations to demonstrate our approach are given. (C) 2010 Elsevier B.V. All rights reserved.

Régression logistique bayésienne : comparaison de densités a priori

La régression logistique est un modèle de régression linéaire généralisée (GLM) utilisé pour des variables à expliquer binaires. Le modèle cherche à estimer la probabilité de succès de cette variable par la linéarisation de variables explicatives. Lorsque l’objectif est d’estimer le plus précisément l’impact de différents incitatifs d’une campagne marketing (coefficients de la régression logistique), l’identification de la méthode d’estimation la plus précise est recherchée. Nous comparons, avec la méthode MCMC d’échantillonnage par tranche, différentes densités a priori spécifiées selon différents types de densités, paramètres de centralité et paramètres d’échelle. Ces comparaisons sont appliquées sur des échantillons de différentes tailles et générées par différentes probabilités de succès. L’estimateur du maximum de vraisemblance, la méthode de Gelman et celle de Genkin viennent compléter le comparatif. Nos résultats démontrent que trois méthodes d’estimations obtiennent des estimations qui sont globalement plus précises pour les coefficients de la régression logistique : la méthode MCMC d’échantillonnage par tranche avec une densité a priori normale centrée en 0 de variance 3,125, la méthode MCMC d’échantillonnage par tranche avec une densité Student à 3 degrés de liberté aussi centrée en 0 de variance 3,125 ainsi que la méthode de Gelman avec une densité Cauchy centrée en 0 de paramètre d’échelle 2,5.

A Statistical Image-Based Shape Model for Visual Hull Reconstruction and 3D Structure Inference

We present a statistical image-based shape + structure model for Bayesian visual hull reconstruction and 3D structure inference. The 3D shape of a class of objects is represented by sets of contours from silhouette views simultaneously observed from multiple calibrated cameras. Bayesian reconstructions of new shapes are then estimated using a prior density constructed with a mixture model and probabilistic principal components analysis. We show how the use of a class-specific prior in a visual hull reconstruction can reduce the effect of segmentation errors from the silhouette extraction process. The proposed method is applied to a data set of pedestrian images, and improvements in the approximate 3D models under various noise conditions are shown. We further augment the shape model to incorporate structural features of interest; unknown structural parameters for a novel set of contours are then inferred via the Bayesian reconstruction process. Model matching and parameter inference are done entirely in the image domain and require no explicit 3D construction. Our shape model enables accurate estimation of structure despite segmentation errors or missing views in the input silhouettes, and works even with only a single input view. Using a data set of thousands of pedestrian images generated from a synthetic model, we can accurately infer the 3D locations of 19 joints on the body based on observed silhouette contours from real images.

A bayesian analysis for the parameters of the exponential-logarithmic distribution

The exponential-logarithmic is a new lifetime distribution with decreasing failure rate and interesting applications in the biological and engineering sciences. Thus, a Bayesian analysis of the parameters would be desirable. Bayesian estimation requires the selection of prior distributions for all parameters of the model. In this case, researchers usually seek to choose a prior that has little information on the parameters, allowing the data to be very informative relative to the prior information. Assuming some noninformative prior distributions, we present a Bayesian analysis using Markov Chain Monte Carlo (MCMC) methods. Jeffreys prior is derived for the parameters of exponential-logarithmic distribution and compared with other common priors such as beta, gamma, and uniform distributions. In this article, we show through a simulation study that the maximum likelihood estimate may not exist except under restrictive conditions. In addition, the posterior density is sometimes bimodal when an improper prior density is used. © 2013 Copyright Taylor and Francis Group, LLC.

Does bacterial density in cystic fibrosis sputum increase prior to pulmonary exacerbation?

These findings strongly suggest that CFPE do not generally result from increased bacterial density within the airways. Instead, data presented here are consistent with alternative models of pulmonary exacerbation.

A Novel Nonparametric Density Estimator

We present a novel nonparametric density estimator and a new data-driven bandwidth selection method with excellent properties. The approach is in- spired by the principles of the generalized cross entropy method. The pro- posed density estimation procedure has numerous advantages over the tra- ditional kernel density estimator methods. Firstly, for the first time in the nonparametric literature, the proposed estimator allows for a genuine incor- poration of prior information in the density estimation procedure. Secondly, the approach provides the first data-driven bandwidth selection method that is guaranteed to provide a unique bandwidth for any data. Lastly, simulation examples suggest the proposed approach outperforms the current state of the art in nonparametric density estimation in terms of accuracy and reliability.

Specific label-free and real-time detection of oxidized low density lipoprotein (oxLDL) using an immunosensor with three monoclonal antibodies

Increased levels of plasma oxLDL, which is the oxidized fraction of Low Density Lipoprotein (LDL), are associated with atherosclerosis, an inflammatory disease, and the subsequent development of severe cardiovascular diseases that are today a major cause of death in modern countries. It is therefore important to find a reliable and fast assay to determine oxLDL in serum. A new immunosensor employing three monoclonal antibodies (mAbs) against oxLDL is proposed in this work as a quick and effective way to monitor oxLDL. The oxLDL was first employed to produce anti-oxLDL monoclonal antibodies by hybridoma cells that were previously obtained. The immunosensor was set-up by selfassembling cysteamine (Cyst) on a gold (Au) layer (4 mm diameter) of a disposable screen-printed electrode. Three mAbs were allowed to react with N-hydroxysuccinimide (NHS) and ethyl(dimethylaminopropyl)carbodiimide (EDAC), and subsequently incubated in the Au/Cys. Albumin from bovine serum (BSA) was immobilized further to ensure that other molecules apart from oxLDL could not bind to the electrode surface. All steps were followed by various characterization techniques such as electrochemical impedance spectroscopy (EIS) and square wave voltammetry (SWV). The analytical operation of the immunosensor was obtained by incubating the sensing layer of the device in oxLDL for 15 minutes, prior to EIS and SWV. This was done by using standard oxLDL solutions prepared in foetal calf serum, in order to simulate patient's plasma with circulating oxLDL. A sensitive response was observed from 0.5 to 18.0 mg mL 1 . The device was successfully applied to determine the oxLDL fraction in real serum, without prior dilution or necessary chemical treatment. The use of multiple monoclonal antibodies on a biosensing platform seemed to be a successful approach to produce a specific response towards a complex multi-analyte target, correlating well with the level of oxLDL within atherosclerosis disease, in a simple, fast and cheap way.

Effects of prior repeated-sprints with different recovery duration on oxygen uptake kinetics during subsequent heavy-exercise

Introduction: Prior repeated-sprints (6) has become an interesting method to resolve the debate surrounding the principal factors that limits the oxygen uptake (V'O2) kinetics at the onset of exercise [i.e., muscle O2 delivery (5) or metabolic inertia (3)]. The aim of this study was to compare the effects of two repeated-sprints sets of 6x6s separated by different recovery duration between the sprints on V'O2 and muscular de-oxygenation [HHb] kinetics during a subsequent heavy-intensity exercise. Methods: 10 male subjects performed a 6-min constant-load cycling test (T50) at intensity corresponding to half of the difference between V'O2max and the ventilatory threshold. Then, they performed two repeated-sprints sets of 6x6s all-out separated by different recovery duration between the sprints (S1:30s and S2:3min) followed, after 7-min-recovery, by the T50 (S1T50 and S2T50, respectively). V'O2, [HHb] of the vastus lateralis (VL) and surface electromyography activity [i.e., root-mean-square (RMS) and the median frequency of the power density spectrum (MDF)] from VL and vastus medialis (VM) were recorded throughout T50. Models using a bi-exponential function for the overall T50 and a mono-exponential for the first 90s of T50 were used to define V'O2 and [HHb] kinetics respectively. Results: V'O2 mean value was higher in S1 (2.9±0.3l.min-1) than in S2 (1.2±0.3l.min-1); (p<0.001). The peripheral blood flow was increased after sprints as attested by a higher basal heart rate (HRbaseline) (S1T50: +22%; S2T50: +17%; p≤0.008). Time delay [HHb] was shorter for S1T50 and S2T50 than for T50 (-22% for both; p≤0.007) whereas the mean response time of V'O2 was accelerated only after S1 (S1T50: 32.3±2.5s; S2T50: 34.4±2.6s; T50: 35.7±5.4s; p=0.031). There were no significant differences in RMS between the three conditions (p>0.05). MDF of VM was higher during the first 3-min in S1T50 than in T50 (+6%; p≤0.05). Conclusion: The study show that V'O2 kinetics was speeded by prior repeated-sprints with a short (30s) but not a long (3min) inter-sprints-recovery even though the [HHb] kinetics was accelerated and the peripheral blood flow was enhanced after both sprints. S1, inducing a greater PCr depletion (1) and change in the pattern of the fibres recruitment (increase in MDF) compared with S2, may decrease metabolic inertia (2), stimulate the oxidative phosphorylation activation (4) and accelerate V'O2 kinetics at the beginning of the subsequent high-intensity exercise.

Effects of prior repeated-sprints with different recovery duration on oxygen uptake kinetics during subsequent heavy-exercise.

Introduction: Prior repeated-sprints (6) has become an interesting method to resolve the debate surrounding the principal factors that limits the oxygen uptake (V'O2) kinetics at the onset of exercise [i.e., muscle O2 delivery (5) or metabolic inertia (3)]. The aim of this study was to compare the effects of two repeated-sprints sets of 6x6s separated by different recovery duration between the sprints on V'O2 and muscular de-oxygenation [HHb] kinetics during a subsequent heavy-intensity exercise. Methods: 10 male subjects performed a 6-min constant-load cycling test (T50) at intensity corresponding to half of the difference between V'O2max and the ventilatory threshold. Then, they performed two repeated-sprints sets of 6x6s all-out separated by different recovery duration between the sprints (S1:30s and S2:3min) followed, after 7-min-recovery, by the T50 (S1T50 and S2T50, respectively). V'O2, [HHb] of the vastus lateralis (VL) and surface electromyography activity [i.e., root-mean-square (RMS) and the median frequency of the power density spectrum (MDF)] from VL and vastus medialis (VM) were recorded throughout T50. Models using a bi-exponential function for the overall T50 and a mono-exponential for the first 90s of T50 were used to define V'O2 and [HHb] kinetics respectively. Results: V'O2 mean value was higher in S1 (2.9±0.3l.min-1) than in S2 (1.2±0.3l.min-1); (p<0.001). The peripheral blood flow was increased after sprints as attested by a higher basal heart rate (HRbaseline) (S1T50: +22%; S2T50: +17%; p≤0.008). Time delay [HHb] was shorter for S1T50 and S2T50 than for T50 (-22% for both; p≤0.007) whereas the mean response time of V'O2 was accelerated only after S1 (S1T50: 32.3±2.5s; S2T50: 34.4±2.6s; T50: 35.7±5.4s; p=0.031). There were no significant differences in RMS between the three conditions (p>0.05). MDF of VM was higher during the first 3-min in S1T50 than in T50 (+6%; p≤0.05). Conclusion: The study show that V'O2 kinetics was speeded by prior repeated-sprints with a short (30s) but not a long (3min) inter-sprints-recovery even though the [HHb] kinetics was accelerated and the peripheral blood flow was enhanced after both sprints. S1, inducing a greater PCr depletion (1) and change in the pattern of the fibres recruitment (increase in MDF) compared with S2, may decrease metabolic inertia (2), stimulate the oxidative phosphorylation activation (4) and accelerate V'O2 kinetics at the beginning of the subsequent high-intensity exercise.

High-density collagen gel tubes as a matrix for primary human bladder smooth muscle cells.

Tissue-engineered grafts for the urinary tract are being investigated for the potential treatment of several urologic diseases. These grafts, predominantly tubular-shaped, usually require in vitro culture prior to implantation to allow cell engraftment on initially cell-free scaffolds. We have developed a method to produce tubular-shaped collagen scaffolds based on plastic compression. Our approach produces a ready cell-seeded graft that does not need further in vitro culture prior to implantation. The tubular collagen scaffolds were in particular investigated for their structural, mechanical and biological properties. The resulting construct showed an especially high collagen density, and was characterized by favorable mechanical properties assessed by axial extension and radial dilation. Young modulus in particular was greater than non-compressed collagen tubes. Seeding densities affected proliferation rate of primary human bladder smooth muscle cells. An optimal seeding density of 10(6) cells per construct resulted in a 25-fold increase in Alamar blue-based fluorescence after 2 wk in culture. These high-density collagen gel tubes, ready seeded with smooth muscle cells could be further seeded with urothelial cells, drastically shortening the production time of graft for urinary tract regeneration.

Different colors of light lead to different adaptation and activation as determined by high-density EEG.

Light adaptation is crucial for coping with the varying levels of ambient light. Using high-density electroencephalography (EEG), we investigated how adaptation to light of different colors affects brain responsiveness. In a within-subject design, sixteen young participants were adapted first to dim white light and then to blue, green, red, or white bright light (one color per session in a randomized order). Immediately after both dim and bright light adaptation, we presented brief light pulses and recorded event-related potentials (ERPs). We analyzed ERP response strengths and brain topographies and determined the underlying sources using electrical source imaging. Between 150 and 261ms after stimulus onset, the global field power (GFP) was higher after dim than bright light adaptation. This effect was most pronounced with red light and localized in the frontal lobe, the fusiform gyrus, the occipital lobe and the cerebellum. After bright light adaptation, within the first 100ms after light onset, stronger responses were found than after dim light adaptation for all colors except for red light. Differences between conditions were localized in the frontal lobe, the cingulate gyrus, and the cerebellum. These results indicate that very short-term EEG brain responses are influenced by prior light adaptation and the spectral quality of the light stimulus. We show that the early EEG responses are differently affected by adaptation to different colors of light which may contribute to known differences in performance and reaction times in cognitive tests.

Effects of prior repeated-sprints with different recovery duration on oxygen uptake kinetics during subsequent heavy-exercise

Introduction: Prior repeated-sprints (6) has become an interesting method to resolve the debate surrounding the principal factors that limits the oxygen uptake (V'O2) kinetics at the onset of exercise [i.e., muscle O2 delivery (5) or metabolic inertia (3)]. The aim of this study was to compare the effects of two repeated-sprints sets of 6x6s separated by different recovery duration between the sprints on V'O2 and muscular de-oxygenation [HHb] kinetics during a subsequent heavy-intensity exercise. Methods: 10 male subjects performed a 6-min constant-load cycling test (T50) at intensity corresponding to half of the difference between V'O2max and the ventilatory threshold. Then, they performed two repeated-sprints sets of 6x6s all-out separated by different recovery duration between the sprints (S1:30s and S2:3min) followed, after 7-min-recovery, by the T50 (S1T50 and S2T50, respectively). V'O2, [HHb] of the vastus lateralis (VL) and surface electromyography activity [i.e., root-mean-square (RMS) and the median frequency of the power density spectrum (MDF)] from VL and vastus medialis (VM) were recorded throughout T50. Models using a bi-exponential function for the overall T50 and a mono-exponential for the first 90s of T50 were used to define V'O2 and [HHb] kinetics respectively. Results: V'O2 mean value was higher in S1 (2.9±0.3l.min-1) than in S2 (1.2±0.3l.min-1); (p<0.001). The peripheral blood flow was increased after sprints as attested by a higher basal heart rate (HRbaseline) (S1T50: +22%; S2T50: +17%; p≤0.008). Time delay [HHb] was shorter for S1T50 and S2T50 than for T50 (-22% for both; p≤0.007) whereas the mean response time of V'O2 was accelerated only after S1 (S1T50: 32.3±2.5s; S2T50: 34.4±2.6s; T50: 35.7±5.4s; p=0.031). There were no significant differences in RMS between the three conditions (p>0.05). MDF of VM was higher during the first 3-min in S1T50 than in T50 (+6%; p≤0.05). Conclusion: The study show that V'O2 kinetics was speeded by prior repeated-sprints with a short (30s) but not a long (3min) inter-sprints-recovery even though the [HHb] kinetics was accelerated and the peripheral blood flow was enhanced after both sprints. S1, inducing a greater PCr depletion (1) and change in the pattern of the fibres recruitment (increase in MDF) compared with S2, may decrease metabolic inertia (2), stimulate the oxidative phosphorylation activation (4) and accelerate V'O2 kinetics at the beginning of the subsequent high-intensity exercise.

Effects of prior repeated-sprints with different recovery duration on oxygen uptake kinetics during subsequent heavy-exercise.

Introduction: Prior repeated-sprints (6) has become an interesting method to resolve the debate surrounding the principal factors that limits the oxygen uptake (V'O2) kinetics at the onset of exercise [i.e., muscle O2 delivery (5) or metabolic inertia (3)]. The aim of this study was to compare the effects of two repeated-sprints sets of 6x6s separated by different recovery duration between the sprints on V'O2 and muscular de-oxygenation [HHb] kinetics during a subsequent heavy-intensity exercise. Methods: 10 male subjects performed a 6-min constant-load cycling test (T50) at intensity corresponding to half of the difference between V'O2max and the ventilatory threshold. Then, they performed two repeated-sprints sets of 6x6s all-out separated by different recovery duration between the sprints (S1:30s and S2:3min) followed, after 7-min-recovery, by the T50 (S1T50 and S2T50, respectively). V'O2, [HHb] of the vastus lateralis (VL) and surface electromyography activity [i.e., root-mean-square (RMS) and the median frequency of the power density spectrum (MDF)] from VL and vastus medialis (VM) were recorded throughout T50. Models using a bi-exponential function for the overall T50 and a mono-exponential for the first 90s of T50 were used to define V'O2 and [HHb] kinetics respectively. Results: V'O2 mean value was higher in S1 (2.9±0.3l.min-1) than in S2 (1.2±0.3l.min-1); (p<0.001). The peripheral blood flow was increased after sprints as attested by a higher basal heart rate (HRbaseline) (S1T50: +22%; S2T50: +17%; p≤0.008). Time delay [HHb] was shorter for S1T50 and S2T50 than for T50 (-22% for both; p≤0.007) whereas the mean response time of V'O2 was accelerated only after S1 (S1T50: 32.3±2.5s; S2T50: 34.4±2.6s; T50: 35.7±5.4s; p=0.031). There were no significant differences in RMS between the three conditions (p>0.05). MDF of VM was higher during the first 3-min in S1T50 than in T50 (+6%; p≤0.05). Conclusion: The study show that V'O2 kinetics was speeded by prior repeated-sprints with a short (30s) but not a long (3min) inter-sprints-recovery even though the [HHb] kinetics was accelerated and the peripheral blood flow was enhanced after both sprints. S1, inducing a greater PCr depletion (1) and change in the pattern of the fibres recruitment (increase in MDF) compared with S2, may decrease metabolic inertia (2), stimulate the oxidative phosphorylation activation (4) and accelerate V'O2 kinetics at the beginning of the subsequent high-intensity exercise.

Modelling Bone Mineral Density in Swiss Breast Cancer Patients Treated with Letrozole, Tamoxifen and Sequences of Letrozole and Tamoxifen in the BIG 1-98 Study (SAKK 21/07).

Background: Bone health is a concern when treating early stage breast cancer patients with adjuvant aromatase inhibitors. Early detection of patients (pts) at risk of osteoporosis and fractures may be helpful for starting preventive therapies and selecting the most appropriate endocrine therapy schedule. We present statistical models describing the evolution of lumbar and hip bone mineral density (BMD) in pts treated with tamoxifen (T), letrozole (L) and sequences of T and L. Methods: Available dual-energy x-ray absorptiometry exams (DXA) of pts treated in trial BIG 1-98 were retrospectively collected from Swiss centers. Treatment arms: A) T for 5 years, B) L for 5 years, C) 2 years of T followed by 3 years of L and, D) 2 years of L followed by 3 years of T. Pts without DXA were used as a control for detecting selection biases. Patients randomized to arm A were subsequently allowed an unplanned switch from T to L. Allowing for variations between DXA machines and centres, two repeated measures models, using a covariance structure that allow for different times between DXA, were used to estimate changes in hip and lumbar BMD (g/cm2) from trial randomization. Prospectively defined covariates, considered as fixed effects in the multivariable models in an intention to treat analysis, at the time of trial randomization were: age, height, weight, hysterectomy, race, known osteoporosis, tobacco use, prior bone fracture, prior hormone replacement therapy (HRT), bisphosphonate use and previous neo-/adjuvant chemotherapy (ChT). Similarly, the T-scores for lumbar and hip BMD measurements were modeled using a per-protocol approach (allowing for treatment switch in arm A), specifically studying the effect of each therapy upon T-score percentage. Results: A total of 247 out of 546 pts had between 1 and 5 DXA; a total of 576 DXA were collected. Number of DXA measurements per arm were; arm A 133, B 137, C 141 and D 135. The median follow-up time was 5.8 years. Significant factors positively correlated with lumbar and hip BMD in the multivariate analysis were weight, previous HRT use, neo-/adjuvant ChT, hysterectomy and height. Significant negatively correlated factors in the models were osteoporosis, treatment arm (B/C/D vs. A), time since endocrine therapy start, age and smoking (current vs. never).Modeling the T-score percentage, differences from T to L were -4.199% (p = 0.036) and -4.907% (p = 0.025) for the hip and lumbar measurements respectively, before any treatment switch occurred. Conclusions: Our statistical models describe the lumbar and hip BMD evolution for pts treated with L and/or T. The results of both localisations confirm that, contrary to expectation, the sequential schedules do not seem less detrimental for the BMD than L monotherapy. The estimated difference in BMD T-score percent is at least 4% from T to L.

Bone mineral density in breast cancer patients treated with adjuvant letrozole, tamoxifen, or sequences of letrozole and tamoxifen in the BIG 1-98 study (SAKK 21/07).

BACKGROUND: The risk of osteoporosis and fracture influences the selection of adjuvant endocrine therapy. We analyzed bone mineral density (BMD) in Swiss patients of the Breast International Group (BIG) 1-98 trial [treatment arms: A, tamoxifen (T) for 5 years; B, letrozole (L) for 5 years; C, 2 years of T followed by 3 years of L; D, 2 years of L followed by 3 years of T]. PATIENTS AND METHODS: Dual-energy X-ray absorptiometry (DXA) results were retrospectively collected. Patients without DXA served as control group. Repeated measures models using covariance structures allowing for different times between DXA were used to estimate changes in BMD. Prospectively defined covariates were considered as fixed effects in the multivariable models. RESULTS: Two hundred and sixty-one of 546 patients had one or more DXA with 577 lumbar and 550 hip measurements. Weight, height, prior hormone replacement therapy, and hysterectomy were positively correlated with BMD; the correlation was negative for letrozole arms (B/C/D versus A), known osteoporosis, time on trial, age, chemotherapy, and smoking. Treatment did not influence the occurrence of osteoporosis (T score < -2.5 standard deviation). CONCLUSIONS: All aromatase inhibitor regimens reduced BMD. The sequential schedules were as detrimental for bone density as L monotherapy.