Multivariate prediction

The problem of prediction is considered in a multidimensional setting. Extending an idea presented by Barndorff-Nielsen and Cox, a predictive density for a multivariate random variable of interest is proposed. This density has the form of an estimative density plus a correction term. It gives simultaneous prediction regions with coverage error of smaller asymptotic order than the estimative density. A simulation study is also presented showing the magnitude of the improvement with respect to the estimative method.

Stochastic delay equations with non-negativity constraints driven by fractional Brownian motion

In this note we prove an existence and uniqueness result for the solution of multidimensional stochastic delay differential equations with normal reflection. The equations are driven by a fractional Brownian motion with Hurst parameter H > 1/2. The stochastic integral with respect to the fractional Brownian motion is a pathwise Riemann¿Stieltjes integral.

Criteria for hitting probabilities with applications to systems of stochastic wave equations

We develop several results on hitting probabilities of random fields which highlight the role of the dimension of the parameter space. This yields upper and lower bounds in terms of Hausdorff measure and Bessel-Riesz capacity, respectively. We apply these results to a system of stochastic wave equations in spatial dimension k >- 1 driven by a d-dimensional spatially homogeneous additive Gaussian noise that is white in time and colored in space.

Stochastic differential equations with random coefficients

In this paper we establish the existence and uniqueness of a solution for different types of stochastic differential equation with random initial conditions and random coefficients. The stochastic integral is interpreted as a generalized Stratonovich integral, and the techniques used to derive these results are mainly based on the path properties of the Brownian motion, and the definition of the Stratonovich integral.

Large deviations for stochastic Volterra equations

This paper is devoted to prove a large-deviation principle for solutions to multidimensional stochastic Volterra equations.

Stochastic delay differential equations driven by fractional Brownian motion with Hurst parameter H 1/2

We consider the Cauchy problem for a stochastic delay differential equation driven by a fractional Brownian motion with Hurst parameter H>¿. We prove an existence and uniqueness result for this problem, when the coefficients are sufficiently regular. Furthermore, if the diffusion coefficient is bounded away from zero and the coefficients are smooth functions with bounded derivatives of all orders, we prove that the law of the solution admits a smooth density with respect to Lebesgue measure on R.

Treatment of ruptured abdominal aortic aneurysm, a permanent challenge or a waste of resources? Prediction of outcome using a multi-organ-dysfunction score.

OBJECTIVES: in a retrospective study, attempts have been made to identify individual organ-dysfunction risk profiles influencing the outcome after surgery for ruptured abdominal aortic aneurysms. METHODS: out of 235 patients undergoing graft replacement for abdominal aortic aneurysms, 57 (53 men, four women, mean age 72 years [s.d. 8.8]) were treated for ruptured aneurysms in a 3-year period. Forty-eight preoperative, 13 intraoperative and 34 postoperative variables were evaluated statistically. A simple multi-organ dysfunction (MOD) score was adopted. RESULTS: the perioperative mortality was 32%. Three patients died intraoperatively, four within 48 h and 11 died later. A significant influence for pre-existing risk factors was identified only for cardiovascular diseases. Multiple linear-regression analysis indicated that a haemoglobin <90 g/l, systolic blood pressure <80 mmHg and ECG signs of ischaemia at admission were highly significant risk factors. The cause of death for patients, who died more than 48 h postoperatively, was mainly MOD. All patients with a MOD score >/=4 died (n=7). These patients required 27% of the intensive-care unit (ICU) days of all patients and 72% of the ICU days of the non-survivors. CONCLUSION: patients with ruptured aortic aneurysms from treatment should not be excluded. However, a physiological scoring system after 48 h appears justifiable in order to decide on the appropriateness of continual ICU support.

Individual prediction of cognitive decline in mild cognitive impairment using support vector machine-based analysis of diffusion tensor imaging data.

Although cross-sectional diffusion tensor imaging (DTI) studies revealed significant white matter changes in mild cognitive impairment (MCI), the utility of this technique in predicting further cognitive decline is debated. Thirty-five healthy controls (HC) and 67 MCI subjects with DTI baseline data were neuropsychologically assessed at one year. Among them, there were 40 stable (sMCI; 9 single domain amnestic, 7 single domain frontal, 24 multiple domain) and 27 were progressive (pMCI; 7 single domain amnestic, 4 single domain frontal, 16 multiple domain). Fractional anisotropy (FA) and longitudinal, radial, and mean diffusivity were measured using Tract-Based Spatial Statistics. Statistics included group comparisons and individual classification of MCI cases using support vector machines (SVM). FA was significantly higher in HC compared to MCI in a distributed network including the ventral part of the corpus callosum, right temporal and frontal pathways. There were no significant group-level differences between sMCI versus pMCI or between MCI subtypes after correction for multiple comparisons. However, SVM analysis allowed for an individual classification with accuracies up to 91.4% (HC versus MCI) and 98.4% (sMCI versus pMCI). When considering the MCI subgroups separately, the minimum SVM classification accuracy for stable versus progressive cognitive decline was 97.5% in the multiple domain MCI group. SVM analysis of DTI data provided highly accurate individual classification of stable versus progressive MCI regardless of MCI subtype, indicating that this method may become an easily applicable tool for early individual detection of MCI subjects evolving to dementia.

Estimating Design-Flood Discharges for Streams in Iowa Using Drainage-Basin and Channel-Geometry Characteristics, HR-322, 1993

Drainage-basin and channel-geometry multiple-regression equations are presented for estimating design-flood discharges having recurrence intervals of 2, 5, 10, 25, 50, and 100 years at stream sites on rural, unregulated streams in Iowa. Design-flood discharge estimates determined by Pearson Type-III analyses using data collected through the 1990 water year are reported for the 188 streamflow-gaging stations used in either the drainage-basin or channel-geometry regression analyses. Ordinary least-squares multiple-regression techniques were used to identify selected drainage-basin and channel-geometry regions. Weighted least-squares multiple-regression techniques, which account for differences in the variance of flows at different gaging stations and for variable lengths in station records, were used to estimate the regression parameters. Statewide drainage-basin equations were developed from analyses of 164 streamflow-gaging stations. Drainage-basin characteristics were quantified using a geographic-information-system (GIS) procedure to process topographic maps and digital cartographic data. The significant characteristics identified for the drainage-basin equations included contributing drainage area, relative relief, drainage frequency, and 2-year, 24-hour precipitation intensity. The average standard errors of prediction for the drainage-basin equations ranged from 38.6% to 50.2%. The GIS procedure expanded the capability to quantitatively relate drainage-basin characteristics to the magnitude and frequency of floods for stream sites in Iowa and provides a flood-estimation method that is independent of hydrologic regionalization. Statewide and regional channel-geometry regression equations were developed from analyses of 157 streamflow-gaging stations. Channel-geometry characteristics were measured on site and on topographic maps. Statewide and regional channel-geometry regression equations that are dependent on whether a stream has been channelized were developed on the basis of bankfull and active-channel characteristics. The significant channel-geometry characteristics identified for the statewide and regional regression equations included bankfull width and bankfull depth for natural channels unaffected by channelization, and active-channel width for stabilized channels affected by channelization. The average standard errors of prediction ranged from 41.0% to 68.4% for the statewide channel-geometry equations and from 30.3% to 70.0% for the regional channel-geometry equations. Procedures provided for applying the drainage-basin and channel-geometry regression equations depend on whether the design-flood discharge estimate is for a site on an ungaged stream, an ungaged site on a gaged stream, or a gaged site. When both a drainage-basin and a channel-geometry regression-equation estimate are available for a stream site, a procedure is presented for determining a weighted average of the two flood estimates.

Experimental analysis and computer prediction of CTF/NFI transcription factor DNA binding sites.

Accurate prediction of transcription factor binding sites is needed to unravel the function and regulation of genes discovered in genome sequencing projects. To evaluate current computer prediction tools, we have begun a systematic study of the sequence-specific DNA-binding of a transcription factor belonging to the CTF/NFI family. Using a systematic collection of rationally designed oligonucleotides combined with an in vitro DNA binding assay, we found that the sequence specificity of this protein cannot be represented by a simple consensus sequence or weight matrix. For instance, CTF/NFI uses a flexible DNA binding mode that allows for variations of the binding site length. From the experimental data, we derived a novel prediction method using a generalised profile as a binding site predictor. Experimental evaluation of the generalised profile indicated that it accurately predicts the binding affinity of the transcription factor to natural or synthetic DNA sequences. Furthermore, the in vitro measured binding affinities of a subset of oligonucleotides were found to correlate with their transcriptional activities in transfected cells. The combined computational-experimental approach exemplified in this work thus resulted in an accurate prediction method for CTF/NFI binding sites potentially functioning as regulatory regions in vivo.

Improvement of cardiovascular risk prediction: time to review current knowledge, debates, and fundamentals on how to assess test characteristics.

Cardiovascular risk assessment might be improved with the addition of emerging, new tests derived from atherosclerosis imaging, laboratory tests or functional tests. This article reviews relative risk, odds ratios, receiver-operating curves, posttest risk calculations based on likelihood ratios, the net reclassification improvement and integrated discrimination. This serves to determine whether a new test has an added clinical value on top of conventional risk testing and how this can be verified statistically. Two clinically meaningful examples serve to illustrate novel approaches. This work serves as a review and basic work for the development of new guidelines on cardiovascular risk prediction, taking into account emerging tests, to be proposed by members of the 'Taskforce on Vascular Risk Prediction' under the auspices of the Working Group 'Swiss Atherosclerosis' of the Swiss Society of Cardiology in the future.

Prediction of Recanalization Trumps Prediction of Tissue Fate: The Penumbra: A Dual-edged Sword.

BACKGROUND AND PURPOSE: To determine whether infarct core or penumbra is the more significant predictor of outcome in acute ischemic stroke, and whether the results are affected by the statistical method used. METHODS: Clinical and imaging data were collected in 165 patients with acute ischemic stroke. We reviewed the noncontrast head computed tomography (CT) to determine the Alberta Score Program Early CT score and assess for hyperdense middle cerebral artery. We reviewed CT-angiogram for site of occlusion and collateral flow score. From perfusion-CT, we calculated the volumes of infarct core and ischemic penumbra. Recanalization status was assessed on early follow-up imaging. Clinical data included age, several time points, National Institutes of Health Stroke Scale at admission, treatment type, and modified Rankin score at 90 days. Two multivariate regression analyses were conducted to determine which variables predicted outcome best. In the first analysis, we did not include recanalization status among the potential predicting variables. In the second, we included recanalization status and its interaction between perfusion-CT variables. RESULTS: Among the 165 study patients, 76 had a good outcome (modified Rankin score ≤2) and 89 had a poor outcome (modified Rankin score >2). In our first analysis, the most important predictors were age (P<0.001) and National Institutes of Health Stroke Scale at admission (P=0.001). The imaging variables were not important predictors of outcome (P>0.05). In the second analysis, when the recanalization status and its interaction with perfusion-CT variables were included, recanalization status and perfusion-CT penumbra volume became the significant predictors (P<0.001). CONCLUSIONS: Imaging prediction of tissue fate, more specifically imaging of the ischemic penumbra, matters only if recanalization can also be predicted.