INFERENCE FOR EIGENVALUES AND EIGENVECTORS OF GAUSSIAN SYMMETRIC MATRICES

This article presents maximum likelihood estimators (MLEs) and log-likelihood ratio (LLR) tests for the eigenvalues and eigenvectors of Gaussian random symmetric matrices of arbitrary dimension, where the observations are independent repeated samples from one or two populations. These inference problems are relevant in the analysis of diffusion tensor imaging data and polarized cosmic background radiation data, where the observations are, respectively, 3 x 3 and 2 x 2 symmetric positive definite matrices. The parameter sets involved in the inference problems for eigenvalues and eigenvectors are subsets of Euclidean space that are either affine subspaces, embedded submanifolds that are invariant under orthogonal transformations or polyhedral convex cones. We show that for a class of sets that includes the ones considered in this paper, the MLEs of the mean parameter do not depend on the covariance parameters if and only if the covariance structure is orthogonally invariant. Closed-form expressions for the MLEs and the associated LLRs are derived for this covariance structure.

The Absence of Coronary Calcification Does Not Exclude Obstructive Coronary Artery Disease or the Need for Revascularization in Patients Referred for Conventional Coronary Angiography

Objectives This study was designed to evaluate whether the absence of coronary calcium could rule out >= 50% coronary stenosis or the need for revascularization. Background The latest American Heart Association guidelines suggest that a calcium score (CS) of zero might exclude the need for coronary angiography among symptomatic patients. Methods A substudy was made of the CORE64 (Coronary Evaluation Using Multi-Detector Spiral Computed Tomography Angiography Using 64 Detectors) multicenter trial comparing the diagnostic performance of 64-detector computed tomography to conventional angiography. Patients clinically referred for conventional angiography were asked to undergo a CS scan up to 30 days before. Results In all, 291 patients were included, of whom 214 (73%) were male, and the mean age was 59.3 +/- 10.0 years. A total of 14 (5%) patients had low, 218 (75%) had intermediate, and 59 (20%) had high pre-test probability of obstructive coronary artery disease. The overall prevalence of >= 50% stenosis was 56%. A total of 72 patients had CS = 0, among whom 14 (19%) had at least 1 >= 50% stenosis. The overall sensitivity for CS = 0 to predict the absence of >= 50% stenosis was 45%, specificity was 91%, negative predictive value was 68%, and positive predictive value was 81%. Additionally, revascularization was performed in 9 (12.5%) CS = 0 patients within 30 days of the CS. From a total of 383 vessels without any coronary calcification, 47 (12%) presented with >= 50% stenosis; and from a total of 64 totally occluded vessels, 13 (20%) had no calcium. Conclusions The absence of coronary calcification does not exclude obstructive stenosis or the need for revascularization among patients with high enough suspicion of coronary artery disease to be referred for coronary angiography, in contrast with the published recommendations. Total coronary occlusion frequently occurs in the absence of any detectable calcification. (Coronary Evaluation Using Multi-Detector Spiral Computed Tomography Angiography Using 64 Detectors [CORE-64]; NCT00738218) (J Am Coll Cardiol 2010;55:627-34) (C) 2010 by the American College of Cardiology Foundation

Coronary CT angiography using 64 detector rows: methods and design of the multi-centre trial CORE-64

Multislice computed tomography (MSCT) for the noninvasive detection of coronary artery stenoses is a promising candidate for widespread clinical application because of its non-invasive nature and high sensitivity and negative predictive value as found in several previous studies using 16 to 64 simultaneous detector rows. A multi-centre study of CT coronary angiography using 16 simultaneous detector rows has shown that 16-slice CT is limited by a high number of nondiagnostic cases and a high false-positive rate. A recent meta-analysis indicated a significant interaction between the size of the study sample and the diagnostic odds ratios suggestive of small study bias, highlighting the importance of evaluating MSCT using 64 simultaneous detector rows in a multi-centre approach with a larger sample size. In this manuscript we detail the objectives and methods of the prospective ""CORE-64"" trial (""Coronary Evaluation Using Multidetector Spiral Computed Tomography Angiography using 64 Detectors""). This multi-centre trial was unique in that it assessed the diagnostic performance of 64-slice CT coronary angiography in nine centres worldwide in comparison to conventional coronary angiography. In conclusion, the multi-centre, multi-institutional and multi-continental trial CORE-64 has great potential to ultimately assess the per-patient diagnostic performance of coronary CT angiography using 64 simultaneous detector rows.

Diagnostic Performance of Coronary Angiography by 64-Row CT

Background: The accuracy of multidetector computed tomographic (CT) angiography involving 64 detectors has not been well established. Methods: We conducted a multicenter study to examine the accuracy of 64-row, 0.5-mm multidetector CT angiography as compared with conventional coronary angiography in patients with suspected coronary artery disease. Nine centers enrolled patients who underwent calcium scoring and multidetector CT angiography before conventional coronary angiography. In 291 patients with calcium scores of 600 or less, segments 1.5 mm or more in diameter were analyzed by means of CT and conventional angiography at independent core laboratories. Stenoses of 50% or more were considered obstructive. The area under the receiver-operating-characteristic curve (AUC) was used to evaluate diagnostic accuracy relative to that of conventional angiography and subsequent revascularization status, whereas disease severity was assessed with the use of the modified Duke Coronary Artery Disease Index. Results: A total of 56% of patients had obstructive coronary artery disease. The patient-based diagnostic accuracy of quantitative CT angiography for detecting or ruling out stenoses of 50% or more according to conventional angiography revealed an AUC of 0.93 (95% confidence interval [CI], 0.90 to 0.96), with a sensitivity of 85% (95% CI, 79 to 90), a specificity of 90% (95% CI, 83 to 94), a positive predictive value of 91% (95% CI, 86 to 95), and a negative predictive value of 83% (95% CI, 75 to 89). CT angiography was similar to conventional angiography in its ability to identify patients who subsequently underwent revascularization: the AUC was 0.84 (95% CI, 0.79 to 0.88) for multidetector CT angiography and 0.82 (95% CI, 0.77 to 0.86) for conventional angiography. A per-vessel analysis of 866 vessels yielded an AUC of 0.91 (95% CI, 0.88 to 0.93). Disease severity ascertained by CT and conventional angiography was well correlated (r=0.81; 95% CI, 0.76 to 0.84). Two patients had important reactions to contrast medium after CT angiography. Conclusions: Multidetector CT angiography accurately identifies the presence and severity of obstructive coronary artery disease and subsequent revascularization in symptomatic patients. The negative and positive predictive values indicate that multidetector CT angiography cannot replace conventional coronary angiography at present. (ClinicalTrials.gov number, NCT00738218.).

Diagnostic Performance of Combined Noninvasive Coronary Angiography and Myocardial Perfusion Imaging Using 320-MDCT: The CT Angiography and Perfusion Methods of the CORE320 Multicenter Multinational Diagnostic Study

OBJECTIVE. Coronary MDCT angiography has been shown to be an accurate noninvasive tool for the diagnosis of obstructive coronary artery disease (CAD). Its sensitivity and negative predictive value for diagnosing percentage of stenosis are unsurpassed compared with those of other noninvasive testing methods. However, in its current form, it provides no information regarding the physiologic impact of CAD and is a poor predictor of myocardial ischemia. CORE320 is a multicenter multinational diagnostic study with the primary objective to evaluate the diagnostic accuracy of 320-MDCT for detecting coronary artery luminal stenosis and corresponding myocardial perfusion deficits in patients with suspected CAD compared with the reference standard of conventional coronary angiography and SPECT myocardial perfusion imaging. CONCLUSION. We aim to describe the CT acquisition, reconstruction, and analysis methods of the CORE320 study.

Coronary Artery Stenoses: Accuracy of 64-Detector Row CT Angiography in Segments with Mild, Moderate, or Severe Calcification-A Subanalysis of the CORE-64 Trial

Purpose: To evaluate the influence of cross-sectional arc calcification on the diagnostic accuracy of computed tomography (CT) angiography compared with conventional coronary angiography for the detection of obstructive coronary artery disease (CAD). Materials and Methods: Institutional Review Board approval and written informed consent were obtained from all centers and participants for this HIPAA-compliant study. Overall, 4511 segments from 371 symptomatic patients (279 men, 92 women; median age, 61 years [interquartile range, 53-67 years]) with clinical suspicion of CAD from the CORE-64 multi-center study were included in the analysis. Two independent blinded observers evaluated the percentage of diameter stenosis and the circumferential extent of calcium (arc calcium). The accuracy of quantitative multidetector CT angiography to depict substantial (>50%) stenoses was assessed by using quantitative coronary angiography (QCA). Cross-sectional arc calcium was rated on a segment level as follows: noncalcified or mild (<90 degrees), moderate (90 degrees-180 degrees), or severe (>180 degrees) calcification. Univariable and multivariable logistic regression, receiver operation characteristic curve, and clustering methods were used for statistical analyses. Results: A total of 1099 segments had mild calcification, 503 had moderate calcification, 338 had severe calcification, and 2571 segments were noncalcified. Calcified segments were highly associated (P < .001) with disagreement between CTA and QCA in multivariable analysis after controlling for sex, age, heart rate, and image quality. The prevalence of CAD was 5.4% in noncalcified segments, 15.0% in mildly calcified segments, 27.0% in moderately calcified segments, and 43.0% in severely calcified segments. A significant difference was found in area under the receiver operating characteristic curves (noncalcified: 0.86, mildly calcified: 0.85, moderately calcified: 0.82, severely calcified: 0.81; P < .05). Conclusion: In a symptomatic patient population, segment-based coronary artery calcification significantly decreased agreement between multidetector CT angiography and QCA to detect a coronary stenosis of at least 50%.

Patient Characteristics as Predictors of Image Quality and Diagnostic Accuracy of MDCT Compared With Conventional Coronary Angiography for Detecting Coronary Artery Stenoses: CORE-64 Multicenter International Trial

OBJECTIVE. The purpose of the study was to investigate patient characteristics associated with image quality and their impact on the diagnostic accuracy of MDCT for the detection of coronary artery stenosis. MATERIALS AND METHODS. Two hundred ninety-one patients with a coronary artery calcification (CAC) score of <= 600 Agatston units (214 men and 77 women; mean age, 59.3 +/- 10.0 years [SD]) were analyzed. An overall image quality score was derived using an ordinal scale. The accuracy of quantitative MDCT to detect significant (>= 50%) stenoses was assessed using quantitative coronary angiography (QCA) per patient and per vessel using a modified 19-segment model. The effect of CAC, obesity, heart rate, and heart rate variability on image quality and accuracy were evaluated by multiple logistic regression. Image quality and accuracy were further analyzed in subgroups of significant predictor variables. Diagnostic analysis was determined for image quality strata using receiver operating characteristic (ROC) curves. RESULTS. Increasing body mass index (BMI) (odds ratio [OR] = 0.89, p < 0.001), increasing heart rate (OR = 0.90, p < 0.001), and the presence of breathing artifact (OR = 4.97, p = 0.001) were associated with poorer image quality whereas sex, CAC score, and heart rate variability were not. Compared with examinations of white patients, studies of black patients had significantly poorer image quality (OR = 0.58, p = 0.04). At a vessel level, CAC score (10 Agatston units) (OR = 1.03, p = 0.012) and patient age (OR = 1.02, p = 0.04) were significantly associated with the diagnostic accuracy of quantitative MDCT compared with QCA. A trend was observed in differences in the areas under the ROC curves across image quality strata at the vessel level (p = 0.08). CONCLUSION. Image quality is significantly associated with patient ethnicity, BMI, mean scan heart rate, and the presence of breathing artifact but not with CAC score at a patient level. At a vessel level, CAC score and age were associated with reduced diagnostic accuracy.