Signal propagation in Bayesian networks and its relationship with intrinsically multivariate predictive variables

A set of predictor variables is said to be intrinsically multivariate predictive (IMP) for a target variable if all properly contained subsets of the predictor set are poor predictors of the. target but the full set predicts the target with great accuracy. In a previous article, the main properties of IMP Boolean variables have been analytically described, including the introduction of the IMP score, a metric based on the coefficient of determination (CoD) as a measure of predictiveness with respect to the target variable. It was shown that the IMP score depends on four main properties: logic of connection, predictive power, covariance between predictors and marginal predictor probabilities (biases). This paper extends that work to a broader context, in an attempt to characterize properties of discrete Bayesian networks that contribute to the presence of variables (network nodes) with high IMP scores. We have found that there is a relationship between the IMP score of a node and its territory size, i.e., its position along a pathway with one source: nodes far from the source display larger IMP scores than those closer to the source, and longer pathways display larger maximum IMP scores. This appears to be a consequence of the fact that nodes with small territory have larger probability of having highly covariate predictors, which leads to smaller IMP scores. In addition, a larger number of XOR and NXOR predictive logic relationships has positive influence over the maximum IMP score found in the pathway. This work presents analytical results based on a simple structure network and an analysis involving random networks constructed by computational simulations. Finally, results from a real Bayesian network application are provided. (C) 2012 Elsevier Inc. All rights reserved.

Pancreatic iron stores assessed by magnetic resonance imaging (MRI) in beta thalassemic patients

Purpose: To assess the correlation between MRI findings of the pancreas with those of the heart and liver in patients with beta thalassemia; to compare the pancreas T2* MRI results with glucose and ferritin levels and labile plasma iron (LPI). Materials and methods: We retrospectively evaluated chronically transfused patients, testing glucose with enzymatic tests, serum ferritin with chemiluminescence, LPI with cellular fluorescence, and T2* MRI to assess iron content in the heart, liver, and pancreas. MRI results were compared with one another and with serum glucose, ferritin, and LPI. Liver iron concentration (LIC) was determined in 11 patients' liver biopsies by atomic absorption spectrometry. Results: 289 MRI studies were available from 115 patients during the period studied. 9.4% of patients had overt diabetes and an additional 16% of patients had impaired fasting glucose. Both pancreatic and cardiac R2* had predictive power (p < 0.0001) for identifying diabetes. Cardiac and pancreatic R2* were modestly correlated with one another (r(2) = 0.20, p < 0.0001). Both were weakly correlated with LIC (r(2) = 0.09, p < 0.0001 for both) and serum ferritin (r(2) = 0.14, p < 0.0001 and r(2) = 0.03, p < 0.02, respectively). None of the three served as a screening tool for single observations. There is a strong log-log, or power-law, relationship between ratio of signal intensity (SIR) values and pancreas R2* with an r(2) of 0.91. Conclusions: Pancreatic iron overload can be assessed by MRI, but siderosis in other organs did not correlate significantly with pancreatic hemosiderosis. (C) 2011 Elsevier Ireland Ltd. All rights reserved.

Sensitivity, specificity and predictive values of linear and nonlinear indices of heart rate variability in stable angina patients

Abstract Background Decreased heart rate variability (HRV) is related to higher morbidity and mortality. In this study we evaluated the linear and nonlinear indices of the HRV in stable angina patients submitted to coronary angiography. Methods We studied 77 unselected patients for elective coronary angiography, which were divided into two groups: coronary artery disease (CAD) and non-CAD groups. For analysis of HRV indices, HRV was recorded beat by beat with the volunteers in the supine position for 40 minutes. We analyzed the linear indices in the time (SDNN [standard deviation of normal to normal], NN50 [total number of adjacent RR intervals with a difference of duration greater than 50ms] and RMSSD [root-mean square of differences]) and frequency domains ultra-low frequency (ULF) ≤ 0,003 Hz, very low frequency (VLF) 0,003 – 0,04 Hz, low frequency (LF) (0.04–0.15 Hz), and high frequency (HF) (0.15–0.40 Hz) as well as the ratio between LF and HF components (LF/HF). In relation to the nonlinear indices we evaluated SD1, SD2, SD1/SD2, approximate entropy (−ApEn), α1, α2, Lyapunov Exponent, Hurst Exponent, autocorrelation and dimension correlation. The definition of the cutoff point of the variables for predictive tests was obtained by the Receiver Operating Characteristic curve (ROC). The area under the ROC curve was calculated by the extended trapezoidal rule, assuming as relevant areas under the curve ≥ 0.650. Results Coronary arterial disease patients presented reduced values of SDNN, RMSSD, NN50, HF, SD1, SD2 and -ApEn. HF ≤ 66 ms2, RMSSD ≤ 23.9 ms, ApEn ≤−0.296 and NN50 ≤ 16 presented the best discriminatory power for the presence of significant coronary obstruction. Conclusion We suggest the use of Heart Rate Variability Analysis in linear and nonlinear domains, for prognostic purposes in patients with stable angina pectoris, in view of their overall impairment.