Compressed sensing (CS) enables measurement reconstruction by using sampling rates below the Nyquist rate, as long as the amplitude vector of interest is sparse. In this paper, we first derive and ...analyze the Bayesian Cramér-Rao bound (BCRB) for the amplitude vector when the set of indices (the support) of its nonzero entries is known. We consider the following context: i) The dictionary is nonstochastic but randomly generated; ii) the number of measurements and the support cardinality grow to infinity in a controlled manner, i.e., the ratio of these quantities converges to a constant; iii) the support is random; and iv) the vector of nonzero amplitudes follow a multidimensional generalized normal distribution. Using results from random matrix theory, we obtain closed-form approximations of the BCRB. These approximations can be formulated in a very compact form in low and high SNR regimes. Second, we provide a statistical analysis of the variance and the statistical efficiency of the oracle linear mean-square-error (LMMSE) estimator. Finally, we present results from numerical investigations in the context of non-bandlimited finite-rate-of-innovation (FRI) signal sampling. We show that the performance of Bayesian mean-square error (BMSE) estimators that are aware of the cardinality of the support, such as OMP and CoSaMP, are in good agreement with the developed lower bounds in the high SNR regime. Conversely, sparse estimators exploiting only the knowledge of the parameter vector and the noise variance in form of a priori distributions of these parameters, like LASSO and BPDN, are not efficient at high SNR. However, at low SNR, their BMSE is lower than that of the former estimators and may be close to the BCRB.
Background and aims
In non‐alcoholic fatty liver disease (NAFLD), fibrosis is the strongest prognostic factor and can be assessed by non‐invasive methods. We evaluated the ability of liver stiffness ...measurement (LSM) to predict overall survival and liver, cardiovascular and oncologic complications.
Methods
We prospectively collected data on 2251 consecutive NAFLD patients (mean age 59 years, male 53%, mean body mass index 28 kg/m2) in two centres. At inclusion, all patients had LSM, clinical and biological evaluation. During follow‐up, we recorded cardiovascular events, cancers, liver complications, liver transplantation and death. The primary endpoint was overall survival. Survival curves according to LSM were first performed using Kaplan‐Meier method for the primary endpoint, and Aalen‐Johansen method for secondary outcomes to take into account competitive risks. In a second step, a Cox proportional hazard model analysis was done to identify independent predictors of overall survival.
Results
Median follow‐up was 27 months IQR: 25‐38. Fifty‐five patients died and three patients had liver transplantation. Overall survival significantly decreased as baseline LSM increased. Twenty‐one patients (0.9%) had a liver event, 142 (6.3%) developed cancer (excluding HCC) and 151 (6.7%) had a cardiovascular event during follow‐up. By multivariable analysis, independent predictors of overall survival were as follows: baseline LSM (adjusted HR (aHR) = 2.85 1.65‐4.92, P = .0002), age (aHR = 1.11 1.08‐1.13, P < .0001) and male sex (aHR = 2.05 1.17‐3.57, P = .012). Patients with elevated LSM were also more likely to develop cardiovascular, and liver events but not other cancers.
Conclusion
LSM can be used to predict survival, cardiovascular and liver complications in NAFLD patients.
Background & Aims The aim of this study was to generate an improved prognostic model for predicting recurrence in liver transplant candidates with hepatocellular carcinoma (HCC). Methods Predictors ...of recurrence were tested by a Cox model analysis in a training cohort of 537 patients transplanted for HCC. A prognostic score was developed and validated in a national cohort of 435 patients followed up prospectively. Results α-Fetoprotein (AFP) independently predicted tumor recurrence and correlated with vascular invasion and differentiation. At a Cox score threshold of 0.7 (area under the receiver operating characteristic curve, 0.701; 95% confidence interval, 0.63–0.76; accuracy, 75.8%), a model combining log10 AFP, tumor size, and number was highly predictive of tumor recurrence and death. By using a simplified version of the model, with untransformed AFP values, a cut-off value of 2 was identified. In the validation cohort, a score greater than 2 predicted a marked increase in 5-year risk of recurrence (50.6% ± 10.2% vs 8.8% ± 1.7%; P < .001) and decreased survival (47.5% ± 8.1% vs 67.8% ± 3.4%; P = .002) as compared with others. Among patients exceeding Milan criteria, a score of 2 or lower identified a subgroup of patients with AFP levels less than 100 ng/mL with a low 5-year risk of recurrence (14.4% ± 5.3% vs 47.6% ± 11.1%; P = .006). Among patients within Milan criteria, a score greater than 2 identified a subgroup of patients with AFP levels greater than 1000 ng/mL at high risk of recurrence (37.1% ± 8.9% vs 13.3% ± 2.0%; P < .001). Net reclassification improvement showed that predictability of the AFP model was superior to Milan criteria. Conclusions Prediction of tumor recurrence is improved significantly by a model that incorporates AFP. We propose the adoption of new selection criteria for HCC transplant candidates, taking into account AFP.
Background & Aims We investigated the effectiveness of the protease inhibitors peginterferon and ribavirin in treatment-experienced patients with hepatitis C virus (HCV) genotype 1 infection and ...cirrhosis. Methods In the Compassionate Use of Protease Inhibitors in Viral C Cirrhosis study, 511 patients with HCV genotype 1 infection and compensated cirrhosis who did not respond to a prior course of peginterferon and ribavirin (44.3% relapsers or patients with viral breakthrough, 44.8% partial responders, and 8.0% null responders) were given either telaprevir (n = 299) or boceprevir (n = 212) for 48 weeks. We assessed percentages of patients with sustained viral responses 12 weeks after therapy and safety. This observational study did not allow for direct comparison of the 2 regimens. Results Among patients given telaprevir, 74.2% of relapsers, 40.0% of partial responders, and 19.4% of null responders achieved SVR12. Among those given boceprevir, 53.9% of relapsers, 38.3% of partial responders, and none of the null responders achieved SVR12. In multivariate analysis, factors associated with SVR12 included prior response to treatment response, no lead-in phase, HCV subtype 1b (vs 1a), and baseline platelet count greater than 100,000/mm3 . Severe adverse events occurred in 49.9% of cases, including liver decompensation, severe infections in 10.4%, and death in 2.2%. In multivariate analysis, baseline serum albumin level less than 35 g/L and baseline platelet counts of 100,000/mm3 or less predicted severe side effects or death. Conclusions Relatively high percentages of real-life, treatment-experienced patients with HCV genotype 1 infection and cirrhosis respond to the combination of peginterferon and ribavirin with telaprevir or boceprevir. However, side effects are frequent and often severe. Baseline levels of albumin and platelet counts can be used to guide treatment decisions. ClinicalTrials.gov number: NCT01514890.
Bayesian hierarchical modelling is a well-established branch of Bayesian inference. In this letter, we derive and study the estimation performance for the Bayesian hierarchical linear model (BHLM). ...Specifically, we consider a linear model with hierarchical priors for the involved amplitude and noise vectors. We provide closed-form expressions of the Bayesian Cramér-Rao bound (BCRB) for the following settings: (i) an arbitrary prior and hyperprior and (ii) a Gaussian-Y prior for the amplitudes, while the prior of noise is a Gaussian-X in both cases. Gaussian-X means that the conditional prior given the hyperparameter is Gaussian and X is the hyperprior. For the hierarchical distribution associated with spherical invariant random variables, the BCRB has a compact closed-form expression and enjoys several interesting properties that are discussed. Finally, we provide a theoretical analysis of the statistical efficiency of the linear minimum mean square error (MMSE) estimator in the low- and high-noise variance regimes when the hyperparameters are stochastically dominant.
The actual impact of transarterial chemoembolization before liver transplantation (LT) for hepatocellular carcinoma (HCC) on patient survival and HCC recurrence is not known. Between 1985 and 1998, ...479 patients with HCC in 14 French centers were evaluated for LT. Among these 479 patients, this case‐control study included 100 patients who received transarterial chemoembolization before LT (TACE group) and 100 control patients who did not receive chemoembolization (no‐TACE group). Patients and controls were matched for the pre‐LT tumor characteristics, the period of transplantation, the time spent on the waiting list, and pre‐ and posttransplantation treatments. Kaplan‐Meier estimates were calculated 5 years after LT and were compared with the log‐rank test. The mean waiting time before LT was 4.2 ± 3.2 months in the TACE group and 4.3 ± 4.4 months in the no‐TACE group. The median number of TACE procedures was 1 (range: 1‐12). Demographic data, median alpha‐fetoprotein level (21.6 ng/mL and 22.0 ng/mL, respectively), and pre‐ and post‐LT morphologic characteristics of the tumors did not differ in the TACE and no‐TACE groups. Overall 5‐year survival was 59.4% with TACE and 59.3% without TACE (ns). Survival rates did not differ significantly between the two groups with respect to the time on the waiting list, the tumor diameter, or the type of TACE (selective or nonselective). In the TACE group, 30 patients had tumor necrosis ≥80% on the liver explant with a 5‐year survival rate of 63.2%, compared with 54.2% among their matched controls (P = 0.9). In conclusion, with a mean waiting period of 4.2 months and 1 TACE procedure, pre‐LT TACE does not influence post‐LT overall survival and disease‐free survival. (Liver Transpl 2005;11:767–775.)
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