An Empirical Bayes Approach to Shrinkage Estimation on the Manifold of Symmetric Positive-Definite Matrices.

The James-Stein estimator is an estimator of the multivariate normal mean and dominates the maximum likelihood estimator (MLE) under squared error loss. The original work inspired great interest in developing shrinkage estimators for a variety of problems. Nonetheless, research on shrinkage estimation for manifold-valued data is scarce. In this article, we propose shrinkage estimators for the parameters of the Log-Normal distribution defined on the manifold of N × N symmetric positive-definite matrices. For this manifold, we choose the Log-Euclidean metric as its Riemannian metric since it is easy to compute and has been widely used in a variety of applications. By using the Log-Euclidean distance in the loss function, we derive a shrinkage estimator in an analytic form and show that it is asymptotically optimal within a large class of estimators that includes the MLE, which is the sample Fréchet mean of the data. We demonstrate the performance of the proposed shrinkage estimator via several simulated data experiments. Additionally, we apply the shrinkage estimator to perform statistical inference in both diffusion and functional magnetic resonance imaging problems.

Honest Importance Sampling with Multiple Markov Chains.

Importance sampling is a classical Monte Carlo technique in which a random sample from one probability density, π1, is used to estimate an expectation with respect to another, π. The importance sampling estimator is strongly consistent and, as long as two simple moment conditions are satisfied, it obeys a central limit theorem (CLT). Moreover, there is a simple consistent estimator for the asymptotic variance in the CLT, which makes for routine computation of standard errors. Importance sampling can also be used in the Markov chain Monte Carlo (MCMC) context. Indeed, if the random sample from π1 is replaced by a Harris ergodic Markov chain with invariant density π1, then the resulting estimator remains strongly consistent. There is a price to be paid however, as the computation of standard errors becomes more complicated. First, the two simple moment conditions that guarantee a CLT in the iid case are not enough in the MCMC context. Second, even when a CLT does hold, the asymptotic variance has a complex form and is difficult to estimate consistently. In this paper, we explain how to use regenerative simulation to overcome these problems. Actually, we consider a more general set up, where we assume that Markov chain samples from several probability densities, π1, …, πk , are available. We construct multiple-chain importance sampling estimators for which we obtain a CLT based on regeneration. We show that if the Markov chains converge to their respective target distributions at a geometric rate, then under moment conditions similar to those required in the iid case, the MCMC-based importance sampling estimator obeys a CLT. Furthermore, because the CLT is based on a regenerative process, there is a simple consistent estimator of the asymptotic variance. We illustrate the method with two applications in Bayesian sensitivity analysis. The first concerns one-way random effects models under different priors. The second involves Bayesian variable selection in linear regression, and for this application, importance sampling based on multiple chains enables an empirical Bayes approach to variable selection.

A physical activity intervention to treat the frailty syndrome in older persons-results from the LIFE-P study.

BACKGROUND: The frailty syndrome is as a well-established condition of risk for disability. Aim of the study is to explore whether a physical activity (PA) intervention can reduce prevalence and severity of frailty in a community-dwelling elders at risk of disability. METHODS: Exploratory analyses from the Lifestyle Interventions and Independence for Elders pilot, a randomized controlled trial enrolling 424 community-dwelling persons (mean age=76.8 years) with sedentary lifestyle and at risk of mobility disability. Participants were randomized to a 12-month PA intervention versus a successful aging education group. The frailty phenotype (ie, ≥3 of the following defining criteria: involuntary weight loss, exhaustion, sedentary behavior, slow gait speed, poor handgrip strength) was measured at baseline, 6 months, and 12 months. Repeated measures generalized linear models were conducted. RESULTS: A significant (p = .01) difference in frailty prevalence was observed at 12 months in the PA intervention group (10.0%; 95% confidence interval = 6.5%, 15.1%), relative to the successful aging group (19.1%; 95% confidence interval = 13.9%,15.6%). Over follow-up, in comparison to successful aging participants, the mean number of frailty criteria in the PA group was notably reduced for younger subjects, blacks, participants with frailty, and those with multimorbidity. Among the frailty criteria, the sedentary behavior was the one most affected by the intervention. CONCLUSIONS: Regular PA may reduce frailty, especially in individuals at higher risk of disability. Future studies should be aimed at testing the possible benefits produced by multidomain interventions on frailty.

Safety and metabolic outcomes of resveratrol supplementation in older adults: results of a twelve-week, placebo-controlled pilot study.

Resveratrol has been found to have potent antioxidant, anti-inflammatory, and anticarcinogenic effects. The safety and efficacy of resveratrol supplementation in older adults are currently unknown. We conducted a double-blind, randomized, placebo-controlled trial to examine the safety and metabolic outcomes in 32 overweight, older adults (mean age, 73±7years). Participants were randomized into one of three treatment groups: (1) placebo, (2) moderate dose resveratrol (300mg/day), and (3) high dose resveratrol (1000mg/day). Both resveratrol and placebo were orally ingested in capsule form twice daily for 90days. Blood chemistry values remained within the normal range, and there were no significant differences in the number of participants reporting adverse events across conditions. Compared to placebo, glucose levels were significantly lower at post-treatment among participants randomized to both resveratrol conditions, with and without adjustment for the corresponding baseline values (ps<0.05). Glucose values of participants in the treatment groups, however, were not significantly different from baseline levels. These findings suggest that short-term resveratrol supplementation at doses of 300mg/day and 1000mg/day does not adversely affect blood chemistries and is well tolerated in overweight, older individuals. These findings support the study of resveratrol for improving cardio-metabolic health in older adults in larger clinical trials.

Estimates and Standard Errors for Ratios of Normalizing Constants from Multiple Markov Chains via Regeneration.

In the classical biased sampling problem, we have k densities π1(·), …, πk (·), each known up to a normalizing constant, i.e. for l = 1, …, k, πl (·) = νl (·)/ml , where νl (·) is a known function and ml is an unknown constant. For each l, we have an iid sample from πl ,·and the problem is to estimate the ratios ml/ms for all l and all s. This problem arises frequently in several situations in both frequentist and Bayesian inference. An estimate of the ratios was developed and studied by Vardi and his co-workers over two decades ago, and there has been much subsequent work on this problem from many different perspectives. In spite of this, there are no rigorous results in the literature on how to estimate the standard error of the estimate. We present a class of estimates of the ratios of normalizing constants that are appropriate for the case where the samples from the πl 's are not necessarily iid sequences, but are Markov chains. We also develop an approach based on regenerative simulation for obtaining standard errors for the estimates of ratios of normalizing constants. These standard error estimates are valid for both the iid case and the Markov chain case.

Polymorphisms associated with asthma are inversely related to glioblastoma multiforme.

A reduced risk of primary malignant adult brain tumors is observed among people reporting asthma, hay fever, and other allergic conditions; however, findings may be attributed to prediagnostic effects of tumors or recall bias. To determine whether asthma and allergic condition polymorphisms are inversely related to glioblastoma multiforme (GBM) risk, we conducted a population-based case-control study of 111 GBM patients and 422 controls. We identified five single nucleotide polymorphisms on three genes previously associated with asthma [interleukin (IL)-4RA, IL-13, ADAM33] and one gene associated with inflammation (cyclooxygenase-2). Confirming previous literature, we found that self-reported asthma, eczema, and fever are inversely related to GBM [e.g., asthma odds ratio (OR), 0.64; 95% confidence interval (CI), 0.33-1.25]. In addition, IL-4RA Ser478Pro TC, CC, and IL-4RA Gln551Arg AG, AA are positively associated with GBM (OR, 1.64; 95% CI, 1.05-2.55; 1.61; 95% CI, 1.05-2.47), whereas IL-13 -1,112 CT, TT is negatively associated with GBM (0.56; 95% CI, 0.33-0.96). Each of these polymorphism-GBM associations is in the opposite direction of a corresponding polymorphism-asthma association, consistent with previous findings that self-reported asthmatics and people with allergic conditions are less likely to have GBM than are people who do not report these conditions. Because we used germ line polymorphisms as biomarkers of susceptibility to asthma and allergic conditions, our results cannot be attributed to recall bias or effects of GBM on the immune system. However, our findings are also consistent with associations between IL-4RA, IL-13, and GBM that are independent of their role in allergic conditions.

Aspirin, ibuprofen, and other non-steroidal anti-inflammatory drugs in cancer prevention: a critical review of non-selective COX-2 blockade (review).

We comprehensively reviewed the published scientific literature on non-steroidal anti-inflammatory drugs (NSAIDs) and cancer and evaluated results based upon epidemiologic criteria of judgment: consistency of results, strength of association, dose response, molecular specificity, and biological plausibility. Sufficient data from 91 epidemiologic studies were available to examine the dose response of relative risk and level of NSAID intake for ten human malignancies. Dose response curves were fitted by exponential regression. Results showed a significant exponential decline in the risk with increasing intake of NSAIDs (primarily aspirin or ibuprofen) for 7-10 malignancies including the four major types: colon, breast, lung, and prostate cancer. Daily intake of NSAIDs, primarily aspirin, produced risk reductions of 63% for colon, 39% for breast, 36% for lung, and 39% for prostate cancer. Significant risk reductions were also observed for esophageal (73%), stomach (62%), and ovarian cancer (47%). NSAID effects became apparent after five or more years of use and were stronger with longer duration. Observed protective effects were also consistently stronger for gastrointestinal malignancies (esophagus, stomach, and colon). Results for pancreatic, urinary bladder, and renal cancer were inconsistent. Initial epidemiologic studies of malignant melanoma, Hodgkin's disease, and adult leukemia also found that NSAIDs are protective. A few studies suggest that ibuprofen has stronger anticancer effects than aspirin, particularly against breast and lung cancer. Overexpression of cyclooxygenase-2 (COX-2) and increased prostaglandin biosynthesis correlates with carcinogenesis and metastasis at most anatomic sites. Preclinical investigations provide consistent evidence that both selective and non-selective NSAIDs effectively inhibit chemically-induced carcinogenesis of epithelial tumors. This review provides compelling and converging evidence that regular intake of NSAIDs that non-selectively block COX-2 protects against the development of many types of cancer.

A meta-analysis of studies on the association of the platelet PlA polymorphism of glycoprotein IIIa and risk of coronary heart disease.

The Pl(A2) polymorphism of the glycoprotein IIIa subunit of the fibrinogen receptor (GPIIb-IIIa) has been reported by some studies to be associated with an increased risk of coronary thrombosis. Following the first paper on the subject in 1996, a large number of studies have investigated the relationship between this polymorphism and coronary thrombosis, either at the epidemiological or at the cellular and molecular levels. The cellular and molecular studies have shown in a consistent manner that this polymorphism increases platelet responsiveness. In contrast, epidemiological studies have generated inconsistent results regarding the clinical impact of Pl(A2). We consider 12 epidemiological studies that investigate the link between presence/absence of this polymorphism and presence/absence of coronary heart disease. Each is a case-control study that reports an odds ratio. The studies are not directly comparable because they differ greatly in their patient pools and also in the way the data are analysed. We present several meta-analyses of these 12 studies. The simplest one is based on a standard frequentist random effects model with a normal distribution for the study effects (the per-study population log-odds ratios). We also consider a Bayesian version of this model, with a diffuse prior for the mean and variance of the normal distribution of the study effects. The conclusions from both of these analyses is about the same, and is that there is evidence that the Pl(A2) polymorphism is associated with an increased risk of coronary heart disease. A look at the reported log-odds ratios across studies suggests that the study effects do not come from a symmetric distribution. For this reason, we also consider semi-parametric priors for the distribution of the study effects. These priors are specifically designed for this kind of meta-analysis, and are based on a certain class of mixtures of Dirichlet priors. They can be designed to concentrate most of their mass around the family of normal distributions, but still allow for any other distribution. The semi-parametric Bayesian model continues to give evidence of an association between the Pl(A2) polymorphism and the risk of coronary heart disease.