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.

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.

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.