Hani Doss

Phylogenetic tree construction using markov chain monte carlo

Abstract We describe a Bayesian method based on Markov chain simulation to study the phylogenetic relationship in a group of DNA sequences. Under simple models of mutational events, our method produces a Markov chain whose stationary distribution is the conditional distribution of the phylogeny given the observed sequences. Our algorithm strikes a reasonable balance between the desire to move globally through the space of phylogenies and the need to make computationally feasible moves in areas of high probability. Because phylogenetic information is described by a tree, we have created new diagnostics to handle this type of data structure. An important byproduct of the Markov chain Monte Carlo phylogeny building technique is that it provides estimates and corresponding measures of variability for any aspect of the phylogeny under study.

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.

An Elementary Approach to Weak Convergence for Quantile Processes, with Applications to Censored Survival Data

Abstract Let ξ be a continuously differentiable function with positive derivative, and let ξ n be a sequence of right-continuous increasing processes. We show that if n 1/2(ξ n − ξ) W, where W is continuous, then n 1/2(ξ−1 n − ξ−1) − W(ξ−1)/ξ′(ξ−1). This result is applied to classical processes such as the empirical distribution function, the Kaplan-Meier estimator, and some other situations. We also prove an analogous result for the bootstrapped version of n 1/2(ξ n − ξ) and show how this allows one to obtain confidence bands for the quantile function ξ−1, based on the bootstrap. Several examples are given.

Confidence Bands for the Median Survival Time as a Function of the Covariates in the Cox Model

Abstract Let ξp (x) be the pth quantile of the distribution of the life length of an individual with covariate vector x in the Cox model. We introduce an estimator ξp (x) of ξp (x) and develop several families of confidence bands for ξ(x) as a function of x. To construct one type of band, we proceed as follows. We show that as n → ∞, where n is the number of individuals in the study, ) converges weakly to a Gaussian process W(x) with a complicated covariance structure. We then estimate this covariance structure from the data, and simulate many Gaussian processes with this estimated covariance structure. The critical constants required for the construction of the confidence bands are obtained from the simulated processes. Another type of bands is obtained by bootstrapping. We obtain an asymptotic theory for both types of bands. Simulation studies are used to compare the two types of bands. The methods are illustrated on the Stanford Heart Transplant Data.

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.

Monte Carlo Methods for Bayesian Analysis of Survival Data Using Mixtures of Dirichlet Process Priors

Consider the model in which the data consist of possibly censored lifetimes, and one puts a mixture of Dirichlet process priors on the common survival distribution. The exact computation of the posterior distribution of the survival function is in general impossible to obtain. This article develops and compares the performance of several simulation techniques, based on Markov chain Monte Carlo and sequential importance sampling, for approximating this posterior distribution. One scheme, whose derivation is based on sequential importance sampling, gives an exactly iid sample from the posterior for the case of right censored data. A second contribution of this article is a battery of programs that implement the various schemes discussed here. The programs and methods are illustrated on a dataset of interval-censored times arising from two treatments for breast cancer.

Estimation of Bayes Factors in a Class of Hierarchical Random Effects Models Using a Geometrically Ergodic MCMC Algorithm

We consider a Ba yesian random effects model that is commonly used in meta-analysis, in which the random effects have a t distribution, with degrees of freedom parameter to be estimated. We develop a Markov chain Monte Carlo algorithm for estimating the posterior distribution in this model, and establish geometric convergence of the algorithm. The geometric convergence rate has important theoretical and practical ramifications. Indeed, it implies that, under standard moment conditions, the ergodic averages used to estimate posterior quantities of interest satisfy central limit theorems. Moreover, it guarantees the consistency of a batch means estimate of the asymptotic variance in the CLT, which in turn allows for the construction of asymptotically valid standard errors. We show how our Markov chain can be used, in conjunction with an importance sampling method, to carry out an empirical Bayes approach for estimating the degrees of freedom parameter. To illustrate our methodology we consider a meta-analysis of studies that link intake of nonsteroidal anti-inflammatory drugs to a reduction in colon cancer risk, in which some of the studies are outliers. To model the distribution of the study effects we consider the family of t distributions, as well as a family of mixtures of Dirichlet process priors centered at the t distributions, and show how our methodology can be used to make a choice of model. Supplemental materials are available online.

Choosing the Resampling Scheme when Bootstrapping: A Case Study in Reliability

Abstract Often when dealing with complex data structures there is no unique way to bootstrap. If the data can be viewed as U 1, …, U n iid from some distribution P, then one can bootstrap by resampling the Us. Alternately, one can resample in a more model-based way; that is, by making use of the structure of the model P. A typical example of this is linear regression, in which the data is (Y i , X i ), i = 1, …, n. One can resample the pairs (Y i , X i ), or one can resample the residuals from a fitted model. This phenomenon arises over quite a wide spectrum of problems, and in many cases the different methods of bootstrapping can give substantially different results. It seems hopeless to come up with a general theory that compares the different ways of bootstrapping. In this article we study in some detail a certain model that arises in reliability theory in which there are two natural ways to bootstrap. This model is described as follows. Available for testing is a sample of n iid systems each having t...

Bayesian estimation in the symmetric location problem

SummaryLet Xi=θ+ɛi for i=1, ..., n, where the ɛis are i.i.d. ∼F and F is symmetric about 0. F is assumed unknown or only partially known, and the problem is to estimate θ. Priors are put on the pair (F,θ). The priors on F are obtained from Doksums neutral to the right priors, and include “symmetrized Dirichlet” priors. The marginal posterior distribution of θ given X1, ..., Xnis computed and its general properties studied. It is found that for certain classes of distributions of the ɛis, the posterior distribution of θ is for all large n a point mass at the true value of θ. If the distribution of the ɛis is not exactly symmetric, the Bayes estimates can behave very poorly.

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.