The power prior: theory and applications

The power prior has been widely used in many applications covering a large number of disciplines. The power prior is intended to be an informative prior constructed from historical data. It has been used in clinical trials, genetics, health care, psychology, environmental health, engineering, economics, and business. It has also been applied for a wide variety of models and settings, both in the experimental design and analysis contexts. In this review article, we give an A‐to‐Z exposition of the power prior and its applications to date. We review its theoretical properties, variations in its formulation, statistical contexts for which it has been used, applications, and its advantages over other informative priors. We review models for which it has been used, including generalized linear models, survival models, and random effects models. Statistical areas where the power prior has been used include model selection, experimental design, hierarchical modeling, and conjugate priors. Frequentist properties of power priors in posterior inference are established, and a simulation study is conducted to further examine the empirical performance of the posterior estimates with power priors. Real data analyses are given illustrating the power prior as well as the use of the power prior in the Bayesian design of clinical trials. Copyright © 2015 John Wiley & Sons, Ltd.     

Bayesian dose‐finding designs for combination of molecularly targeted agents assuming partial stochastic ordering

Molecularly targeted agent (MTA) combination therapy is in the early stages of development. When using a fixed dose of one agent in combinations of MTAs, toxicity and efficacy do not necessarily increase with an increasing dose of the other agent. Thus, in dose‐finding trials for combinations of MTAs, interest may lie in identifying the optimal biological dose combinations (OBDCs), defined as the lowest dose combinations (in a certain sense) that are safe and have the highest efficacy level meeting a prespecified target. The limited existing designs for these trials use parametric dose–efficacy and dose–toxicity models. Motivated by a phase I/II clinical trial of a combination of two MTAs in patients with pancreatic, endometrial, or colorectal cancer, we propose Bayesian dose‐finding designs to identify the OBDCs without parametric model assumptions. The proposed approach is based only on partial stochastic ordering assumptions for the effects of the combined MTAs and uses isotonic regression to estimate partially stochastically ordered marginal posterior distributions of the efficacy and toxicity probabilities. We demonstrate that our proposed method appropriately accounts for the partial ordering constraints, including potential plateaus on the dose–response surfaces, and is computationally efficient. We develop a dose‐combination‐finding algorithm to identify the OBDCs. We use simulations to compare the proposed designs with an alternative design based on Bayesian isotonic regression transformation and a design based on parametric change‐point dose–toxicity and dose–efficacy models and demonstrate desirable operating characteristics of the proposed designs. © 2014 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.     

Predictive distributions for between‐study heterogeneity and simple methods for their application in Bayesian meta‐analysis

Numerous meta‐analyses in healthcare research combine results from only a small number of studies, for which the variance representing between‐study heterogeneity is estimated imprecisely. A Bayesian approach to estimation allows external evidence on the expected magnitude of heterogeneity to be incorporated. The aim of this paper is to provide tools that improve the accessibility of Bayesian meta‐analysis. We present two methods for implementing Bayesian meta‐analysis, using numerical integration and importance sampling techniques. Based on 14 886 binary outcome meta‐analyses in the Cochrane Database of Systematic Reviews, we derive a novel set of predictive distributions for the degree of heterogeneity expected in 80 settings depending on the outcomes assessed and comparisons made. These can be used as prior distributions for heterogeneity in future meta‐analyses. The two methods are implemented in R, for which code is provided. Both methods produce equivalent results to standard but more complex Markov chain Monte Carlo approaches. The priors are derived as log‐normal distributions for the between‐study variance, applicable to meta‐analyses of binary outcomes on the log odds‐ratio scale. The methods are applied to two example meta‐analyses, incorporating the relevant predictive distributions as prior distributions for between‐study heterogeneity. We have provided resources to facilitate Bayesian meta‐analysis, in a form accessible to applied researchers, which allow relevant prior information on the degree of heterogeneity to be incorporated. © 2014 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.     

北京男男性行为人群HIV-1序列和流行趋势分析

目的 分析北京MSM人群HIV序列特征,预测北京该人群中HIV流行趋势。方法 汇总本实验室获得的北京MSM人群HIV序列,下载Los Alamos HIV Database中我国MSM人群及其他人群中流行的HIV序列,利用PhyML 3.0、BEAST等软件重建北京MSM人群系统发育树、估算突变速率、推断tMRCA、重建群体流行动态参数、计算再生指数R₀值,分析北京MSM人群与其他人群HIV流行的相关关系,推断进化和流行特征。结果 北京MSM人群中流行的HIV-1亚型包括B、CRF01_AE和CRF07_BC。在全国HIV毒株ML进化树中,北京MSM簇(北京MSM人群所占比例≥40%)共有3簇,即B-1簇、CRF01_AE-1簇、CRF01_AE-2簇。B1簇毒株是由至少3次传入事件进入北京MSM人群的,传入时间分别为1991年3月(1984年7月至1997年2月)、1994年1月(1989年1月至1998年1月)、1991年4月(1984年8月至1996年8月)。CRF01_AE毒株由2次传入事件进入北京MSM人群,传入时间分别为2000年12月(1998年3月至2003年1月)和2001年12月(2000年1月至2003年7月)。流行特征重塑分析显示,CRF01_AE-1簇近年来增长速度较快、突变速率较高。结论 北京MSM人群中存在多种HIV亚型毒株流行,其中B亚型毒株传入时间最早,但增长趋势趋于平稳;CRF01_AE毒株传入时间较晚、但增长迅速,对HIV在北京地区的流行具有明显的推动作用,因此对CRF01_AE毒株的防控有助于减少该地区HIV的流行。     

Analysis of transtheoretical model of health behavioral changes in a nutrition intervention study—a continuous time Markov chain model with Bayesian approach

Continuous time Markov chain (CTMC) models are often used to study the progression of chronic diseases in medical research but rarely applied to studies of the process of behavioral change. In studies of interventions to modify behaviors, a widely used psychosocial model is based on the transtheoretical model that often has more than three states (representing stages of change) and conceptually permits all possible instantaneous transitions. Very little attention is given to the study of the relationships between a CTMC model and associated covariates under the framework of transtheoretical model. We developed a Bayesian approach to evaluate the covariate effects on a CTMC model through a log‐linear regression link. A simulation study of this approach showed that model parameters were accurately and precisely estimated. We analyzed an existing data set on stages of change in dietary intake from the Next Step Trial using the proposed method and the generalized multinomial logit model. We found that the generalized multinomial logit model was not suitable for these data because it ignores the unbalanced data structure and temporal correlation between successive measurements. Our analysis not only confirms that the nutrition intervention was effective but also provides information on how the intervention affected the transitions among the stages of change. We found that, compared with the control group, subjects in the intervention group, on average, spent substantively less time in the precontemplation stage and were more/less likely to move from an unhealthy/healthy state to a healthy/unhealthy state. Copyright © 2015 John Wiley & Sons, Ltd.     

A mixed‐effect model for positive responses augmented by zeros

In this research article, we propose a class of models for positive and zero responses by means of a zero‐augmented mixed regression model. Under this class, we are particularly interested in studying positive responses whose distribution accommodates skewness. At the same time, responses can be zero, and therefore, we justify the use of a zero‐augmented mixture model. We model the mean of the positive response in a logarithmic scale and the mixture probability in a logit scale, both as a function of fixed and random effects. Moreover, the random effects link the two random components through their joint distribution and incorporate within‐subject correlation because of the repeated measurements and between‐subject heterogeneity. A Markov chain Monte Carlo algorithm is tailored to obtain Bayesian posterior distributions of the unknown quantities of interest, and Bayesian case‐deletion influence diagnostics based on the q‐divergence measure is performed. We apply the proposed method to a dataset from a 24hour dietary recall study conducted in the city of São Paulo and present a simulation study to evaluate the performance of the proposed methods. Copyright © 2015 John Wiley & Sons, Ltd.     

LEAP: Biomarker Inference Through Learning and Evaluating Association Patterns

Single nucleotide polymorphism (SNP) high‐dimensional datasets are available from Genome Wide Association Studies (GWAS). Such data provide researchers opportunities to investigate the complex genetic basis of diseases. Much of genetic risk might be due to undiscovered epistatic interactions, which are interactions in which combination of several genes affect disease. Research aimed at discovering interacting SNPs from GWAS datasets proceeded in two directions. First, tools were developed to evaluate candidate interactions. Second, algorithms were developed to search over the space of candidate interactions. Another problem when learning interacting SNPs, which has not received much attention, is evaluating how likely it is that the learned SNPs are associated with the disease. A complete system should provide this information as well. We develop such a system. Our system, called LEAP, includes a new heuristic search algorithm for learning interacting SNPs, and a Bayesian network based algorithm for computing the probability of their association. We evaluated the performance of LEAP using 100 1,000‐SNP simulated datasets, each of which contains 15 SNPs involved in interactions. When learning interacting SNPs from these datasets, LEAP outperformed seven others methods. Furthermore, only SNPs involved in interactions were found to be probable. We also used LEAP to analyze real Alzheimer's disease and breast cancer GWAS datasets. We obtained interesting and new results from the Alzheimer's dataset, but limited results from the breast cancer dataset. We conclude that our results support that LEAP is a useful tool for extracting candidate interacting SNPs from high‐dimensional datasets and determining their probability.     

风险评估模型在血吸虫病传播风险研究中的应用

随着血吸虫病研究的深入,风险评估模型被广泛应用到血吸虫病防治研究领域。本文对常见的血吸虫病风险评估模型和贝叶斯模型的理论基础和实际应用作一综述,以期为我国消除血吸虫病工作提供参考。