定性临床试验资料meta分析的经验贝叶斯模型原理和应用

目的 研究meta分析经验贝叶斯分层模型的原理及其在定性临床试验资料分析中的应用.方法 以一个激素预防新生儿肺透明膜病的临床试验数据为例,建立分层模型,采用经验贝叶斯的方法进行参数估计和后验推断,尝试应用三种不同的方法估计分层模型中的超参数v.结果 分层模型的经验贝叶斯分析结果表明临床使用激素能够降低新生儿肺透明膜病的发生.结论 相对meta分析的随机效应模型,经验贝叶斯分层模型提供了更灵活的分析策略.     

两种假设检验思想的比较

探讨经典统计学派与贝叶斯学派设检验思想的异同。 方法总结和概括两种思想，并结合一个实例对两种思想进行比较，结果两种思想统一于贝叶斯定理，并特定场合下相互等价；贝叶斯方法在先验信息的利用，等方面经典方法具有明显的优势。结论贝叶斯学派的理论应用受到重视。     

GeoBUGS疾病制图法在条件自回归模型中的应用

<正>贝叶斯统计起源于英国学者贝叶斯在1763年的一篇题为"机遇理论中一个问题的解"的论文,他提出了著名的贝叶斯公式~[1]。贝叶斯统计方法与经典统计方法最根本的区别在于不仅利用总体信息和样本信息进行统计推断,而且充分利用了参数的先验信息,它将每一个不确定的参数都看成一个随机变量,通过给予先验分布,结合马尔科夫链蒙特卡洛(markov chain monte carlo,MCMC)法进行Gibbs抽样,得出参数的     

时间序列预测模型的贝叶斯统计分析

贝叶斯(Bayes)统计预测方法是一种以动态模型为研究对象的时间序列预测方法,其基本思想是将人们的经验信息作为已知条件结合到实际模型中,即利用模型信息、数据信息及先验信息(有关总体分布的未知参数的信息)来进行预测.由于结合了分析人员的主观经验及判断,因此可以利用模型监控和干预的方法,合理、科学地处理突发事件等异常情况,和传统的预测方法相比,克服了传统的静态模型难以处理突发事件的缺陷,具有灵活、易于适应外部变化的特点.本文以英国1969～1984年因车祸伤亡人数为资料,探讨贝叶斯统计预测方法在医学领域中的应用.     

贝叶斯统计及其在诊断和筛检试验评价中的应用

贝叶斯统计是当今世界两大主要统计学派之一，它与经典统计学派（又称频率学派）在统计推断理论和方法上存在重大差异。多年来两大学派之间的争论从未停止过，正是这种论战推动了双方向更加合理的方向前进。值得注意的是，近年来，由于现代计算机技术的发展较好地解决了高维积分这一限制贝叶斯统计应用的“瓶颈”问题，使得贝叶斯统计不论在理论研究还是在应用方法上都取得了较经典统计学更快的发展。美国统计学会主席斯坦福大学生物统计学教授Bradley Efron最近指出“我强烈地感到统计学正处于新一轮理论和方法论爆发的时代，而且这个爆发将以贝叶斯学派与频率学派合并为特色”。我国统计学家陈希孺院士指出“托马斯．贝叶斯以其一篇遗作的思想重大地影响了两个世纪以后的统计学界，顶住了统计学的半边天”。目前，贝叶斯统计在我国的研究尚属起步阶段，本文试图通过贝叶斯统计和经典统计的比较，介绍贝叶斯学派的一些基本思想，并以我们目前正在进行的诊断和筛检试验评价研究为例，说明贝叶斯统计在医学上的应用。     

基于潜分类方法评价无金标准条件下诊断试验的准确性

[目的]探讨无金标准条件下诊断试验准确性评价的潜分类方法。[方法]介绍潜分类模型在无金标准诊断试验评价中的原理、试验设计和评价方法,用两人群两试验实例说明潜分类方法的应用。[结果]对于二分类反应变量,假设条件独立和试验准确性稳定,至少需要两个人群两种试验方法或一个人群三种试验方法才能满足模型可识别性并用于频率学派统计评价;贝叶斯统计不需满足模型的可识别性,但需引入先验分布,且存在先验依赖性。[结论]潜分类方法可用于无金标准时的诊断试验评价,但要选择适合的试验设计和评价方法。     

一种基于折扣因子D的贝叶斯方法在MRCT中的应用研究

目的在折扣因子D的基础上,提出一种新的贝叶斯方法用于评价多区域临床试验中目标区药物的疗效,并探讨本方法的可行性。方法以Ⅱ期临床试验中收集到目标药物的种族信息作为样本信息,类似药物或同类药物的临床试验收集到的种族信息作为先验信息,构建折扣因子D的后验分布,并进一步计算加权Z检验统计量Z_W的后验分布,比较先验分布分别为无信息先验、共轭先验和分层先验时D后验分布的特点,并比较不同类型D的后验分布对试验检验效能的影响。结果当历史信息的信息量相对样本信息很小时,则后验均值主要由样本信息决定,后验分布的信息量基本接近样本信息的量,当历史信息的量逐渐增大时,后验均值逐渐向历史信息均值靠拢,后验分布的信息量也逐渐增大。检验效能由D的后验均值决定,与D的变异程度无关。结论本研究提出的贝叶斯方法可以较好地模拟实际情况,具有良好的实际意义和可操作性。     

贝叶斯网络在映射法中的应用

目的:通过介绍贝叶斯法的基本原理及贝叶斯网络的主要内容,探究贝叶斯网络在映射法的优势及应用现状,进一步推进其在映射法的应用。方法:采用文献研究的方法,对国内外已发表的贝叶斯网络在映射法中应用的文献进行回顾分析,研究其在映射法中的应用现状与发展前景。结果与结论:目前,关于映射法中映射模型的优劣性尚无一致定论。贝叶斯网络作为一种基于反应水平的映射转换模型,以节点间的概率分布表作为模型构建的直接结果,从而确定一种健康状态。同时,该方法综合利用先验信息和样本信息,提高了统计推断的精确度和可信性,能够较好地弥补目前常用映射模型的不足。     

无金标准诊断实验条件下贝叶斯先验参数的确定方法及SAS实现

目的探讨无金标准诊断实验条件下,贝叶斯先验参数的确定方法,并比较不同方法的应用条件。方法根据贝叶斯共轭先验分布原理,对二项分布的共轭贝塔分布中的α、β两个先验参数的确定方法进行分析比较,编写SAS程序确定先验参数。结果在共轭先验分布的条件下,先验矩、分位数、众数与分位数三种方法确定的先验分布参数结果一致。结论在实际工作中,应根据已知条件和具体情况决定采用何种方法计算先验分布参数。     

贝叶斯层次模型在嵌套结构调查数据中的应用研究北大核心CSCD

目的针对分层抽样流行病调查数据的结构特点,构建两种基于分层嵌套思想的贝叶斯层次模型,并探讨其优缺点。方法以贝叶斯层次模型为基础,利用嵌套结构中的层级关系构建模型,其中,模型一以嵌套层效应分解为特点构建,模型二以嵌套层效应逐级传递为特点构建。以重庆市出生缺陷调查数据为例,采用Open BUGS软件进行模型拟合及分析。结果以偏差信息准则(deviance information criterion,DIC)作为拟合优度评价,模型一和模型二的DIC值分别为101.8和101.6,大致相等;敏感性分析显示,在总体率的超参数μ设置不同先验信息下,模型一和模型二对总效应估计的变异性分别为(用标准差度量,10-4):后验均数1.191和27.546;后验中位数1.038和7.617,模型一的变异性比模型二小。结论模型一和模型二均可用于嵌套结构的调查数据建模分析及预测,拟合效果相当;但模型一比模型二受先验信息影响小,稳健性更好,更适合先验信息欠缺时的数据分析。     

Using exact Poisson likelihood functions in Bayesian interpretation of counting measurements

A technique for computing the exact marginalized (integrated) Poisson likelihood function for counting measurement processes involving a background subtraction is described. An empirical Bayesian method for determining the prior probability distribution of background count rates from population data is recommended and would seem to have important practical advantages. The exact marginalized Poisson likelihood function may be used instead of the commonly used Gaussian approximation. Differences occur in some cases of small numbers of measured counts, which are discussed. Optional use of exact likelihood functions in our Bayesian internal dosimetry codes has been implemented using an interpolation-table approach, which means that there is no computation time penalty except for the initial setup of the interpolation tables.     

Bayesian predictive approach to interim monitoring in clinical trials

This paper reviews Bayesian strategies for monitoring clinical trial data. It focuses on a Bayesian stochastic curtailment method based on the predictive probability of observing a clinically significant outcome at the scheduled end of the study given the observed data. The proposed method is applied to derive efficacy and futility stopping rules in clinical trials with continuous, normally distributed and binary endpoints. The sensitivity of the resulting stopping rules to the choice of prior distributions is examined and guidelines for choosing a prior distribution of the treatment effect are discussed. The Bayesian predictive approach is compared to the frequentist (conditional power) and mixed Bayesian-frequentist (predictive power) approaches. The interim monitoring strategies discussed in the paper are illustrated using examples from a small proof-of-concept study and a large mortality trial.     

Fast Bayesian scan statistics for multivariate event detection and visualization

The multivariate Bayesian scan statistic (MBSS) is a recently proposed, general framework for event detection and characterization in multivariate space-time data. MBSS integrates prior information and observations from multiple data streams in a Bayesian framework, computing the posterior probability of each type of event in each space-time region. MBSS has been shown to have many advantages over previous event detection approaches, including improved timeliness and accuracy of detection, easy interpretation and visualization of results, and the ability to model and accurately differentiate between multiple event types. This work extends the MBSS framework to enable detection and visualization of irregularly shaped clusters in multivariate data, by defining a hierarchical prior over all subsets of locations. While a naive search over the exponentially many subsets would be computationally infeasible, we demonstrate that the total posterior probability that each location has been affected can be efficiently computed, enabling rapid detection and visualization of irregular clusters. We compare the run time and detection power of this 'Fast Subset Sums' method to our original MBSS approach (assuming a uniform prior over circular regions) on semi-synthetic outbreaks injected into real-world Emergency Department data from Allegheny County, Pennsylvania. We demonstrate substantial improvements in spatial accuracy and timeliness of detection, while maintaining the scalability and fast run time of the original MBSS method.     

Using full probability models to compute probabilities of actual interest to decision makers

The objective of this paper is to illustrate the advantages of the Bayesian approach in quantifying, presenting, and reporting scientific evidence and in assisting decision making. Three basic components in the Bayesian framework are the prior distribution, likelihood function, and posterior distribution. The prior distribution describes analysts' belief a priori, the likelihood function captures how data modify the prior knowledge; and the posterior distribution synthesizes both prior and likelihood information. The Bayesian approach treats the parameters of interest as random variables, uses the entire posterior distribution to quantify the evidence, and reports evidence in a "probabilistic" manner. Two clinical examples are used to demonstrate the value of the Bayesian approach to decision makers. Using either an uninformative or a skeptical prior distribution, these examples show that the Bayesian methods allow calculations of probabilities that are usually of more interest to decision makers, e.g., the probability that treatment A is similar to treatment B, the probability that treatment A is at least 5% better than treatment B, and the probability that treatment A is not within the "similarity region" of treatment B, etc. In addition, the Bayesian approach can deal with multiple endpoints more easily than the classic approach. For example, if decision makers wish to examine mortality and cost jointly, the Bayesian method can report the probability that a treatment achieves at least 2% mortality reduction and less than $20,000 increase in costs. In conclusion, probabilities computed from the Bayesian approach provide more relevant information to decision makers and are easier to interpret.     

Probabilistic Sensitivity Analysis: Be a Bayesian

Objective:  To give guidance in defining probability distributions for model inputs in probabilistic sensitivity analysis (PSA) from a full Bayesian perspective.
Methods:  A common approach to defining probability distributions for model inputs in PSA on the basis of input-related data is to use the likelihood of the data on an appropriate scale as the foundation for the distribution around the inputs. We will look at this approach from a Bayesian perspective, derive the implicit prior distributions in two examples (proportions and relative risks), and compare these to alternative prior distributions.
Results:  In cases where data are sparse (in which case sensitivity analysis is crucial), commonly used approaches can lead to unexpected results. Weshow that this is because of the prior distributions that are implicitly assumed, namely that these are not as "uninformative" or "vague" as believed. We propose priors that we believe are more sensible for two examples and which are just as easy to apply.
Conclusions:  Input probability distributions should not be based on the likelihood of the data, but on the Bayesian posterior distribution calculated from this likelihood and an explicitly stated prior distribution.     

Use of a Bayesian approach to decide when to stop a therapeutic trial: the case of a chemoprophylaxis trial in human immunodeficiency virus infection

From 1996 to 1998, a phase III, placebo-controlled, therapeutic trial was conducted in Abidjan, Ivory Coast, to assess the efficacy of cotrimoxazole prophylaxis in reducing severe morbidity in adults at early stages of human immunodeficiency virus infection. The authors used the real data from this trial to simulate three Bayesian interim analyses. Three prior distributions were considered: a noninformative one, a skeptical one, and one based on external information. The posterior distribution was calculated by using directed acyclic graphs and Gibbs sampling. This Bayesian approach showed different results according to the prior distribution chosen. Although use of the noninformative prior would have led to stopping the trial at the same time that the frequentist approach would have, the skeptical prior would have led to continuing it, and the prior based on external data would have led to stopping it 1 year earlier.     

Bayesian noninferiority test for 2 binomial probabilities as the extension of Fisher exact test

Noninferiority trials have recently gained importance for the clinical trials of drugs and medical devices. In these trials, most statistical methods have been used from a frequentist perspective, and historical data have been used only for the specification of the noninferiority margin Δ>0. In contrast, Bayesian methods, which have been studied recently are advantageous in that they can use historical data to specify prior distributions and are expected to enable more efficient decision making than frequentist methods by borrowing information from historical trials. In the case of noninferiority trials for response probabilities π ₁,π ₂, Bayesian methods evaluate the posterior probability of H ₁:π ₁>π ₂?Δ being true. To numerically calculate such posterior probability, complicated Appell hypergeometric function or approximation methods are used. Further, the theoretical relationship between Bayesian and frequentist methods is unclear. In this work, we give the exact expression of the posterior probability of the noninferiority under some mild conditions and propose the Bayesian noninferiority test framework which can flexibly incorporate historical data by using the conditional power prior. Further, we show the relationship between Bayesian posterior probability and the P value of the Fisher exact test. From this relationship, our method can be interpreted as the Bayesian noninferior extension of the Fisher exact test, and we can treat superiority and noninferiority in the same framework. Our method is illustrated through Monte Carlo simulations to evaluate the operating characteristics, the application to the real HIV clinical trial data, and the sample size calculation using historical data.     

A valid and reliable belief elicitation method for Bayesian priors

ObjectiveBayesian inference has the advantage of formally incorporating prior beliefs about the effect of an intervention into analyses of treatment effect through the use of prior probability distributions or “priors.” Multiple methods to elicit beliefs from experts for inclusion in a Bayesian study have been used; however, the measurement properties of these methods have been infrequently evaluated. The objectives of this study were to evaluate the feasibility, validity, and reliability of a belief elicitation method for Bayesian priors.Study Design and SettingA single-center, cross-sectional study using a sample of academic specialists who treat pulmonary hypertension patients was conducted to test the feasibility, face and construct validity, and reliability of a belief elicitation method. Using this method, participants expressed the probability of 3-year survival with and without warfarin. Applying adhesive dots or “chips,” each representing 5% probability, in “bins” on a line, participants expressed their uncertainty and weight of belief about the effect of warfarin on 3-year survival.ResultsOf the 12 participants, 11 (92%) reported that the belief elicitation method had face validity, 10 (83%) found the questions clear, and 11 (92%) found the response option easy to use. The median time to completion was 10 minutes (5–15 minutes). Internal validity testing found moderate agreement (weighted kappa = 0.54–0.57). The intraclass correlation coefficient for test–retest reliability was 0.93.ConclusionThis method of belief elicitation for Bayesian priors is feasible, valid, and reliable. It can be considered for application in Bayesian clinical studies.     

Bayesian sensitivity analysis for unmeasured confounding in observational studies

We consider Bayesian sensitivity analysis for unmeasured confounding in observational studies where the association between a binary exposure, binary response, measured confounders and a single binary unmeasured confounder can be formulated using logistic regression models. A model for unmeasured confounding is presented along with a family of prior distributions that model beliefs about a possible unknown unmeasured confounder. Simulation from the posterior distribution is accomplished using Markov chain Monte Carlo. Because the model for unmeasured confounding is not identifiable, standard large-sample theory for Bayesian analysis is not applicable. Consequently, the impact of different choices of prior distributions on the coverage probability of credible intervals is unknown. Using simulations, we investigate the coverage probability when averaged with respect to various distributions over the parameter space. The results indicate that credible intervals will have approximately nominal coverage probability, on average, when the prior distribution used for sensitivity analysis approximates the sampling distribution of model parameters in a hypothetical sequence of observational studies. We motivate the method in a study of the effectiveness of beta blocker therapy for treatment of heart failure.