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Bayesian second-order sensitivity of longitudinal inferences to non-ignorability: an application to antidepressant clinical trial data. 纵向推论对不可忽略性的贝叶斯二阶敏感性:抗抑郁药临床试验数据的应用。
IF 1.2 4区 数学 Pub Date : 2023-11-27 DOI: 10.1515/ijb-2022-0014
Elahe Momeni Roochi, Samaneh Eftekhari Mahabadi

Incomplete data is a prevalent complication in longitudinal studies due to individuals' drop-out before intended completion time. Currently available methods via commercial software for analyzing incomplete longitudinal data at best rely on the ignorability of the drop-outs. If the underlying missing mechanism was non-ignorable, potential bias arises in the statistical inferences. To remove the bias when the drop-out is non-ignorable, joint complete-data and drop-out models have been proposed which involve computational difficulties and untestable assumptions. Since the critical ignorability assumption is unverifiable based on the observed part of the sample, some local sensitivity indices have been proposed in the literature. Specifically, Eftekhari Mahabadi (Second-order local sensitivity to non-ignorability in Bayesian inferences. Stat Med 2018;59:55-95) proposed a second-order local sensitivity tool for Bayesian analysis of cross-sectional studies and show its better performance for handling bias compared with the first-order ones. In this paper, we aim to extend this index for the Bayesian sensitivity analysis of normal longitudinal studies with drop-outs. The index is driven based on a selection model for the drop-out mechanism and a Bayesian linear mixed-effect complete-data model. The presented formulas are calculated using the posterior estimation and draws from the simpler ignorable model. The method is illustrated via some simulation studies and sensitivity analysis of a real antidepressant clinical trial data. Overall, the numerical analysis showed that when repeated outcomes are subject to missingness, regression coefficient estimates are nearly approximated well by a linear function in the neighbourhood of MAR model, but there are a considerable amount of second-order sensitivity for the error term and random effect variances in Bayesian linear mixed-effect model framework.

在纵向研究中,由于个体在预期完成时间之前退出,数据不完整是一个普遍的并发症。目前可用的通过商业软件分析不完整纵向数据的方法,最多依赖于辍学的可忽略性。如果潜在的缺失机制是不可忽略的,则在统计推断中产生潜在的偏差。为了消除drop-out不可忽略时的偏差,提出了联合完整数据和drop-out模型,该模型涉及计算困难和不可检验的假设。由于临界可忽略性假设无法根据样本的观测部分进行验证,因此文献中提出了一些局部敏感性指标。具体地说,Eftekhari Mahabadi(二阶局部灵敏度对贝叶斯推理的不可忽略性)。Stat Med 2018;59:55-95)提出了一种用于横断面研究贝叶斯分析的二阶局部灵敏度工具,与一阶工具相比,其处理偏倚的性能更好。在本文中,我们的目标是将该指标扩展到具有辍学的正常纵向研究的贝叶斯灵敏度分析。该指标基于退出机制的选择模型和贝叶斯线性混合效应完整数据模型驱动。给出的公式是用后验估计计算的,并从更简单的可忽略模型中得出。通过模拟研究和对真实抗抑郁药物临床试验数据的敏感性分析来说明该方法。总体而言,数值分析表明,当重复结果存在缺失时,回归系数估计可以通过MAR模型邻域的线性函数近似地逼近,但贝叶斯线性混合效应模型框架中误差项和随机效应方差存在相当大的二阶敏感性。
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引用次数: 0
Revisiting incidence rates comparison under right censorship. 在正确的审查制度下重温发病率比较。
IF 1.2 4区 数学 Pub Date : 2023-11-14 DOI: 10.1515/ijb-2023-0025
Pablo Martínez-Camblor, Susana Díaz-Coto

Data description is the first step for understanding the nature of the problem at hand. Usually, it is a simple task that does not require any particular assumption. However, the interpretation of the used descriptive measures can be a source of confusion and misunderstanding. The incidence rate is the quotient between the number of observed events and the sum of time that the studied population was at risk of having this event (person-time). Despite this apparently simple definition, its interpretation is not free of complexity. In this piece of research, we revisit the incidence rate estimator under right-censorship. We analyze the effect that the censoring time distribution can have on the observed results, and its relevance in the comparison of two or more incidence rates. We propose a solution for limiting the impact that the data collection process can have on the results of the hypothesis testing. We explore the finite-sample behavior of the considered estimators from Monte Carlo simulations. Two examples based on synthetic data illustrate the considered problem. The R code and data used are provided as Supplementary Material.

数据描述是理解手头问题本质的第一步。通常,这是一个简单的任务,不需要任何特定的假设。然而,对所使用的描述性度量的解释可能是混淆和误解的来源。发病率是观察到的事件数与研究人群有发生该事件风险的时间总和(人-时间)之间的商。尽管这个定义看起来很简单,但它的解释并非没有复杂性。在这篇研究中,我们重新审视了权利审查下的发生率估计器。我们分析了审查时间分布对观测结果的影响,以及它在两个或多个发病率比较中的相关性。我们提出了一个解决方案来限制数据收集过程对假设检验结果的影响。我们从蒙特卡洛模拟中探讨了所考虑的估计器的有限样本行为。基于综合数据的两个示例说明了所考虑的问题。R代码和使用的数据作为补充材料提供。
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引用次数: 0
Frontmatter 头版头条
4区 数学 Pub Date : 2023-11-01 DOI: 10.1515/ijb-2023-frontmatter2
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引用次数: 0
Testing for association between ordinal traits and genetic variants in pedigree-structured samples by collapsing and kernel methods. 通过折叠和核方法测试系谱结构样本中序数性状和遗传变异之间的关联。
IF 1.2 4区 数学 Pub Date : 2023-09-26 DOI: 10.1515/ijb-2022-0123
Li-Chu Chien

In genome-wide association studies (GWAS), logistic regression is one of the most popular analytics methods for binary traits. Multinomial regression is an extension of binary logistic regression that allows for multiple categories. However, many GWAS methods have been limited application to binary traits. These methods have improperly often been used to account for ordinal traits, which causes inappropriate type I error rates and poor statistical power. Owing to the lack of analysis methods, GWAS of ordinal traits has been known to be problematic and gaining attention. In this paper, we develop a general framework for identifying ordinal traits associated with genetic variants in pedigree-structured samples by collapsing and kernel methods. We use the local odds ratios GEE technology to account for complicated correlation structures between family members and ordered categorical traits. We use the retrospective idea to treat the genetic markers as random variables for calculating genetic correlations among markers. The proposed genetic association method can accommodate ordinal traits and allow for the covariate adjustment. We conduct simulation studies to compare the proposed tests with the existing models for analyzing the ordered categorical data under various configurations. We illustrate application of the proposed tests by simultaneously analyzing a family study and a cross-sectional study from the Genetic Analysis Workshop 19 (GAW19) data.

在全基因组关联研究(GWAS)中,逻辑回归是最流行的二元性状分析方法之一。多项式回归是二元逻辑回归的扩展,允许多个类别。然而,许多GWAS方法在二元性状上的应用受到限制。这些方法经常被不恰当地用于解释有序特征,这导致了不恰当的I型错误率和较差的统计能力。由于缺乏分析方法,序列性状的GWAS一直存在问题,并引起了人们的关注。在本文中,我们开发了一个通用的框架,用于通过折叠和核方法识别谱系结构样本中与遗传变异相关的有序性状。我们使用局部优势比GEE技术来解释家庭成员和有序分类特征之间的复杂相关性结构。我们使用回顾性的思想将遗传标记作为随机变量来计算标记之间的遗传相关性。所提出的遗传关联方法可以适应序数性状,并允许协变量调整。我们进行了模拟研究,将所提出的测试与现有的模型进行比较,以分析各种配置下的有序分类数据。我们通过同时分析遗传分析工作坊19(GAW19)数据的一项家庭研究和一项横断面研究来说明所提出的测试的应用。
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引用次数: 0
Frontmatter 头版头条
4区 数学 Pub Date : 2023-05-01 DOI: 10.1515/ijb-2023-frontmatter1
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引用次数: 0
Approximate reciprocal relationship between two cause-specific hazard ratios in COVID-19 data with mutually exclusive events 在具有互斥事件的COVID-19数据中,两个病因特异性风险比之间存在近似的倒数关系
IF 1.2 4区 数学 Pub Date : 2021-04-27 DOI: 10.1101/2021.04.22.21255955
Wentian Li, S. Cetin, A. Ulgen, M. Cetin, Hakan Şıvgın, Yaning Yang
Abstract COVID-19 survival data presents a special situation where not only the time-to-event period is short, but also the two events or outcome types, death and release from hospital, are mutually exclusive, leading to two cause-specific hazard ratios (csHR d and csHR r ). The eventual mortality/release outcome is also analyzed by logistic regression to obtain odds-ratio (OR). We have the following three empirical observations: (1) The magnitude of OR is an upper limit of the csHR d : |log(OR)| ≥ |log(csHR d )|. This relationship between OR and HR might be understood from the definition of the two quantities; (2) csHR d and csHR r point in opposite directions: log(csHR d ) ⋅ log(csHR r ) < 0; This relation is a direct consequence of the nature of the two events; and (3) there is a tendency for a reciprocal relation between csHR d and csHR r : csHR d ∼ 1/csHR r . Though an approximate reciprocal trend between the two hazard ratios is in indication that the same factor causing faster death also lead to slow recovery by a similar mechanism, and vice versa, a quantitative relation between csHR d and csHR r in this context is not obvious. These results may help future analyses of data from COVID-19 or other similar diseases, in particular if the deceased patients are lacking, whereas surviving patients are abundant.
摘要新冠肺炎生存数据呈现出一种特殊情况,即不仅事件发生时间短,而且死亡和出院这两种事件或结果类型相互排斥,导致两种原因特异性风险比(csHR d和csHR r)。最终的死亡率/释放结果也通过逻辑回归进行分析,以获得比值比(OR)。我们有以下三个经验观察结果:(1)OR的大小是csHR d:|log(OR)|≥|log(csHR d)|的上限。OR和HR之间的这种关系可以从这两个量的定义中理解;(2) csHR d和csHR r指向相反的方向:log(csHR d)-log(csHRr)<0;这种关系是这两个事件性质的直接结果;和(3)csHR d和csHR r之间存在一种相互关系的趋势:csHR d~1/csHR r。尽管两个危险比之间的近似倒数趋势表明,导致更快死亡的同一因素也会通过类似的机制导致缓慢恢复,反之亦然,但在这种情况下,csHR d和csHR r之间的定量关系并不明显。这些结果可能有助于未来分析新冠肺炎或其他类似疾病的数据,特别是如果死亡患者缺乏,而幸存患者充足。
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引用次数: 3
Asymptotic properties of the two one-sided t-tests – new insights and the Schuirmann-constant 两个单侧t检验的渐近性质——新见解和Schuirmann常数
IF 1.2 4区 数学 Pub Date : 2021-01-08 DOI: 10.1515/IJB-2020-0057
Christian Palmes, Tobias Bluhmki, Benedikt Funke, E. Bluhmki
Abstract The two one-sided t-tests (TOST) method is the most popular statistical equivalence test with many areas of application, i.e., in the pharmaceutical industry. Proper sample size calculation is needed in order to show equivalence with a certain power. Here, the crucial problem of choosing a suitable mean-difference in TOST sample size calculations is addressed. As an alternative concept, it is assumed that the mean-difference follows an a-priori distribution. Special interest is given to the uniform and some centered triangle a-priori distributions. Using a newly developed asymptotical theory a helpful analogy principle is found: every a-priori distribution corresponds to a point mean-difference, which we call its Schuirmann-constant. This constant does not depend on the standard deviation and aims to support the investigator in finding a well-considered mean-difference for proper sample size calculations in complex data situations. In addition to the proposed concept, we demonstrate that well-known sample size approximation formulas in the literature are in fact biased and state their unbiased corrections as well. Moreover, an R package is provided for a right away application of our newly developed concepts.
摘要双单侧t检验(TOST)方法是最常用的统计等价检验方法,在许多领域都有应用,如制药行业。为了在一定的幂次下显示等值,需要适当的样本量计算。在这里,选择一个合适的平均差在TOST样本大小计算的关键问题是解决。作为一种替代概念,假设均值差遵循先验分布。对均匀分布和一些有中心的三角形先验分布特别感兴趣。利用一个新发展的渐近理论,我们发现了一个有用的类比原理:每个先验分布对应于一个点均值差,我们称之为它的舒尔曼常数。这个常数不依赖于标准偏差,旨在支持研究者在复杂的数据情况下找到一个经过深思熟虑的平均差异,以进行适当的样本量计算。除了提出的概念外,我们还证明了文献中众所周知的样本量近似公式实际上是有偏的,并说明了它们的无偏修正。此外,还提供了一个R包,可以立即应用我们新开发的概念。
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引用次数: 1
Estimation of semi-Markov multi-state models: a comparison of the sojourn times and transition intensities approaches 半马尔可夫多状态模型的估计:逗留时间和转移强度方法的比较
IF 1.2 4区 数学 Pub Date : 2020-05-29 DOI: 10.1515/IJB-2020-0083
A. Asanjarani, B. Liquet, Y. Nazarathy
Abstract Semi-Markov models are widely used for survival analysis and reliability analysis. In general, there are two competing parameterizations and each entails its own interpretation and inference properties. On the one hand, a semi-Markov process can be defined based on the distribution of sojourn times, often via hazard rates, together with transition probabilities of an embedded Markov chain. On the other hand, intensity transition functions may be used, often referred to as the hazard rates of the semi-Markov process. We summarize and contrast these two parameterizations both from a probabilistic and an inference perspective, and we highlight relationships between the two approaches. In general, the intensity transition based approach allows the likelihood to be split into likelihoods of two-state models having fewer parameters, allowing efficient computation and usage of many survival analysis tools. Nevertheless, in certain cases the sojourn time based approach is natural and has been exploited extensively in applications. In contrasting the two approaches and contemporary relevant R packages used for inference, we use two real datasets highlighting the probabilistic and inference properties of each approach. This analysis is accompanied by an R vignette.
摘要半马尔可夫模型广泛用于生存分析和可靠性分析。一般来说,有两个相互竞争的参数化,每个参数化都有自己的解释和推理特性。一方面,半马尔可夫过程可以基于逗留时间的分布来定义,通常通过风险率,以及嵌入马尔可夫链的转移概率。另一方面,可以使用强度转移函数,通常称为半马尔可夫过程的风险率。我们从概率和推理的角度总结和比较了这两种参数化,并强调了两种方法之间的关系。通常,基于强度转换的方法允许将似然性划分为具有较少参数的两状态模型的似然性,从而允许高效计算和使用许多生存分析工具。然而,在某些情况下,基于逗留时间的方法是自然的,并且在应用中得到了广泛的利用。在对比这两种方法和用于推理的当代相关R包时,我们使用了两个真实数据集,突出了每种方法的概率和推理特性。此分析附有一个R小插曲。
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引用次数: 14
Incorporating Contact Network Uncertainty in Individual Level Models of Infectious Disease using Approximate Bayesian Computation 用近似贝叶斯计算纳入传染病个体水平模型中的接触网络不确定性
IF 1.2 4区 数学 Pub Date : 2019-12-10 DOI: 10.1515/ijb-2017-0092
Waleed Almutiry, R. Deardon
Abstract Infectious disease transmission between individuals in a heterogeneous population is often best modelled through a contact network. However, such contact network data are often unobserved. Such missing data can be accounted for in a Bayesian data augmented framework using Markov chain Monte Carlo (MCMC). Unfortunately, fitting models in such a framework can be highly computationally intensive. We investigate the fitting of network-based infectious disease models with completely unknown contact networks using approximate Bayesian computation population Monte Carlo (ABC-PMC) methods. This is done in the context of both simulated data, and data from the UK 2001 foot-and-mouth disease epidemic. We show that ABC-PMC is able to obtain reasonable approximations of the underlying infectious disease model with huge savings in computation time when compared to a full Bayesian MCMC analysis.
摘要异质人群中个体之间的传染病传播通常最好通过接触网络进行建模。然而,这样的联系网络数据往往是不被注意到的。这种缺失的数据可以在使用马尔可夫链蒙特卡罗(MCMC)的贝叶斯数据增强框架中解释。不幸的是,在这样的框架中拟合模型可能是高度计算密集型的。我们使用近似贝叶斯计算群体蒙特卡罗(ABC-PCC)方法研究了具有完全未知接触网络的基于网络的传染病模型的拟合。这是在模拟数据和英国2001年口蹄疫疫情数据的背景下进行的。我们表明,与完整的贝叶斯MCMC分析相比,ABC-PC能够获得潜在传染病模型的合理近似值,并节省了大量的计算时间。
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引用次数: 7
Bayesian Autoregressive Frailty Models for Inference in Recurrent Events 递归事件推理的贝叶斯自回归脆弱性模型
IF 1.2 4区 数学 Pub Date : 2019-11-21 DOI: 10.1515/ijb-2018-0088
Marta Tallarita, M. De Iorio, A. Guglielmi, J. Malone‐Lee
Abstract We propose autoregressive Bayesian semi-parametric models for gap times between recurrent events. The aim is two-fold: inference on the effect of possibly time-varying covariates on the gap times and clustering of individuals based on the time trajectory of the recurrent event. Time-dependency between gap times is taken into account through the specification of an autoregressive component for the frailty parameters influencing the response at different times. The order of the autoregression may be assumed unknown and is an object of inference. We consider two alternative approaches to perform model selection under this scenario. Covariates may be easily included in the regression framework and censoring and missing data are easily accounted for. As the proposed methodologies lie within the class of Dirichlet process mixtures, posterior inference can be performed through efficient MCMC algorithms. We illustrate the approach through simulations and medical applications involving recurrent hospitalizations of cancer patients and successive urinary tract infections.
摘要:我们提出了自回归的贝叶斯半参数模型来描述重复事件之间的间隔时间。目的是双重的:推断可能时变的协变量对间隔时间和基于重复事件的时间轨迹的个体聚类的影响。通过对影响不同时间响应的脆弱参数的自回归分量的说明,考虑了间隙时间之间的时间依赖性。自回归的阶数可以假定为未知,并作为推理的对象。在这种情况下,我们考虑了两种可选的方法来执行模型选择。协变量可以很容易地包含在回归框架中,并且很容易解释删减和丢失的数据。由于所提出的方法属于Dirichlet过程混合类,后验推理可以通过高效的MCMC算法来执行。我们通过模拟和涉及癌症患者反复住院和连续尿路感染的医学应用来说明该方法。
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引用次数: 2
期刊
International Journal of Biostatistics
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