A Bayesian multivariate model with a structured covariance matrix for multi-way nested data is proposed. This flexible modeling framework allows for positive and for negative associations among clustered observations, and generalizes the well-known dependence structure implied by random effects. A conjugate shifted-inverse gamma prior is proposed for the covariance parameters which ensures that the covariance matrix remains positive definite under posterior analysis. A numerically efficient Gibbs sampling procedure is defined for balanced nested designs, and is validated using two simulation studies. For a top-layer unbalanced nested design, the procedure requires an additional data augmentation step. The proposed data augmentation procedure facilitates sampling latent variables from (truncated) univariate normal distributions, and avoids numerical computation of the inverse of the structured covariance matrix. The Bayesian multivariate (linear transformation) model is applied to two-way nested interval-censored event times to analyze differences in adverse events between three groups of patients, who were randomly allocated to treatment with different stents (BIO-RESORT). The parameters of the structured covariance matrix represent unobserved heterogeneity in treatment effects and are examined to detect differential treatment effects.
翻译:提出了一个包含多路巢数据结构共变矩阵的Bayesian多变量模型。 这个灵活的模型框架允许集束观测中出现正和负的关联,并概括了随机效应所隐含的众所周知的依附性结构。 为共变参数建议了一个共变偏移前方,以确保共变矩阵在后继分析中仍然是肯定的。一个数字高效的Gbs抽样程序是为平衡的巢式设计而定义的,并使用两个模拟研究加以验证。对于顶层不平衡的巢式设计,程序要求增加一个数据增强步骤。拟议的数据增强程序有利于从(连续的)正常分布中取样潜在变量,避免对结构化共变异矩阵的反向进行数字计算。Bayesian多变式(线性变换)模型适用于双向嵌入的嵌入间间隔事件,以分析三组病人之间的不利事件差异,这些病人被随机分配给不同用途的治疗(BIO-RESORT),拟议的数据增强程序要求增加一个数据增强步骤。拟议的数据增强程序有助于从(连续)未流正常分布式分布式分布式分布式分布,并避免对结构变式治疗效果的参数进行检测结果的参数。