Missing data are frequently encountered in longitudinal clinical trials. To better monitor and understand the progress over time, one must handle the missing data appropriately and examine whether the missing data mechanism is ignorable or nonignorable. In this article, we develop a new probit model for longitudinal binary response data. It resolves a challenging issue for estimating the variance of the random effects, and substantially improves the convergence and mixing of the Gibbs sampling algorithm. We show that when improper uniform priors are specified for the regression coefficients of the joint multinomial model via a sequence of one-dimensional conditional distributions for the missing data indicators under nonignorable missingness, the joint posterior distribution is improper. A variation of Jeffreys prior is thus established as a remedy for the improper posterior distribution. In addition, an efficient Gibbs sampling algorithm is developed using a collapsing technique. Two model assessment criteria, the deviance information criterion (DIC) and the logarithm of the pseudomarginal likelihood (LPML), are used to guide the choices of prior specifications and to compare the models under different missing data mechanisms. We report on extensive simulations conducted to investigate the empirical performance of the proposed methods. The proposed methodology is further illustrated using data from an HIV prevention clinical trial.

中文翻译：

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贝叶斯建模和推断不可忽视的纵向二元反应数据与 HIV 预防试验的应用

在纵向临床试验中经常会遇到数据缺失的情况。为了更好地监控和了解随时间推移的进展，必须适当处理缺失数据并检查缺失数据机制是可忽略的还是不可忽略的。在本文中，我们为纵向二元响应数据开发了一个新的概率模型。它解决了估计随机效应方差的一个具有挑战性的问题，并大大提高了 Gibbs 采样算法的收敛性和混合性。我们表明，当通过不可忽略缺失下缺失数据指标的一维条件分布序列为联合多项式模型的回归系数指定不正确的均匀先验时，联合后验分布是不正确的。因此，Jeffreys 先验的变体被确立为对不正确的后验分布的补救。此外，使用折叠技术开发了一种高效的吉布斯采样算法。两个模型评估标准，偏差信息标准（DIC）和伪边际似然的对数（LPML），用于指导先验规范的选择，并在不同的缺失数据机制下比较模型。我们报告了为研究所提出方法的经验性能而进行的广泛模拟。使用来自 HIV 预防临床试验的数据进一步说明了所提议的方法。偏差信息准则 (DIC) 和伪边际似然的对数 (LPML) 用于指导先验规范的选择并比较不同缺失数据机制下的模型。我们报告了为研究所提出方法的经验性能而进行的广泛模拟。使用来自 HIV 预防临床试验的数据进一步说明了所提议的方法。偏差信息准则 (DIC) 和伪边际似然的对数 (LPML) 用于指导先验规范的选择并比较不同缺失数据机制下的模型。我们报告了为研究所提出方法的经验性能而进行的广泛模拟。使用来自 HIV 预防临床试验的数据进一步说明了所提议的方法。