Momeni Roochi Elahe, Eftekhari Mahabadi Samaneh
School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran.
Int J Biostat. 2023 Nov 27;20(2):599-629. doi: 10.1515/ijb-2022-0014. eCollection 2024 Nov 1.
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.
由于个体在预定完成时间之前退出，不完整数据是纵向研究中普遍存在的并发症。目前通过商业软件分析不完整纵向数据的可用方法充其量依赖于退出的可忽略性。如果潜在的缺失机制不可忽略，则统计推断中会出现潜在偏差。为了在退出不可忽略时消除偏差，已经提出了联合完整数据和退出模型，这些模型存在计算困难和无法检验的假设。由于基于样本的观察部分无法验证关键的可忽略性假设，文献中提出了一些局部敏感性指标。具体而言，Eftekhari Mahabadi（贝叶斯推断中对不可忽略性的二阶局部敏感性。统计医学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敏感性工具，并表明其在处理偏差方面比一阶工具具有更好的性能。在本文中，我们旨在将该指标扩展到具有退出情况的正态纵向研究的贝叶斯敏感性分析。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。给出的公式使用后验估计计算，并从更简单的可忽略模型中抽取。通过一些模拟研究和对真实抗抑郁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，在MAR模型附近，回归系数估计值几乎可以由线性函数很好地近似，但在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数量的二阶敏感性。
