Two-pronged Strategy for Using DIC to Compare Selection Models with Non-Ignorable Missing Responses
Two-pronged Strategy for Using DIC to Compare Selection Models with Non-Ignorable Missing Responses
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DOI：
10.1214/12-ba704
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发表时间：
2012-03
影响因子：
4.4
通讯作者：
A. Mason;S. Richardson;N. Best
中科院分区：
文献类型：
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作者：
A. Mason;S. Richardson;N. Best
通过对响应和指示响应是观察到的还是缺失的二元变量进行联合建模，可以分析由不可验证的缺失机制生成的缺失响应的数据。使用选择模型因子分解，得到的联合模型由感兴趣的模型和缺失模型组成。在不可验证的缺失情况下，模型选择是困难的，因为关于缺失模型的假设永远无法从手头的数据中得到验证。对于完整的数据，偏差信息标准（DIC）通常用于贝叶斯模型比较。然而，当分析包括缺失数据时，DIC可以以不同的方式构建，并且其使用和解释并不简单。在本文中，我们提出了一个战略，比较选择模型相结合的信息，从两个措施，从不同的建设DIC。使用基于观测数据似然的DIC来比较具有不同感兴趣模型但具有相同缺失模型的联合模型，并且使用条件DIC的缺失部分模型来执行具有相同感兴趣模型但具有不同缺失模型的模型的比较。该策略旨在用于敏感性分析，该分析探讨了模型两部分不同假设的影响，并通过模拟缺失的示例和使用临床试验数据比较三种抑郁症治疗方法的应用进行了说明。我们还研究了有关的DIC的计算所观察到的数据的可能性的基础上的问题。
Data with missing responses generated by a non-ignorable missing- ness mechanism can be analysed by jointly modelling the response and a binary variable indicating whether the response is observed or missing. Using a selection model factorisation, the resulting joint model consists of a model of interest and a model of missingness. In the case of non-ignorable missingness, model choice is di-cult because the assumptions about the missingness model are never veriflable from the data at hand. For complete data, the Deviance Information Criterion (DIC) is routinely used for Bayesian model comparison. However, when an anal- ysis includes missing data, DIC can be constructed in difierent ways and its use and interpretation are not straightforward. In this paper, we present a strategy for comparing selection models by combining information from two measures taken from difierent constructions of the DIC. A DIC based on the observed data likeli- hood is used to compare joint models with difierent models of interest but the same model of missingness, and a comparison of models with the same model of interest but difierent models of missingness is carried out using the model of missingness part of a conditional DIC. This strategy is intended for use within a sensitivity analysis that explores the impact of difierent assumptions about the two parts of the model, and is illustrated by examples with simulated missingness and an appli- cation which compares three treatments for depression using data from a clinical trial. We also examine issues relating to the calculation of the DIC based on the observed data likelihood.