Joint modelling rationale for chained equations.
Joint modelling rationale for chained equations.
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DOI：
10.1186/1471-2288-14-28
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发表时间：
2014-02-21
影响因子：
4
通讯作者：
Sterne JA
中科院分区：
文献类型：
--
作者：
Hughes RA;White IR;Seaman SR;Carpenter JR;Tilling K;Sterne JA
链式方程插补在医学研究中有着广泛的应用。它使用一组条件模型，因此比联合建模插补更灵活，可以插补不同类型的变量（例如二元，有序或无序分类）。然而，当条件模型不相容时，链式方程插补不对应于从联合分布绘制。与我们的工作同时，其他作者已经证明了有限样本中两种插补方法的等价性。采取不同的方法，我们证明，在有限的样本，充分条件链式方程和联合建模产生插补从相同的预测分布。此外，我们应用这个证明在四个特定的情况下，并进行模拟研究，探讨的后果时，条件模型是兼容的，但条件不满足。我们提供了一个额外的“非信息性的利润”的条件，连同兼容性，是足够的。我们表明，非信息利润率条件是不满足的，尽管兼容的条件模型，在两个连续变量和一个二进制变量一样简单的情况下。我们的模拟研究表明，由于这种违反顺序的影响可能会发生，也就是说，系统的差异取决于在链式方程算法的变量的顺序。然而，顺序效应似乎很小，特别是当变量之间的关联很弱时。由于链式方程通常用于医学研究中具有不同类型变量的数据集，研究人员必须意识到顺序效应可能无处不在，但我们的结果表明它们可能小到可以忽略不计。
Chained equations imputation is widely used in medical research. It uses a set of conditional models, so is more flexible than joint modelling imputation for the imputation of different types of variables (e.g. binary, ordinal or unordered categorical). However, chained equations imputation does not correspond to drawing from a joint distribution when the conditional models are incompatible. Concurrently with our work, other authors have shown the equivalence of the two imputation methods in finite samples. Taking a different approach, we prove, in finite samples, sufficient conditions for chained equations and joint modelling to yield imputations from the same predictive distribution. Further, we apply this proof in four specific cases and conduct a simulation study which explores the consequences when the conditional models are compatible but the conditions otherwise are not satisfied. We provide an additional “non-informative margins” condition which, together with compatibility, is sufficient. We show that the non-informative margins condition is not satisfied, despite compatible conditional models, in a situation as simple as two continuous variables and one binary variable. Our simulation study demonstrates that as a consequence of this violation order effects can occur; that is, systematic differences depending upon the ordering of the variables in the chained equations algorithm. However, the order effects appear to be small, especially when associations between variables are weak. Since chained equations is typically used in medical research for datasets with different types of variables, researchers must be aware that order effects are likely to be ubiquitous, but our results suggest they may be small enough to be negligible.
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