Multiple imputation (MI) is a powerful statistical method for handling missing data. Standard implementations of MI are valid under the unverifiable assumption of missing at random (MAR), which is often implausible in practice. The delta-adjustment method, implemented within the MI framework, can be used to perform sensitivity analyses that assess the impact of departures from the MAR assumption on the final inference. This method requires specification of unknown sensitivity parameter(s) (termed as delta(s)). We illustrate the application of the delta-adjustment method using data from the Longitudinal Study of Australian Children, where the epidemiological question is to estimate the association between exposure to maternal emotional distress at age 4–5 years and total (social, emotional, and behavioural) difficulties at age 8–9 years. We elicited the sensitivity parameters for the outcome (????????) and exposure (????????) variables from a panel of experts. The elicited quantile judgements from each expert were converted into a suitable parametric probability distribution and combined using the linear pooling method. We then applied MI under MAR followed by sensitivity analyses under missing not at random (MNAR) using the delta-adjustment method. We present results from sensitivity analyses that used different percentile values of the pooled distributions for the delta parameters for ???????? and ????????, and demonstrate that twofold increases in the magnitude of the association between maternal distress and total difficulties are only observed for large departures from MAR.

中文翻译：

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在多插补框架内使用增量调整进行敏感性分析：在澳大利亚儿童纵向研究中的应用

多重插补（MI）是一种用于处理缺失数据的强大统计方法。MI的标准实现在不可验证的随机缺失（MAR）假设下有效，这在实践中通常是不可信的。在MI框架内实现的增量调整方法可用于执行敏感性分析，以评估偏离MAR假设对最终推断的影响。该方法需要指定未知的灵敏度参数（称为增量）。我们使用来自澳大利亚儿童纵向研究的数据说明了增量调整方法的应用，其中流行病学问题是估计4-5岁时母体情绪困扰的暴露与总体（社会，情感和行为）之间的关联）8-9岁的困难。我们从一个专家小组中得出了结果（??????????）和暴露（??????????）变量的敏感性参数。由每个专家得出的分位数判断被转换为合适的参数概率分布，并使用线性合并方法进行组合。然后，我们在MAR下应用MI，然后使用增量调整法在不随机缺失（MNAR）下进行敏感性分析。我们提供了灵敏度分析的结果，该灵敏度分析使用了合并分布的不同百分数值作为ΔεΔεδ的增量参数。，并证明，只有在与MAR大相径庭的情况下，才能观察到孕产妇窘迫与总困难之间的关联程度增加了两倍。