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Sensitivity analysis within multiple imputation framework using delta-adjustment: Application to Longitudinal Study of Australian Children

Panteha Hayati Rezvan, Katherine J. Lee, Julie A. Simpson


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 (𝑌𝑌) and exposure (𝑋𝑋) 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 𝑌𝑌 and 𝑋𝑋, 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.


Missing data; multiple imputation; missing not at random; sensitivity analysis; delta-adjustment method; elicitation

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Copyright (c) 2018 Panteha Hayati Rezvan, Katherine J. Lee, Julie A. Simpson

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