Sensitivity analysis for missing-not-at-random mechanisms in complex survey data using delta-adjusted multiple imputation

Abstract

Missing data are common in complex surveys studies and can compromise statistical inference when assumptions about the missing data mechanism are violated. Although multiple imputation is widely used under the missing at random (MAR) assumption, MAR is inherently unverifiable and may be implausible in large population-based surveys. This study aimed to evaluate delta-adjustment sensitivity analysis as a principled approach for assessing the robustness of MAR-based inferences to missing not at random (MNAR) mechanisms in complex survey data. We assessed the performance of complete case analysis, multiple imputation under MAR and delta-adjusted pattern-mixture models in a survey-weighted logistic regression framework with data on 20,200 children from the 2022–2023 Yemen Multiple Indicator Cluster Survey. The assumption of missing completely at random (MCAR) was rejected. Multiple imputation yielded more efficient estimates than complete case analysis. Effect estimates were robust in terms of direction and magnitude and the inferential conclusions did not change across a wide range of prespecified delta values which represent increasingly extreme MNAR scenarios. No tipping point was found where the substantive conclusions diverged from those under MAR. These findings demonstrate the potential to routinely embed delta-adjustment sensitivity analysis within multiple imputation in order to enhance the transparency, believability and interpretability of analyses of incomplete complex survey data.