Analyses of Sensitivity to the Missing-at-Random Assumption Using Multiple Imputation With Delta Adjustment: Application to a Tuberculosis/HIV Prevalence Survey With Incomplete HIV-Status Data

Abstract

Multiple imputation with delta adjustment provides a flexible and transparent means to impute univariate missing data under general missing-not-at-random mechanisms. This facilitates the conduct of analyses assessing sensitivity to the missing-at-random (MAR) assumption. We review the delta-adjustment procedure and demonstrate how it can be used to assess sensitivity to departures from MAR, both when estimating the prevalence of a partially observed outcome and when performing parametric causal mediation analyses with a partially observed mediator. We illustrate the approach using data from 34,446 respondents to a tuberculosis and human immunodeficiency virus (HIV) prevalence survey that was conducted as part of the Zambia–South Africa TB and AIDS Reduction Study (2006–2010). In this study, information on partially observed HIV serological values was supplemented by additional information on self-reported HIV status. We present results from 2 types of sensitivity analysis: The first assumed that the degree of departure from MAR was the same for all individuals with missing HIV serological values; the second assumed that the degree of departure from MAR varied according to an individual's self-reported HIV status. Our analyses demonstrate that multiple imputation offers a principled approach by which to incorporate auxiliary information on self-reported HIV status into analyses based on partially observed HIV serological values.

Analytical methods used in estimating the prevalence of HIV/AIDS from demographic and cross-sectional surveys with missing data: a systematic review

“…The use of doubly robust methods and extension of Heckman's selection models are the current methods identified as suitable when data are assumed to be MNAR. With the assumption that the missing data on HIV prevalence studies not being MAR, and the possibility of MNAR [54,68], it is important to explore more methods than identified from this review. Further to the analysis, a report from National Research Council (NRC) [73] explains the importance of conducting sensitivity analysis to assess the robustness of the results and conclusion of the assumptions used on the application of methods used to adjust for missing data.…”

Dealing with missing outcome data in meta‐analysis

“…In principle, a distribution of IMPs could be used for each reason group, but this is not currently available in statistical software. IPD would facilitate more complex analyses, perhaps using multiple imputation with MNAR mechanisms (see, eg, Leacy et al). Alternative fully Bayesian approaches have been proposed …”

Do Maternal Dietary Antioxidants Modify the Relationship Between Binge Drinking and Small for Gestational Age? Findings from a Longitudinal Cohort Study

“…Variables were imputed using the following models: maternal age, education, housing tenure, HCI, vitamin C, vitamin E, and carotenoids using an ordinal logistic regression model; and SGA, binge drinking, smoking, parity, ethnicity, child gender, and breastfeeding (auxiliary variable), using binary logistic regression models. We conducted a sensitivity analysis to test the MAR assumption (Héraud‐Bousquet et al., ) by exploring the extreme effect estimates compatible with the observed data (Leacy et al., ). We hypothesized that, due to social‐desirability bias, pregnant women who do binge drink are less likely to report this (Meiklejohn et al., ; Wild et al., ).…”