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

<span class="paragraphSection"><div class="boxTitle">Abstract</div>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.</span>

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