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.