Motivated by the Swedish Betula study, we consider the joint modeling of longitudinal memory assessments and the hazard of dementia. In the Betula data, the time-to-dementia onset or its absence is available for all participants, while some memory measurements are missing. In longitudinal studies of aging, one cannot rule out the possibility of dropout due to health issues resulting in missing not at random longitudinal measurements. We, therefore, propose a pattern-mixture sensitivity analysis for missing not-at-random data in the joint modeling framework. The sensitivity analysis is implemented via multiple imputation as follows: (i) multiply impute missing not at random longitudinal measurements under a set of plausible pattern-mixture imputation models that allow for acceleration of memory decline after dropout, (ii) fit the joint model to each imputed longitudinal memory and time-to-dementia dataset, and (iii) combine the results of step (ii). Our work illustrates that sensitivity analyses via multiple imputations are an accessible, pragmatic method to evaluate the consequences of missing not at-random data on inference and prediction. This flexible approach can accommodate a range of models for the longitudinal and event-time processes. In particular, the pattern-mixture modeling approach provides an accessible way to frame plausible missing not at random assumptions for different missing data patterns. Applying our approach to the Betula study shows that worse memory levels and steeper memory decline were associated with a higher risk of dementia for all considered scenarios.