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Rubin (1976) classified missing data as MCAR, MAR, and MNAR. Given that models for missing data often make unverifiable assumptions about the missing value mechanism, sensitivity analysis is needed. In joint modeling of time-to-event and longitudinal data, similar issues arise. The longitudinal covariate may be measured with error, its values are likewise only available at the specific time points at that the patient appears at the clinic for longitudinal measurements, and the time-to-event may also be censored.
Undeniably, there is a strong connection between the missing data and the joint longitudinal and time-to-event settings, the theme of this work. We build an extended shared random effects joint model, similar in spirit to that of Creemers et al (2011). An added layer of complexity is that data can be coarsened in various ways: the longitudinal sequence can be incomplete; the time-to-event outcome can be censored; both of these can occur simultaneously. Within the extended framework, we provide a characterization of MAR, consistent to the one in the missing data setting, and juxtapose it with more conventional joint models. This opens routes for sensitivity analysis.
Njeru Njagi, E., Molenberghs, G., Kenward, M.G., Verbeke, G., and Rizopoulos, D. (2014). A Characterization of Missingness at Random in a Generalized Shared-parameter Joint modelling Framework for Longitudinal and Time-to-Event Data, and Sensitivity Analysis. Biometrical Journal, 56, 1001-1015.


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