Analysis of ordinal longitudinal data under nonignorable missingness and misreporting: An application to Alzheimer's disease study

In many epidemiological and clinical studies, observations on individuals are recorded longitudinally on a Likert-type scale. In the process of recording, or due to some other causes, a proportion of outcomes and time-dependent covariates may be missing in one or more follow-up visits (non monotone missing). Even when the number of patients with intermittent missing data is small, exclusion of those patients from the study seems unsatisfactory. This apart, often due to misreporting, miscategorization of response can occur that results in potentially invalid inference when no correction is made. We propose a joint mixed model that corrects the likelihood function to account for missing response and/or covariates and adjusts the likelihood to tackle miscategorization of response. Under this extreme complex but useful setup, we seek to estimate the parameters of the proposed model that accounts for baseline and/or time dependent covariates. Monte Carlo expectation-maximization (MCEM) is a convenient approach for estimating the parameters in the model. A simulation study was carried out to assess the approach. We also analyzed Alzheimer's Disease Neuroimaging Initiative (ADNI) data where some responses and covariates are missing and some responses are possibly miscategorized. Our investigation reveals that apolipo-protein plays a significant role in Alzheimer's disease progression. This was not visible in earlier analyses of ADNI data.