Local sensitivity to non-ignorability in joint models

This article deals with the analysis of sensitivity to the non-ignorability of the dropout process in joint models (JMs). We investigate the behaviour of the maximum likelihood estimates for the longitudinal process in a neighbourhood of ignorability through the Index of Local Sensitivity to Non Ignorability (ISNI). Some concerns may arise since the ISNI is an absolute measure of change in parameter estimates induced by departures from the MAR assumption; for this reason, we introduce a relative index based on the ratio between the ISNI and a measure of its variability under the MAR assumption, highlighting potential interpretation and drawbacks of this approach. The local sensitivity of the JM and the performance of the relative index are discussed in a simulation study, by varying the number of repeated measurements per individual and the random effect covariance structure. The approach is also applied to a benchmark dataset on Primary Biliary Cirrhosis (PBC).