An index of local sensitivity to non-ignorability for multivariate longitudinal mixed data with potential non-random dropout.

Multivariate longitudinal data with mixed continuous and discrete responses with the possibility of non-ignorable missingness are often common in follow-up medical studies and their analysis needs to be developed. Standard methods of analysis based on the strong and the unverifiable assumption of missing at random (MAR) mechanism could be highly misleading. A way out of this problem is to start with methods that simultaneously allow modelling non-ignorable mechanism, which includes somehow troubling computations that are often time consuming, then we can use a sensitivity analysis, in which one estimates models under a range of assumptions about non-ignorability parameters to study the impact of these parameters on key inferences. A general index of sensitivity to non-ignorability (ISNI) to measure sensitivity of key inferences in a neighborhood of MAR model without fitting a complicated not MAR (NMAR) model for univariate generalized linear models and for models used for univariate longitudinal normal and non-Gaussian data with potentially NMAR dropout are well presented in the literature. In this paper we extend ISNI methodology to analyze multivariate longitudinal mixed data subject to non-ignorable dropout in which the non-ignorable dropout model could be dependent on the mixed responses. The approach is illustrated by analyzing a longitudinal data set in which the general substantive goal of the study is to better understand the relations between parental assessment of child's antisocial behavior and child's reading recognition skill.