A bi-dimensional finite mixture model for longitudinal data subject to dropout

TL;DR

This paper introduces a bi-dimensional finite mixture model for longitudinal data with non-ignorable dropout, capturing complex dependence structures and heterogeneity to improve analysis accuracy.

Contribution

It proposes a novel bi-dimensional latent class structure that models dependence between longitudinal outcomes and dropout, extending standard finite mixture models.

Findings

The model effectively captures dependence within and between margins.

Application to elderly cognitive data demonstrates practical utility.

Sensitivity analysis highlights impact of non-ignorability assumptions.

Abstract

In longitudinal studies, subjects may be lost to follow-up, or miss some of the planned visits, leading to incomplete response sequences. When the probability of non-response, conditional on the available covariates and the observed responses, still depends on unobserved outcomes, the dropout mechanism is said to be non ignorable. A common objective is to build a reliable association structure to account for dependence between the longitudinal and the dropout processes. Starting from the existing literature, we introduce a random coefficient based dropout model where the association between outcomes is modeled through discrete latent effects. These effects are outcome-specific and account for heterogeneity in the univariate profiles. Dependence between profiles is introduced by using a bi-dimensional representation for the corresponding distribution. In this way, we define a flexible latent class structure which allows to efficiently describe both dependence within the two margins of interest and dependence between them. By using this representation we show that, unlike standard (unidimensional) finite mixture models, the non ignorable dropout model properly nests its ignorable counterpart. We detail the proposed modeling approach by analyzing data from a longitudinal study on the dynamics of cognitive functioning in the elderly. Further, the effects of assumptions about non ignorability of the dropout process on model parameter estimates are (locally) investigated using the index of (local) sensitivity to non-ignorability.