Pattern Mixture Models and Latent Class Models for the Analysis of Multivariate Longitudinal Data with Informative Dropouts

Abstract

Missing data and especially dropouts frequently arise in longitudinal data. Maximum likelihood estimates are consistent when data are missing at random (MAR) but, as this assumption is not checkable, pattern mixture models (PMM) have been developed to deal with informative dropout. More recently, latent class models (LCM) have been proposed as a way to relax PMM assumptions. The aim of this paper is to compare PMM and LCM in order to tackle informative dropout in a longitudinal study of cognitive ageing measured by several psychometric tests. Using a multivariate longitudinal model with a latent process, a sensitivity analysis was performed to compare estimates under the MAR assumption, from a PMM and from two LCM. In the PMM, dropout patterns are included as covariates in the multivariate longitudinal model. In the simple LCM, they are predictors of the class membership probabilities while, in the joint LCM, the dropout time is jointly modeled using a proportional hazard model depending on latent classes. We show that parameter interpretation is different in the two kinds of models and thus can lead to different estimated values. PMM parameters are adjusted on the dropout patterns while LCM parameters are adjusted on the latent classes. This difference is highlighted in our data set because the latent classes exhibit much more heterogeneity than dropout patterns. We suggest several complementary analyses to investigate the characteristics of latent classes in order to understand the meaning of the parameters when using LCM to deal with informative dropout.

Mixed hidden Markov quantile regression models for longitudinal data with possibly incomplete sequences

“…al. 40 to formally test this hypothesis, at least for the observed data. For each quantile and for the chosen [G, m] combination, we estimated a lqHMM+LDO adding in the linear predictor the time to drop-out (we will refer to this model specification as M Ti (τ )) and its logarithm (we will refer to this model specification as M logTi (τ )), while keeping fixed the ML estimates for the LDO classes, as well as the corresponding posterior probabilities.…”

Analysis of NMAR missing data without specifying missing-data mechanisms in a linear latent variate model

“…with Σ ℓ and Γ ℓ given in (17). The asymptotic covariance matrix between the sample mean and variance matrix given R = r (ℓ) is given as C ℓ in (17) in a similar derivation.…”

“…The key concept of the modeling is conditional independence between Y and R given z or c. Albert and Follman [1] developed the continuous shared-parameter model in linear mixed models, and [17,47] have used latent class shared-parameter models in structural equation modeling. In their studies, the missing-data mechanisms are explicitly specified in estimation, and hence, it is useful only if an appropriate missing-data mechanism and its functional form can be found.…”

Analysis of Multivariate Longitudinal Data Subject to Nonrandom Dropout

“…Roy (2003) introduced a shared-parameter model in which the dependence between the measurement process and time of dropout is due to a shared latent variable that is assumed to be discrete, so that the marginal distribution of the measurement is a mixture over the dropout classes of the latent variable. Dantan, Proust-Lima, Letenneur, and Jacqmin-Gadda (2008) compare pattern-mixture models and latent class models in dealing with informative dropout.…”