Linear Mixed Effects Models for Non-Gaussian Continuous Repeated Measurement Data

Abstract

We consider the analysis of continuous repeated measurement outcomes that are collected longitudinally. A standard framework for analysing data of this kind is a linear Gaussian mixed effects model within which the outcome variable can be decomposed into fixed effects, time invariant and time-varying random effects, and measurement noise. We develop methodology that, for the first time, allows any combination of these stochastic components to be non-Gaussian, using multivariate normal variance-mean mixtures. To meet the computational challenges that are presented by large data sets, i.e. in the current context, data sets with many subjects and/or many repeated measurements per subject, we propose a novel implementation of maximum likelihood estimation using a computationally efficient subsampling-based stochastic gradient algorithm. We obtain standard error estimates by inverting the observed Fisher information matrix and obtain the predictive distributions for the random effects in both filtering (conditioning on past and current data) and smoothing (conditioning on all data) contexts. To implement these procedures, we introduce an R package: ngme. We reanalyse two data sets, from cystic fibrosis and nephrology research, that were previously analysed by using Gaussian linear mixed effects models.

Functional data analysis and prediction tools for continuous glucose-monitoring studies

“…The main effects are linearly included in model (1); however, the model is able to predict nonlinear curves. It was shown to outperform traditional random slope-intercept models when data has long sequences of repeated measurements [32,33] which is the case for our CGM data. Some model details are provided below.…”

Scale mixture of skew‐normal linear mixed models with within‐subject serial dependence

“…38 It is worth emphasizing that even though the model formulation ensures that the random effect and the error terms are UNC, they are not independent in general. In this regard, an interesting extension would be to consider different mixing variables for the random effect and for the error, as in Asar et al, 16 but in this case the likelihood function has no closed form and therefore the use of approximated approaches, such as a Monte Carlo EM algorithm, is necessary. Another promising avenue for future research is to consider the class of generalized hyperbolic (GH) distributions 39 which is generated by a variance-mean mixture of a multivariate Gaussian with a generalized inverse Gaussian distribution.…”

“…There are some recent proposes in the literature that account for the time dependence in longitudinal data. For instance, Chang and Zimmerman 15 proposed to use SN antedependence models for modeling skewed longitudinal data exhibiting serial correlation, Asar et al 16 proposed a methodology using multivariate normal variance-mean mixtures to fit linear mixed effects models for non-Gaussian continuous repeated measurement data, and Lachos et al 17 considered a robust generalization of the multivariate censored LMM based on the scale mixtures of normal (SMN) distributions, with a damped exponential correlation (DEC) structure to take into account the autocorrelation among measurements.…”

Dynamic predictions of kidney graft survival in the presence of longitudinal outliers

“…We indeed follow the setting that was conducted in Asar et al. 36 Landmark time point 4, i.e. s = 4, was considered for forecasting.…”

“…The idea behind 100 replications was to obtain data from the desired distribution, whereas the idea behind two subjects was to keep heterogeneity due to individuals low. We indeed follow the setting that was conducted in Asar et al 36 Landmark time point 4, i.e. s ¼ 4, was considered for forecasting.…”