Fast and accurate modelling of longitudinal and repeated measures neuroimaging data

Abstract

Despite the growing importance of longitudinal data in neuroimaging, the standard analysis methods make restrictive or unrealistic assumptions (e.g., assumption of Compound Symmetry—the state of all equal variances and equal correlations—or spatially homogeneous longitudinal correlations). While some new methods have been proposed to more accurately account for such data, these methods are based on iterative algorithms that are slow and failure-prone. In this article, we propose the use of the Sandwich Estimator method which first estimates the parameters of interest with a simple Ordinary Least Square model and second estimates variances/covariances with the “so-called” Sandwich Estimator (SwE) which accounts for the within-subject correlation existing in longitudinal data. Here, we introduce the SwE method in its classic form, and we review and propose several adjustments to improve its behaviour, specifically in small samples. We use intensive Monte Carlo simulations to compare all considered adjustments and isolate the best combination for neuroimaging data. We also compare the SwE method to other popular methods and demonstrate its strengths and weaknesses. Finally, we analyse a highly unbalanced longitudinal dataset from the Alzheimer's Disease Neuroimaging Initiative and demonstrate the flexibility of the SwE method to fit within- and between-subject effects in a single model. Software implementing this SwE method has been made freely available at http://warwick.ac.uk/tenichols/SwE.

Less Efficient Neural Processing Related to Irregular Sleep and Less Sustained Attention in Toddlers

“…The clustered regression models were fit using the rms package (Harrell Jr, 2014) in R 3.0 (R Core Team, 2012) that calculates robust standard errors using a robust (Huber-White sandwich) estimator of the covariance matrix (Huber, 1967; White, 1980). Sandwich estimators are widely used to account for data dependency in regression models (for an example using sandwich estimators in the context of longitudinal neuroimaging, see Guillaume et al, 2014). …”

STGP: Spatio-temporal Gaussian process models for longitudinal neuroimaging data

“…The second one is the sparse sampling design, in that the number of observations per subject is relatively small, that is, max i m i < ∞. In this case, we may consider a parametric function of μ ( d , x i ( t )) based on either linear (or nonlinear) mixed effects models or generalized estimating equations μ ( d , x i ( t )) [Bernal-Rusiel et al, 2013, Li et al, 2013, Guillaume et al, 2014, Skup et al, 2012]. Moreover, even under this scenario, if time points t ij are randomly drawn, we may fit a nonparametric function of μ ( d , x i ( t )).…”

“…These models usually cannot capture complex spatial-temporal correlation of longitudinal neuroimaging data. The second one, usually identified as voxel-based analysis, is to fit some parametric or semi-parametric regression models (e.g., linear mixed effects and estimating equations) at each voxel of registered images [Bernal-Rusiel et al, 2013, Li et al, 2013, Yuan et al, 2013, Guillaume et al, 2014, Skup et al, 2012]. These models usually ignore the moderate-to-long range spatial correlation of imaging data, even though local spatial correlation is usually introduced by the use of Gaussian smoothing with some apriori kernel size.…”

Bayesian longitudinal low-rank regression models for imaging genetic data from longitudinal studies

“…A standard statistical method used in longitudinal imaging and genetics studies is the massive marginal association (MMA) framework (Li et al, 2013; Zhang et al, 2014; Guillaume et al, 2014; Hibar and et al, 2011; Shen et al, 2010; Bernal-Rusiel et al, 2013; Zhang et al, 2014). This approach repeatedly fits a linear mixed effects model (or generalized estimating equations) for paired imaging phenotypes and genetic markers.…”