Longitudinal Statistics

This page describes ways of analyzing longitudinal data after processing it using the longitudinal stream in Freesurfer.

Longitudinal data is different from cross sectional data, as repeated measures are correlated within each subject. A statistical analysis should consider this correlation.

Freesurfer currently comes with (at least) three different frameworks for the analysis of longitudinal data:

  1. Simplified repeated measures ANOVA (ignores correlation)
  2. Direct analysis of atrophy rates or percent changes (avoids treatment of correlation)
  3. Linear mixed effects models (considers correlation)

Simplified Repeated Measures ANOVA

This method can be used to check for differences between individual time points or compare time point differences across groups. This simple version, however, does NOT consider the correlation of the repeated measures! For two time points it simplifies to a PairedAnalysis.

For details see: RepeatedMeasuresAnova

Analysis of Rates or Percent Changes

To analyze, e.g. anualzied percent change or atropy rates for 2 or more time points, one can run a two stage model. This avoids dealing with the longitudinal correlation. The two stages are:

This can be done both for individual ROI stats (aseg or aparc.stats) or for thickness maps on the cortex. This model is quite simple and can be a good choice if all subjects have the same number of time points. The time points can be differently spaced, this is compensated by the time variable. Linear fits into each subject data are often meaningful, as longitudinal change is almost linear within a short time frame of a few years. However, this model does not consider that slopes of subjects with only a few time points are not as reliable as the ones obtained from subjects with many time points.

For details see: LongitudinalTwoStageModel

Linear Mixed Effects Model

A Linear Mixed Effects (LME) model is the most powerful approach and can deal well with differently many time points. Even subjects with only a single time point can be included into these models (make sure they also run through the longitudinal stream, available with version FS 5.2, to avoid a bias due to different processing). LMEs consider the temporal correlation and our mass-univariate method can deal very well with the spacial correlation of measures on the cortex. Furthermore, LMEs can be used to model more complex longitudinal behaviour (e.g. quadratic, or piecewise linear trajectories). Currently our implementation is in Matlab.

For details see: LinearMixedEffectsModels