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) <-- recommended, but more complex


Simplified Repeated Measures ANOVA

This method can be used to check for differences between individual time points or compare time point differences across groups. For two time points it simplifies to a PairedAnalysis.

Disadvantages:

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:

  1. first, simplify the statistic to a single number for each subject (the difference of two time points, or the slope of the fitting line, or the annualized percent change, etc.)
  2. then analyze the obtained measure across subjects or groups with a standard GLM.

This model is quite simple and can be a good choice if all subjects have the same number of time points. Linear fits into each subject data are often meaningful, as longitudinal change is almost linear within a short time frame of a few years.

Advantages:

Disadvantages:

The linear mixed effects model overcomes this limitation and should be used if subjects have differently many time points (or for more complex modeling).

For details see: LongitudinalTwoStageModel


Linear Mixed Effects Model

A Linear Mixed Effects (LME) model is the most powerful approach

Advantages:

Disadvantages:

For details see: LinearMixedEffectsModels