Longitudinal Statistics

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

Longitudinal data are more complex than cross-sectional data, as repeated measures are correlated within each subject. The strength of this correlation will depend on the time separation between scans. In addition, extra care must be taken when the data exhibit significant between-subject variation in number of time points and between-scan intervals (imperfect timing). A statistical analysis should then consider these data features in order to obtain valid statistical inferences.

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

  1. Simplified repeated measures ANOVA (ignores correlation and timing of the measurement occasions)

  2. Direct analysis of atrophy rates or percent changes (ignores correlation and single time points)

  3. Linear mixed effects models <-- 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.

Advantages:

Disadvantages:

For details see: RepeatedMeasuresAnova


Analysis of Rates or Percent Changes

To analyze, e.g. annualized percent change or atrophy 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 summary measure across subjects or groups with a standard GLM.

This model is quite simple and can be an option if all subjects have the same number of time points, approximately equally spaced. Linear fits into each subject data are often meaningful, as longitudinal change can be assumed to be almost linear within a short time frame in several applications.

Advantages:

Disadvantages:

The linear mixed effects model overcomes these limitations 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 and principled approach. We recommend this approach.

Advantages:

Disadvantages:

LinearMixedEffectsModels allow ROI analysis as well as advanced longitudinal analysis for cortical maps. Here we only discuss how to prepare your data for that analysis. The analysis itself is performed in matlab.

Similar to regular (cross sectional) processing, ROI stats data is contained in stats files (cf. the ROI tutorial). You could, e.g., open the stats text files in each tpN.long.templateID/stats/ dir, containing statistics such as volume of subcortical structures or thickness averages for cortical regions. These statistics can be fed into any external statistical packages to run whatever analysis you are interested in. Helpful commands to grab the data from all subjects and time points and create a single table are asegstats2table and aparcstats2table.

For example to create a table with subcoritical ROI's from all subjects and all time points you would run this :

asegstats2table --qdec-long long.qdec.table.dat --stats aseg.stats --tablefile aseg.table.txt

This will automatically grab the stats from the longitudinal directories (tpN.long.templateID/stats/) and create a table (rows: subject/time points, columns: structures). Similarly you can use aparcstats2table for surface ROI analysis.

To run LinearMixedEffectsModels on surface maps, you need to map all the data to a template (usually fsaverage) and smooth the data:

mris_preproc --qdec-long long.qdec.table.dat --target fsaverage --hemi lh --meas thickness --out lh.thickness.stack.mgh
mri_surf2surf --hemi lh --s fsaverage --sval lh.thickness.stack.mgh --tval lh.thickness.stack.fwhm10.mgh --fwhm-trg 10 --cortex --noreshape

For details see: LinearMixedEffectsModels


MartinReuter