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.

Disadvantages:

• does NOT consider the correlation of the repeated measures
• is not a true repeated measure ANOVA.

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:

• modeling the correlation structure of repeated measures can be avoided
• can deal with differently spaced time points
• works on ROI stat (e.g. aseg.stats or aparc.stats) and on cortical maps (e.g. thickness)
• the second stage can be performed with QDEC (simple GUI) or directly with mri_glmfit
• the second stage analysis can make use of different multiple comparison methods that come with mri_glmfit
• scripts are available ( long_mris_slopes and long_stats_slopes ), no matlab needed
• for the simple case of two time points and when looking at simple differences this model simplifies to a paired analysis, but can additionally compute (symmetrized) percent changes
• includes code for intersecting cortex labels (across time and across subjects) to make sure that all non-cortex measures are excluded

Disadvantages:

• does not account for different certainty of within subject slopes depending on the number of time points
• difficult to model non-linear temporal behaviour
• difficult to deal with time varying co-variates (slopes would need to be fit into those for each subject to reduce these to a single number)
• cannot include information from subjects with only a single time point

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:

• 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)
• considers the temporal correlation and works for stats (univariate) or surface analysis (mass-univariate)
• our mass-univariate method can deal very well with the spacial correlation of measures on the cortex and is very fast by working with spacial regions
• can be used to model more complex longitudinal behavior (e.g. quadratic, or piecewise linear trajectories) and time-varying covariates

Disadvantages:

• more complicated use (distinguish mixed effects, fixed effects ...)
• currently our implementation is in Matlab
• and only offers FDR for multiple comparision correction.

For details see: LinearMixedEffectsModels

MartinReuter