Differences between revisions 6 and 26 (spanning 20 versions)

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:

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.)
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

-  ⇤ ← Revision 6 as of 2012-11-09 17:24:22 → 
  Size: 4099
  Editor: jbernal
  Comment:
+   ← Revision 26 as of 2012-12-05 01:27:04 → ⇥
  Size: 4838
  Editor: jbernal
  Comment:
-Deletions are marked like this.
+Additions are marked like this.
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-#acl LcnGroup:read,write,delete,revert All:
+#acl LcnGroup:read,write,delete,revert All:read
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-LME Matlab tools. Author: Jorge Luis Bernal Rusiel, 2012. jbernal@nmr.mgh.harvard.edu or jbernal0019@yahoo.es
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+Line 5:
-If you use these tools in your analysis please cite:
+This page describes ways of analyzing longitudinal data after processing it using the [[ LongitudinalProcessing | longitudinal stream ]] in Freesurfer.
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+Line 7:
-Bernal-Rusiel J.L., Greve D.N., Reuter M., Fischl B., Sabuncu M.R., 2012. Statistical Analysis of Longitudinal Neuroimage Data with Linear Mixed Effects Models, NeuroImage, doi:10.1016/j.neuroimage.2012.10.065.
+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.
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+Line 9:
-These Matlab tools are freely distributed and intended to help neuroimaging researchers when analysing longitudinal neuroimaging (LNI) data. The statistical analysis of such type of data is arguable more challenging than the cross-sectional or time series data traditionally encountered in the neuroimaging field. This is because the timing associated with the measurement occasions and the underlying biological process under study are not usually under full experimental control.
+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
-Line 12:
+Line 14:
-There are two aspects of longitudinal data that require correct modeling: The mean response over time and the covariance among repeated measures on the same individual. I hope these tools can serve for such modeling purpose as they provide functionality for exploratory data visualization, model specification, model selection, parameter estimation, inference and power analysis including sample size estimation. They are specially targeted to be used with Freesurfer's data but can be used with any other data as long as they are loaded into Matlab and put into the appropriate format. Here are some recommendations about how to use these tools.
+----
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+Line 16:
+== Simplified Repeated Measures ANOVA ==
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+Line 18:
-<<TableOfContents>>
+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 ]].
-Line 17:
+Line 20:
+'''Disadvantages:'''
 * does NOT consider the correlation of the repeated measures
 * is not a true repeated measure ANOVA.
-Line 18:
+Line 24:
+For details see: [[ RepeatedMeasuresAnova ]]
-Line 19:
+Line 26:
-== Preparing your data ==
There are two types of analyses that can be done: univariate and mass-univariate. The first step is to load your data into Matlab. If you are working with Freesurfer then univariate data (eg. Hippocampus volume) can be loaded using Qdec tables. There are, under the Qdec directory, some simple example scripts for reading and writing Freesurfer's Qdec tables.
+----
-Line 22:
+Line 28:
-In order to read mass-univariate data you should use the following scripts:
+== Analysis of Rates or Percent Changes ==
-Line 24:
+Line 30:
-fs_read_label.m
fs_read_surf.m
fs_read_Y.m
+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.
-Line 28:
+Line 34:
-The last two depend on Freesurfer's scripts so you need to have installed Freesurfer software package and included the Freesurfer's matlab subdirectory in the Matlab's search path.
+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.
-Line 30:
+Line 36:
-Previously, the mass-univariate data is generated in Freesurfer by running variants of the following commands:
+'''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
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+Line 46:
-mris_preproc --qdec qdec.table.dat --target study_average --hemi lh --meas thickness --out lh.thickness.mgh (assembles your thickness data into a single lh.thickness.mgh file)
+'''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
-Line 34:
+Line 52:
-mri_surf2surf --hemi lh --s study_average --sval lh.thickness.mgh --tval lh.thickness_sm10.mgh --fwhm-trg 10 --cortex  --noreshape (smooths the cortical thickness maps with FWHM=10 mm. Note the --cortex and --noreshape options)
+The linear mixed effects model overcomes this limitation and should be used if subjects have differently many time points (or for more complex modeling).
-Line 36:
+Line 54:
-Then you can load the cortical thickness data lh.thickness_sm10.mgh into Matlab using
+For details see: [[ LongitudinalTwoStageModel ]]
-Line 38:
+Line 56:
-fs_read_Y.m 
eg. [Y,mri] = fs_read_Y('lh.thickness_sm10.mgh');
+----
-Line 41:
+Line 58:
-You should also read the spherical surface (lh.sphere) and cortex label (lh.cortex.label) of study_average.
+== Linear Mixed Effects Model ==
-Line 43:
+Line 60:
-eg. lhsphere = fs_read_surf('$FsDir/freesurfer/subjects/fsaverage/surf/lh.sphere'); 
    lhcortex = fs_read_label('$FsDir/freesurfer/subjects/fsaverage/label/lh.cortex.label');
+A Linear Mixed Effects (LME) model is the most powerful approach
-Line 46:
+Line 62:
-Once you have your data in Matlab you need to build your design matrix. For computational efficiency reasons, these tools require the data ordered according to time for each individual (that is, your design matrix needs to have all the repeated assessments for the first subject, then all for the second and so on). You can use the script:
+'''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
-Line 48:
+Line 69:
-sortData
+'''Disadvantages:'''
 * more complicated use (distinguish mixed effects, fixed effects ...)
 * currently our implementation is in Matlab
 * and only offers FDR for multiple comparision correction.
-Line 50:
+Line 74:
-For example, if you have your covariates in a Qdec table then you can use the following code
+For details see: [[ LinearMixedEffectsModels ]]
-Line 52:
+Line 76:
-eg. Qdec = fReadQdec('qdec.table.dat');  
    Qdec = rmQdecCol(Qdec,1);  
    sids = Qdec(:,1);  
    Qdec = rmQdecCol(Qdec,1); 
    M = Qdec2num(Qdec); 
    [M,Y,ni] = sortData(M,2,Y,sids); 

== Model specification ==
== Parameter estimation ==
== Model selection ==
== Inference ==
== Power analysis ==
== Example data analyses ==
+----
MartinReuter