Differences between revisions 6 and 31 (spanning 25 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:

Simplified repeated measures ANOVA (ignores correlation and timing of the measurement occasions)
Direct analysis of atrophy rates or percent changes (ignores correlation and single time points)
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:

Does not assume any specific trend in the mean response over time and thus can capture complex trajectories.
Can make use of different multiple comparisons methods that come with mri_glmfit.

Disadvantages:

Does NOT consider the correlation among the repeated measures, and thus, there is a significant reduction in statistical power.
Does NOT consider the timing of the measurement occasions which may result in a further reduction in power.
Can only be applied to balanced data (all subject have their scans acquired at the same set of measurement occasions) with a small number of repeated measures (<=3.

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:

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 summary 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 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 comparisons 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 model the correlation among the repeated measures, and thus, there is a significant reduction in statistical power.
Does NOT account for different certainty of within subject slopes depending on the number of time points and therefore it has the highest propensity to false positives (type I family wise error in the mass-univariate setting).
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 and thus the results are likely to be biased. This also results in a further reduction in statistical power.

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.

Advantages:

Works for both stats (univariate) and surface analysis (mass-univariate).
Can handle imperfect timing and different number of time points across subjects (missing data).
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)
Appropriately models the temporal correlation.
Can model different variances across measurement occasions.
Our mass-univariate method can deal very well with the spatial correlation among measurements on the cortex and is very fast by working with spatial regions.
Can be used to model more complex longitudinal behavior (e.g. quadratic, or piecewise linear trajectories) and time-varying covariates.
It must be kept in mind that because longitudinal mixed-effects model tools are now publicly available it is likely that journal reviewers will demand those appropriate statistical models for your longitudinal studies.

Disadvantages:

More complicated use (eg. requires distinguishing mixed effects, fixed effects ...).
Currently our implementation is in Matlab.
Only offers FDR for multiple comparisons correction.

For details see: LinearMixedEffectsModels

MartinReuter

-  ⇤ ← Revision 6 as of 2012-11-09 17:24:22 → 
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+   ← Revision 31 as of 2012-12-05 01:48:25 → ⇥
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  Editor: jbernal
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-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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-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 15:
-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.
+== 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:'''
 * Does not assume any specific trend in the mean response over time and thus can capture complex trajectories.
 * Can make use of different multiple comparisons methods that come with mri_glmfit.
-Line 15:
+Line 24:
-<<TableOfContents>>
+'''Disadvantages:'''
 * Does NOT consider the correlation among the repeated measures, and thus, there is a significant reduction in statistical power.
 * Does NOT consider the timing of the measurement occasions which may result in a further reduction in power. 
 * Can only be applied to balanced data (all subject have their scans acquired at the same set of measurement occasions) with a small number of repeated measures (<=3.

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 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 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 comparisons 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 model the correlation among the repeated measures, and thus, there is a significant reduction in statistical power.
 * Does NOT account for different certainty of within subject slopes depending on the number of time points and therefore it has the highest  propensity to false positives (type I family wise error in the mass-univariate setting).
 * 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 and thus the results are likely to be biased. This also results in a further reduction in statistical power.

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. 

'''Advantages:'''
 * Works for both stats (univariate) and surface analysis (mass-univariate).
 * Can handle imperfect timing and different number of time points across subjects (missing data).
 * 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) 
 * Appropriately models the temporal correlation.
 * Can model different variances across measurement occasions.
 * Our mass-univariate method can deal very well with the spatial correlation among measurements on the cortex and is very fast by working with spatial regions.
 * Can be used to model more complex longitudinal behavior (e.g. quadratic, or piecewise linear trajectories) and time-varying covariates. 
 * It must be kept in mind that because longitudinal mixed-effects model tools are now publicly available it is likely that journal reviewers will demand those appropriate statistical models for your longitudinal studies.
-Line 18:
+Line 79:
+'''Disadvantages:'''
 * More complicated use (eg. requires distinguishing mixed effects, fixed effects ...).
 * Currently our implementation is in Matlab.
 * Only offers FDR for multiple comparisons correction.
-Line 19:
+Line 84:
-== 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.
+For details see: [[ LinearMixedEffectsModels ]]
-Line 22:
+Line 86:
-In order to read mass-univariate data you should use the following scripts:

fs_read_label.m
fs_read_surf.m
fs_read_Y.m

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. 

Previously, the mass-univariate data is generated in Freesurfer by running variants of the following commands:

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)

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)

Then you can load the cortical thickness data lh.thickness_sm10.mgh into Matlab using 

fs_read_Y.m 
eg. [Y,mri] = fs_read_Y('lh.thickness_sm10.mgh'); 

You should also read the spherical surface (lh.sphere) and cortex label (lh.cortex.label) of study_average. 

eg. lhsphere = fs_read_surf('$FsDir/freesurfer/subjects/fsaverage/surf/lh.sphere'); 
    lhcortex = fs_read_label('$FsDir/freesurfer/subjects/fsaverage/label/lh.cortex.label');

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:

sortData

For example, if you have your covariates in a Qdec table then you can use the following code

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