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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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| 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. 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. 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. |
Longitudinal data is different from cross sectional data, as repeated measures are correlated within each subject. A statistical analysis should consider this correlation. |
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| <<TableOfContents>> | Freesurfer currently comes with (at least) three different frameworks for the analysis of longitudinal data: |
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| 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 |
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| == 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. |
== Simplified Repeated Measures ANOVA == |
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| In order to read mass-univariate data you should use the following scripts: | 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 ]]. |
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| fs_read_label.m fs_read_surf.m fs_read_Y.m |
'''Disadvantages:''' * does NOT consider the correlation of the repeated measures * is not a true repeated measure ANOVA. |
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| 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. | For details see: [[ RepeatedMeasuresAnova ]] |
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| Previously, the mass-univariate data is generated in Freesurfer by running variants of the following commands: | == Analysis of Rates or Percent Changes == |
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| 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) | 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. |
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| 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) | 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. |
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| Then you can load the cortical thickness data lh.thickness_sm10.mgh into Matlab using | '''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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| fs_read_Y.m eg. [Y,mri] = fs_read_Y('lh.thickness_sm10.mgh'); |
'''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 |
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| You should also read the spherical surface (lh.sphere) and cortex label (lh.cortex.label) of study_average. | The linear mixed effects model overcomes this limitation and should be used if subjects have differently many time points (or for more complex modeling). |
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| eg. lhsphere = fs_read_surf('$FsDir/freesurfer/subjects/fsaverage/surf/lh.sphere'); lhcortex = fs_read_label('$FsDir/freesurfer/subjects/fsaverage/label/lh.cortex.label'); |
For details see: [[ LongitudinalTwoStageModel ]] |
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| 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: | == Linear Mixed Effects Model == |
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| sortData | A Linear Mixed Effects (LME) model is the most powerful approach |
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| For example, if you have your covariates in a Qdec table then you can use the following code | '''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 |
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| 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); |
'''Disadvantages:''' * more complicated use (distinguish mixed effects, fixed effects ...) * currently our implementation is in Matlab * and only offers FDR for multiple comparision correction. |
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| == Model specification == == Parameter estimation == == Model selection == == Inference == == Power analysis == == Example data analyses == |
For details see: [[ LinearMixedEffectsModels ]] |
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:
- Simplified repeated measures ANOVA (ignores correlation)
- Direct analysis of atrophy rates or percent changes (avoids treatment of correlation)
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:
- 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