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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 == == Model specification == == Parameter estimation == == Model selection == == Inference == == Power analysis == == Example data analyses == |
== Simplified Repeated Measures ANOVA == This method can be used to check for differences between individual time points or compare time point differences across groups. This simple version, however, does NOT consider the correlation of the repeated measures! It is not a true repeated measure ANOVA. For two time points it simplifies to a [[ PairedAnalysis ]]. 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 can be done both for individual ROI stats (aseg or aparc.stats) or for thickness maps on the cortex. This model is quite simple and can be a good choice if all subjects have the same number of time points. The time points can be differently spaced, this is compensated by the time variable. Linear fits into each subject data are often meaningful, as longitudinal change is almost linear within a short time frame of a few years. The second stage can make use of different multiple comparison methods available in mri_glmfit. For the simple case of two time points and when looking at simple differences this model simplifies to the PairedAnalysis, but can additionally compute (symmetrized) percent changes and adjust for different time intervals. A disadvantage of this model is, that it does not consider that slopes of subjects with only a few time points are not as reliable as the ones obtained from subjects with many time points. 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 and 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). LMEs consider 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. Furthermore, LMEs can be used to model more complex longitudinal behavior (e.g. quadratic, or piecewise linear trajectories) and time-varying covariates. Currently our implementation is in Matlab and only offers FDR for multiple comparision correction. 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. This simple version, however, does NOT consider the correlation of the repeated measures! It is not a true repeated measure ANOVA. For two time points it simplifies to a PairedAnalysis.
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 can be done both for individual ROI stats (aseg or aparc.stats) or for thickness maps on the cortex. This model is quite simple and can be a good choice if all subjects have the same number of time points. The time points can be differently spaced, this is compensated by the time variable. Linear fits into each subject data are often meaningful, as longitudinal change is almost linear within a short time frame of a few years. The second stage can make use of different multiple comparison methods available in mri_glmfit. For the simple case of two time points and when looking at simple differences this model simplifies to the PairedAnalysis, but can additionally compute (symmetrized) percent changes and adjust for different time intervals. A disadvantage of this model is, that it does not consider that slopes of subjects with only a few time points are not as reliable as the ones obtained from subjects with many time points. 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 and 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). LMEs consider 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. Furthermore, LMEs can be used to model more complex longitudinal behavior (e.g. quadratic, or piecewise linear trajectories) and time-varying covariates. Currently our implementation is in Matlab and only offers FDR for multiple comparision correction.
For details see: LinearMixedEffectsModels