Intersubject Heterogeneity in fMRI RFX Analysis Morning Workshop, OHBM 2005 Organizers Thomas Nichols, Stephen Smith & Jean-Baptist Poline Speakers Thomas Nichols, Jean-Baptist Poline, Christian Beckmann Morning Workshop, OHBM 2005 Organizers Thomas Nichols, Stephen Smith & Jean-Baptist Poline Speakers Thomas Nichols, Jean-Baptist Poline, Christian Beckmann 2005 Thomas Nichols Subj. 1 Subj. 2 Subj. 3 Subj. 4 Subj. 5 Subj. 6 0 Fixed vs. Random Effects in fMRI Fixed Effects Intra-subject variation suggests all these subjects different from zero Random Effects Intersubject variation suggests population not very different from zero Distribution of each subjects estimated effect Distribution of population effect 2 FFX 2 RFX 2005 Thomas Nichols Multisubject fMRI Analyses Fixed Effects Analyses Compare effect magnitude to scan-to-scan variation, measurement error Inferences only suitable for that cohort Random Effects (RFX) analyses Compare effect magnitude to combination of scan-to- scan & subject-to-subject Inferences can be generalized to the population sampled (Assuming you have a random sample from the population of interest!) 2005 Thomas Nichols RFX Analyses Assumptions 2 nd level parametric models make more assumptions! 1 st level: Measurement error Normal 2 nd level: True subject responses Normal Normality needed for... Optimally precise estimates Accurate P-values & thresholds 2005 Thomas Nichols Normality means... Symmetric No skew Unimodal No mixture of populations Thin tails No outliers 2005 Thomas Nichols But Non-Normality may be interesting! Bimodality In controls, two populations of responses could be explained by behavior differences In patients, could point to disease sub-groups Outliers Exceptional individuals could be performing task in completely different manner All different aspects of heterogeneity... 2005 Thomas Nichols Purpose of Workshop Raise awareness of heterogeneity in group analyses Talk 1: Traditional assumption checking Thomas Nichols, University of Michigan Talk 2: Finding unusual subjects, multivariately Jean-Baptist Poline, CEA- SHFJ Talk 3: Finding multivariate structure without models Christian Beckmann, Oxford University 2005 Thomas Nichols Massively Univariate Model Diagnosis for Group fMRI Data Thomas Nichols Department of Biostatistics, University of Michigan joint with Hui Zhang, University of Michigan Wen-Lin Luo, Merck & Co, IncOHBM Morning WorkshopJune 14, 2005 2005 Thomas Nichols Statistical Commandments But its not easy with imaging data! 100,000 voxels, 1,000 scans, 20 subjects Look at all 2 billion data points!? Check all 100,000 models? I.Thou shalt look at your data II.Thou shalt check your assumptions 2005 Thomas Nichols Our Solution Decompose data into signal & noise Y = X + and explore each, using... Model and scan summaries Each sensitive to different violations of assumptions Dynamic graphical tool Explore many summaries simultaneously Efficiently jump from summary to raw or residual data End Result Swiftly localize and understand problems 2005 Thomas Nichols Methods: Model Linear model fit at each voxel Assumptions on errors Mean 0, Constant Var. E ( i )=0, Var ( i )= 2 Uncorrelated Cov ( i, j )=0 Plot e i vs e i+1, spectrum Normality P ( i x) = (x) QQ plot, e (i) vs. E(z (i) ) Checked with residuals e Random Error + True Fit = Data + XX =y Residuals + Estimated Fit = e+= XX Plot e vs X, X , anything 2005 Thomas Nichols Methods: Model Summaries Create images of diagnostic statistics StatisticAssessesNull Distribution Cook-Weisberg Var ( i ) = 2 Chi-Squared Durbin-Watson Cov ( i, j )=0 Beta Cumulative Periodogram Var (e)= 2 I Kolmogorov-Smirnov Shapiro-Wilk ~ Normal (tabulated) Outlier CountArtifactsBinomial Std. DeviationArtifacts 2005 Thomas Nichols Methods: Scan Summaries No spatial model explicitly fit But several ad hoc measures useful SummaryInterpretation Global intensityWhole-brain signals or artifacts Outlier CountShot noise, artifacts Preprocessing parameters e.g. head motion Suggests cause of artifacts Experimental predictorsFor investigating mismodeled signal in residuals 2005 Thomas Nichols Methods: Graphical Tool Scan Summaries Parallel time series w/ cursor Scan Summaries Model Summaries Orthogonal Slice Viewers, MIPs Model Summaries Model Detail Raw data, fitted & residual time series, and diagnostic plots Model Detail Scan Detail Series of standardized residual images Scan Detail Scan Summaries Model Summaries Model Detail Scan Detail 2005 Thomas Nichols Methods: General Strategies Scan Summaries One bad subject? Several? Model Summaries Explore noise & signal Assess assumptions w/ diagnostics Find problem voxels Model Detail For a problem voxel, find which subjects involved Model Detail For a problem subject, assess spatial extent of problem 2005 Thomas Nichols Data: FIAC Data Acquisition 3 TE Bruker Magnet For each subject: 2 (block design) sessions, 195 EPI images each TR=2.5s, TE=35ms, 64 64 30 volumes, 3 3 4mm vx. Experiment (Block Design only) Passive sentence listening 2 2 Factorial Design Sentence Effect: Same sentence repeated vs different Speaker Effect: Same speaker vs. different Analysis Slice time correction, motion correction, sptl. norm. 5 5 5 mm FWHM Gaussian smoothing Box-car convolved w/ canonical HRF Drift fit with DCT, 1/128Hz 2005 Thomas Nichols Look at the Data! With small n, really can do it! Start with anatomical Alignment OK? Yup Any horrible anatomical anomalies? Nope 2005 Thomas Nichols Look at the Data! Mean & Standard Deviation also useful Variance lowest in white matter Highest around ventricles 2005 Thomas Nichols Look at the Data! Then the functionals Set same intensity window for all [-10 10] Last 6 subjects good Some variability in occipital cortex 2005 Thomas Nichols Feel the Void! Compare functional with anatomical to assess extent of signal voids 2005 Thomas Nichols Check Scan Summaries Not so interesting but... Note subject 9 (FIAC8) has 1% outliers 2005 Thomas Nichols Check Model Summaries Expected signal Auditory cortex in both T& con Unexpected structure Stdev shows visual cortex, MCA variability T stat Con. Stdev Norm. Test Out- liers 2005 Thomas Nichols Check Model Detail Visual cortex variable, especially in subj 2, 8, 9, 10 2005 Thomas Nichols Check Model Detail Normality test big in cingulate Subject 9 again! 2005 Thomas Nichols Check Scan Detail Standardized residuals confirm subject 9 is weird Ant/Superior Cingulate deactivated (in addition to V1) 2005 Thomas Nichols Conclusions Group data should be explored To understand anomalies To generate new hypotheses Assumptions must be checked For unbiased and optimal estimates For valid p-values Assumptions in group fMRI can be checked efficiently Model and scan diagnostic summaries Explore with dynamic visualization software Localize and understand artifacts Software: Statistical Parametric Mapping Diagnosis http://www.sph.umich.edu/~nichols/SPMdhttp://www.sph.umich.edu/~nichols/SPMd Luo & Nichols, NeuroImage, 2003, 19(3):