Contents. design. Experimental design Introduction & recap Experimental design «Take home» message. N εˆ. DISCOS SPM course, CRC, Liège, 2009

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1 DISCOS SPM course, CRC, Liège, 2009 Contents Experimental design Introduction & recap Experimental design «Take home» message C. Phillips, Centre de Recherches du Cyclotron, ULg, Belgium Based on slides from: C. Rush, JB. Poline image data parameter estimates Statistical Parametric Map corrected p-values Mass univariate approach K p K realignment & motion correction normalisation General Linear Linear Model Model model model fitting fitting statistic statistic image image smoothing correction for for multiple comparisons Random effect effectanalysis N Y = N X p K βˆ anatomical reference kernel design matrix Dynamic causal causal modelling, Functional & effective connectivity, PPI, PPI, Y = Xβ + ε + N εˆ

2 raw fmri time series scaled for global changes fitted high-pass filter GLM fitted adjusted for global & low Hz effects fitted box-car residuals t-statistic - Computations Y = Xβ + ε ˆβ : least squares estimates c c = = X T c ˆ β t = T Std ˆ ( c ˆ) β T Std ˆ ( c ˆ) β = 2 ˆ σ = df 2 ( y X ˆ β ) compute df df using using Satterthwaite approximation ˆ 2 σ c T X VX T V c ReML ReML BOLD Impulse Response Advantages of Event-related fmri Function of blood oxygenation, flow, volume (Buxton et al, 1998) Peak (max. oxygenation) 4-6s poststimulus; baseline after 20-30s Initial undershoot can be observed (Malonek & Grinvald, 1996) Similar across V1, A1, S1 but differences across: other regions (Schacter et al 1997) individuals (Aguirre et al, 1998) Brief Stimulus Peak Undershoot 1. Randomised trial order c.f. confounds of blocked designs 2. Post hoc / subjective classification of trials e.g, according to subsequent memory 3. Some events can only be indicated by subject (in (in time) e.g,, spontaneous perceptual changes 4. Some trials cannot be blocked e.g, oddball designs 5. More accurate models even for blocked designs? e.g, state-item interactions

3 BOLD Response Latency (Linear) Contents Delayed Responses (green/ yellow) Canonical Basis Functions Canonical Derivative Parameter Estimates ß 1 ß 2 ß 1 ß 2 ß 1 ß 2 Introduction & recap Experimental design «Take home» message Actual latency, dt, vs. ß 2 / ß 1 ß 2 /ß 1 Face repetition reduces latency as well as magnitude of fusiform response Experimental design Categorical designs Subtraction - Pure insertion, evoked / differential responses Conjunction - Testing multiple hypotheses Parametric designs Linear - Adaptation, cognitive dimensions Nonlinear - Polynomial expansions, neurometric functions Factorial designs Categorical - Interactions and pure insertion Parametric - Linear and nonlinear interactions Subtraction Logic Cognitive subtraction originated with reaction time experiments (F. C. Donders, a Dutch physiologist). Measure the time for a process to occur by comparing two reaction times, one which has the same components as the other + the process of interest. Example: T1: Hit a button when you see a light T2: Hit a button when the light is green but not red T3: Hit the left button when the light is green and the right button when the light is red T2 T1 = time to make discrimination between light color T3 T2 = time to make a decision Franciscus Cornelis Donders ( ) Assumption of pure insertion: You can insert a component process into a task without disrupting the other components. Widely criticized (we ll come back to this when we talk about parametric studies)

4 Activation and Baseline Conditions Aim: To reveal brain activation related to a cognitive or sensori-motor process of interest (PI) Cognitive Subtraction: Contrast Activation task (engages PI) to a Baseline task (no PI). Difference = Brain regions associated with PI. Example: PI = Object recognition Activation task: with PI Baseline task: no PI Cognitive Subtractions: Stimulus or task changes Stimulus Change Activation condition Task: (constant) View picture Stimulus (constant) Activation condition _ Baseline condition _ View picture = Baseline condition Object Recognition = Name Retrieval Difference = Brain regions associated with Object Recognition Task: Change: Name Object Say: Yes Distant stimuli Cognitive Subtraction: Baseline-problems - Several components differ! Cognitive Subtractions: Serial subtraction Baseline condition for one contrast acts as activation condition for another contrast Related stimuli Example: Condition A. Condition B. Condition C. - P implicit in control task? Stimulus: - - Queen! Aunt Jenny? Same stimuli,, different task - Interaction of process and task? Name Person! Name Gender! Task: Name Object A-B = Name Retrieval B-C = Object Recognition Say: Yes Say: Yes Very limited

5 Problems with Serial Subtractions Stimulus: Condition A Condition B Condition C Task: Say: Name of Say: Yes Say: Yes Object Assumptions: A - B = only changes processing associated with Name Retrieval B - C = only changes processing associated with Object Recognition BUT 1. There may be implicit naming in condition B. In which case: naming component is removed from A-B and introduced into B-C. 2. Name Retrieval may increase the demands on object recognition (Interactions). i.e A - B : May reveal Object recognition NOT Name retrieval. B - C : May reveal Object Recognition AND Name Retrieval Implicit processing and interactions between processing components make it difficult to find baseline tasks that control for all but the process of interest. SPM{F} testing for evoked responses BOLD EPI fmri at 2T, TR 3.2sec. Words presented every 16 secs; ; (i) studied words or (ii) new words Evoked responses Differential event-related fmri Parahippocampal responses to words Baseline here corresponds to session mean (and thus processing during rest ) Null events or long SOAs essential for estimation Cognitive interpretation hardly possible, but useful to define regions generally involved in the task SPM{F} testing for evoked responses Differential responses Differential event-related fmri Parahippocampal responses to words Experimental design Word generation G Word repetition R A categorical analysis R G R G R G R G R G R G SPM{F} testing for differences BOLD EPI fmri at 2T, TR 3.2sec. Words presented every 16 secs; ; (i) studied words or (ii) new words studied words new words Peri-stimulus time {secs} G - R = Intrinsic word generation under assumption of pure insertion

6 Overview Categorical designs Subtraction - Pure insertion, evoked / differential responses Conjunction - Testing multiple hypotheses Parametric designs Linear - Adaptation, cognitive dimensions Nonlinear - Polynomial expansions, neurometric functions Factorial designs Categorical - Interactions and pure insertion Parametric - Linear and nonlinear interactions Conjunctions One way to minimise the baseline/pure insertion problem is to isolate the same process by two or more separate comparisons, and inspect the resulting simple effects for commonalities A test for such activation common to several independent contrasts ts is called Conjunction Conjunctions can be conducted across a whole variety of different contexts: tasks stimuli senses (vision, audition) etc. But the contrasts entering a conjunction have to be truly independent! Conjoint effects from multiple contrasts. A. Name Object B. View Nonobject Contrast 1 Contrast 2 Contrast 3 CONJUNCTION DESIGNS _ A - B = Name retrieval confounded with object recognition C. Name Colour D. View Nonobject C - D = Name retrieval _ confounded with colour processing E. Name Word BUS _ F. View XXXs XXX E - F = Name retrieval confounded with word recognition. Name Retrieval = Areas activated by Conjunction of A-B and C-D and E-F Example: Which neural structures support object recognition, independent of task (naming vs viewing)? Visual Processing V Object Recognition R Phonological Retrieval P [ R,V - V ] & [ P,R,V - P,V ] = R & R = R (assuming no interaction RxP; ; see later) Conjunctions Stimuli (A/B) Objects Colours Task (1/2) Viewing A1 B1 Naming (Object - Colour viewing) & (Object - Colour naming) Common object recognition [ ] & [ ] Price et al, 1997 response (R) A2 B2

7 Conjunctions Two flavours of inference about conjunctions SPM5/8 offers two general ways to test the significance of conjunctions: Test of global null hypothesis: Significant set of consistent effects which voxels show effects of similar direction (but not necessarily individual significance) across contrasts? Test of conjunction null hypothesis: Set of consistently significant effects which voxels show, for each specified contrast, effects > threshold? Choice of test depends on hypothesis and congruence of contrasts; the global null test is more sensitive (i.e., when direction of effects hypothesised) B1-B2 + p(a1=a2)<p + A1-A2 p(b1=b2)<p Friston et al. (2005). Neuroimage, 25: Nichols et al. (2005). Neuroimage, 25: Overview Parametric Designs: General Approach Categorical designs Subtraction - Pure insertion, evoked / differential responses Conjunction - Testing multiple hypotheses Parametric designs Linear - Adaptation, cognitive dimensions Nonlinear - Polynomial expansions, neurometric functions Factorial designs Categorical - Interactions and pure insertion Parametric - Linear and nonlinear interactions Parametric designs approach the baseline problem by: Varying the stimulus-parameter of of interest on a continuum, in in multiple (n>2) steps and relating blood-flow to to this parameter Possible tests for such relations are manifold: Linear Nonlinear: Quadratic/cubic/etc. Data-driven (e.g., neurometric functions)

8 A linear parametric contrast A nonlinear parametric contrast Linear effect of time The nonlinear effect of time assessed with the SPM{T} Nonlinear parametric design matrix versus Parametric Designs: Neurometric functions Coding of tactile stimuli in Anterior Cingulate Cortex: Stimulus (a) presence,, (b) intensity,, and (c) pain intensity Variation of of intensity of a heat stimulus applied to the right hand (300, 400, 500, and 600 mj) Assumptions: Rees,, G., et al. (1997). Neuroimage, 6: 6 : Rees,, G., et al. (1997). Neuroimage, 6: 6 : Inverted U response to increasing word presentation rate in the DLPFC Büchel et al. (2002). The Journal of Neuroscience,, 22: : 970-6

9 Parametric Designs: Neurometric functions Nonlinear parametric design matrix Stimulus intensity E.g,, F-contrast F [0 1 0] on Quadratic Parameter => Inverted U response to increasing word presentation rate in the DLPFC SPM{F} Linear Quadratic Stimulus presence Polynomial expansion: f(x) ) ~ b 1 x + b 2 x up to (N-1)th order for N levels Pain intensity Büchel et al. (2002). The Journal of Neuroscience,, 22: : (SPM8 GUI offers polynomial expansion as option during creation of parametric modulation regressors) Correlation design Overview No need to find baseline that controls for all but the process of interest Segregates areas showing differential effects (linear and nonlinear effects) But: Common effects can not be revealed without a baseline. Limited to continuous variables (e.g. duration, frequency, word length, R.T.s etc) Categorical designs Subtraction - Pure insertion, evoked / differential responses Conjunction - Testing multiple hypotheses Parametric designs Linear - Adaptation, cognitive dimensions Nonlinear - Polynomial expansions, neurometric functions Factorial designs Categorical - Interactions and pure insertion Parametric - Linear and nonlinear interactions

10 Stimuli (A/B) Objects Colours Factorial designs: : Main effects and Interactions Task (1/2) Main effect of task: Viewing Naming (A1 + B1) (A2 + B2) Main effect of stimuli: (A1 + A2) (B1 + B2) Interaction of task and stimuli: Can show a failure of pure insertion (A1 B1) (A2 B2) interaction effect (Stimuli x Task) Colours Objects Colours Viewing Naming Objects A1 B1 A2 B2 dissociate interactions B2 B1 = Object Recognition during naming Factorial Designs Naming Object No Object Recognition Recognition A. Name (Object) B. Name (Colour) A2 A1 = C. View D. View Object Recognition during viewing No Naming The Interaction effect (B2-B1) B1) - (A2-A1) A1) i.e. The effect of Naming on Object recognition (B2-A2) - (B1-A1) i.e. The effect of object recognition on Naming. Conjunction of B2-B1 and A2-A1 reveals areas involved in object recognition irrespective of naming. Conjunction of B2-A2and B1-A1 reveals areas involved in naming irrespective of object recognition. Overview Linear Parametric Interaction Categorical designs Subtraction - Pure insertion, evoked / differential responses Conjunction - Testing multiple hypotheses A (Linear) Time-by-Condition Interaction ( Generation strategy?) Parametric designs Linear - Adaptation, cognitive dimensions Nonlinear - Polynomial expansions, neurometric functions Factorial designs Categorical - Interactions and pure insertion Parametric - Linear and nonlinear interactions Contrast: [ ] [-1 1 1] = [-5[ ]

11 Nonlinear Parametric Interaction Model selection F-contrast tests for nonlinear Generation-by-Time by-time interaction (including both linear and Quadratic components) Factorial Design with 2 factors: 1. Gen/Rep (Categorical, 2 levels) 2. Time (Parametric, 6 levels) Time effects modelled with both linear and quadratic components G-R Time Lin Time Quad G x T G x T Lin Quad Model must fit i.e. i.e. model assumptions met met at every voxel Omitting relevant effects effects contribute to variance residuals not iid.. Normal model not valid outcomes? variance (usually, but but can can ) ) increased residual d.f. invalid inference Including irrelevant effects waste degrees of freedom conservative tests but safest! A real example (almost!)!) Asking ourselves some questions... Experimental Design Design Matrix Factorial design with 2 factors : modality and category 2 levels for modality (eg. Visual/Auditory) 3 levels for category (eg. 3 categories of words) V A C1 C2 C3 C1 C2 C3 V A C 1 C 2 C 3 V A C 1 C 2 C 3 Test C1 > C2 : c = [ ] Test V > A : c = [ ] [ ] Test C1,C2,C3? (F) c = [ ] [ ] Test the interaction MxC? Design Matrix not orthogonal Many contrasts are non estimable Interactions MxC are not modelled

12 Modelling the interactions Asking ourselves some questions... C 1 C 1 C 2 C 2 C 3 C 3 Test C1 > C2 : c = [ ] V A V A V A Test V > A : c = [ ] Test the category effect : [ ] c = [ ] [ ] Test the interaction MxC : [ ] c = [ ] [ ] Design Matrix orthogonal All contrasts are estimable Interactions MxC modelled If no interaction...? Model is too big! Asking ourselves some questions... With a more flexible model Convolution model Design and contrast SPM(t) or SPM(F) Fitted and adjusted data C 1 C 1 C 2 C 2 C 3 C 3 V A V A V A Test C1 > C2? Test C1 different from C2? from c = [ ] to c = [ ] [ ] becomes an F test! Test V > A? c = [ ] is possible, but is OK only if the regressors coding for the delay are all equal

13 Toy example: take home... Contents F tests have to be used when - Testing for >0 and <0 effects - Testing for more than 2 levels - Conditions are modelled with more than one regressor F tests can be viewed as testing for - the additional variance explained by a larger model wrt a simpler model, or - the sum of the squares of one or several combinations of the betas (here the F test b1 b2 is the same as b2 b1, but two tailed compared to a t-test). t test). Introduction & recap Experimental design «Take home» message Conclusions General Linear Model (simple) standard statistical technique temporal autocorrelation a Generalised Linear Model single general framework for many statistical analyses flexible modelling basis functions design matrix visually characterizes model fit data with combinations of columns of design matrix statistical inference: contrasts t tests: tests: planned comparisons of the parameters F tests: general linear hypotheses, model comparison Way to proceed Prepare your questions. ALL the questions! Find a model which allows contrasts that translates these questions. takes into account ALL the effects (interaction, sessions,etc) Devise task & stimulus presentation. Acquire the data & analyse. Not the other way round!!!

14 Three Stages of an Experiment 1. Sledgehammer Approach brute force experiment : powerful stimulus & don t try to control for everything look at was done before or by others run a couple of subjects -- see if it looks promising if it doesn t look great, tweak the stimulus or task try to be a subject yourself so you can notice any problems with stimuli or subject strategies Three Stages of an Experiment 1. Sledgehammer Approach 2. Real Experiment at some point, you have to stop changing things and collect enough subjects run with the same conditions to publish it how many subjects do you need some psychophysical studies test two or three subjects, many studies test 6-10 subjects, random effects analysis requires at least 15 subjects,... some subjects WILL be rejected, so acquire more than the minimum! can run all subjects in one or two days pro: minimize setup and variability con: bad magnet day means a lot of wasted time make sure all the data are treated the same way. (script) Three Stages of an Experiment 1. Sledgehammer Approach 2. Real Experiment 3. Whipped Cream experiment after the real experiment works, then think about a whipped cream version going straight to whipped cream is a huge endeavor, especially if you re new to imaging and it gives you a second paper!