Brain imaging applications of multilevel modeling: Multilevel mediation analysis. Expectancy paradigm 10/3/2011. Lauren Y. Atlas NYU Sept.

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1 Brain imaging applications of multilevel modeling: Multilevel mediation analysis Lauren Y. Atlas NYU Sept. 29, 2011 Tor Wager Dept of Psychology, University of Colorado, Boulder Niall Bolger Dept of Psychology, Columbia University Martin Lindquist Dept of Statistics, Columbia University Expectancy effects on subjective experience Expectancy paradigm 1. Pain calibration procedure 3. Learning task PAIN Expectations Experience Level 5 (Medium pain) Level 2 (Slight pain) Low Pain High Pain Accuracy Level 8 (Max pain) 2. Verbal instructions 4. Expectancy ratings Low Pain High Pain (Counterbalanced) TASTE INTOICATION REWARD EMOTION 1

2 Expectancy paradigm EPERIMENTAL CONDITIONING PHASE Analysis Expectancy 1: Pain-evoked paradigm responses EPERIMENTAL PHASE LL Anticipatory delay HH HEAT HEAT How Painful? LL LOW PAIN (Level 2) HIGH PAIN (Level HH 8) LL Moderately painful stimulation (Level 5) HH Two Six Experimental Conditioning Runs Moderately painful stimulation (Level 5) Analysis Expectancy 1: Pain-evoked paradigm responses IV Brain HEAT Moderately painful stimulation (Level 5) DV How Painful? Expectancy Questions Reported pain Which brain pathways underlie expectancy effects on pain? Pain-processing network (PPN), decision making, affective value Which psychological processes underlie expectancy effects on pain? Changes in attention? Do beliefs about pain (ind diffs) moderate expectancy effects on pain? 2

3 Mediation analysis Provides a formal test of whether the relationship between input () and output(y) can be explained by an intervening variable (M) M Y Mediation analysis 1. Test hypothesized pathways 2. Voxel-wise search for, M, or Y 3. Multi-level (mixed effects) model Test individual differences in pathway strength Overview Introduction, Single level mediation Multi-level mediation: Identifying brain regions that link independent and dependent variables Connectivity analysis Level 2 moderators Practical aspects Matlab code, M3 toolbox I. Which brain regions underlie expectancy effects on subjective pain? II. Which brain regions give rise to expectancy effects on pain matrix regions? III. Do individual differences influence the brain pathways that link noxious input and subjective pain? Overview Introduction, Single level mediation Multi-level mediation: Identifying brain regions that link independent and dependent variables Connectivity analysis Level 2 moderators Practical aspects Matlab code, M3 toolbox 3

4 S Mediation O M Woodworth, 1928 R Y Provides a formal test of whether the relationship between input (S/) and output (R/Y) can be explained by a mediator (M; brain activity) x Demonstrating Mediation Reduced model, without mediator c y = cx e y y Full model, with mediator x a c m m = ax e m y = bm c x e y Baron and Kenny (1986) conjunction of 3 effects: 1) c effect: There is a relationship to be mediated 2) a effect: initial variable related to mediator 3) b effect: mediator relates to outcome, controlling for initial variable And, if m is a complete mediator, c = 0 b y Demonstrating Mediation Reduced model, without mediator x c y = cx e y y Full model, with mediator Does m explain some of the x-y relationship (c)? c-c = a*b c Counterfactual: If we were to prevent m from varying, the effect of x on y would be reduced or absent. x a m m = ax e m y = bm c x e y b y Moderation Mediation: does [M] explain some or all of the relationship btwn [] and [Y]? x Moderation: does the level of [M] influence the relationship btwn [] and [Y]? x m m y y 4

5 Full model, with mediator and moderator Interpretating mediation x mo m d y Individuals higher in [] show greater [Y] because of changes in [M] The effect of [] on [Y] can be explained by individual differences in [M] m = i m ax e m y = i y bm c'x d(mo*x) e y Moderator: Level of mo predicts x-y covariance Mo*x interaction Should center x and y to reduce correlation between moderation and x effects Slide from Tor Wager Group differences in [Y] are due to group differences in [M] Interpretating mediation Stronger inferences about directionality if variables are randomly assigned, separated in time Strongest inference when you can experimentally manipulate AND M (e.g. using TMS) see Holland, Rubin Single level mediation in neuroimaging Racial bias score (IAT) Richeson et al., NatNeuro 2003 µ-opioid receptor gene polymorphism (G allele / A allele) Way et al., PNAS 2009 Age Samanez- Larkin et al., JNeuro 2010 R DLPFC (Black vs baseline) dacc response to rejection [Exclude Include] NAcc temporal Variability (MSSD) Stroop impairment (Black White) Rejection sensitivity Risk-seeking mistakes R VLPFC [Neg Rea] DLPFC response to regulation cues [Later Now] Trait anxiety - NAcc [Neg Rea] Amygdala [Neg Rea] -- - Striatal response to regulation cues [Later Now] Interpretation: Those individuals high in show greater responses to M, and that in turn leads to effects in Y. If you could disrupt M, effect on Y would be reduced or abolished. Amygdala response to fear cues [CS CS-] Reappraisal success [Neg Rea] Wager et al., Neuron 2008 Craving: [Now Later] Kober et al., PNAS 2010 Fear acquisition (SCR): [CS CS-] Indovina et al., Neuron

6 Brain [C P] Pain C-P Y (Pain [C-P]) Y (Pain [C-P]) 10/3/2011 Single level mediation in neuroimaging Mediation Effect Parametric Mapping R VLPFC [Neg Rea] Voxel-wise mediation effect parametric mapping (MEPM) - NAcc [Neg Rea] BRAIN REGION Amygdala [Neg Rea] Reappraisal success [Neg Rea] Wager et al., Neuron 2008 (initial variable) is A between-subjects experimental variable: Healthy controls vs Chronic pain patients Brain? M is Contrast values from a voxel [Control Placebo] Y (outcome) Y is A behavioral variable Pain reports for [Control Placebo]: Placebo analgesia Mediation Effect Parametric Mapping Mediation vs. Conjunction (Patients vs Controls) Indirect Path a Path a is A two sample t-test for Control vs Patients Brain? Conjunction Indirect Path b Y (Placebo analgesia) Path b is A brain-behavior correlation, controlling for group Controls Chronic pain patients b c a M (ACC) a a*b = c-c b c Effect of Group and ACC on Placebo analgesia, but little/no mediation c ~= c Group Brain [C P] (a*b) is a test of whether group differences in placebo effect are explained by brain activity (c-c ) b c c a M (ACC) Mediated effect of Group () on Placebo analgesia (Y) through anterior cingulate (ACC) c, group difference in intercept, ~= 0 Slide from Tor Wager 6

7 Testing the significance of a*b Sobel test Aroian, L. A (1944) ab Z b 2 se(a) 2 a 2 se(b) 2 se(a) 2 se(b) 2 Assumes a, b are normally distributed Usually conservative (p-values higher than needed) a a*b = c-c b Bootstrap test : Efron, 1994; Shrout & Bolger, 2002; Preacher & Hayes, 2004 Histogram of bootstrapped Indirect (a*b) effects Overview Introduction, Single level mediation Multi-level mediation: Identifying brain regions that link independent and dependent variables Connectivity analysis Level 2 moderators Practical aspects Matlab code, M3 toolbox Mediation analysis: Single vs multilevel mediation c-c = a*b cov(a,b) Rather than one value per subject, model the entire timeseries, assess within-subjects effects Kenny, Korchmaros, & Bolger (2003) Path strengths vary across subjects c Observations x y on each variable are nested a b within subjects m Subject-level pathway Particular type of mixedeffect model: Random strengths (a, b, c, c ) are random variables intercept, random slope model, with subject as random effect Repeated measures Random intercept, fixed slope Assumes all subjects have same variance Error based on condition x subjects interaction observed predicted Multilevel path analysis Multi-level model Random intercept and slope Variation comes from 2 levels of analysis: within-subject and betweensubject Can test for inter-individual variability 7

8 Multilevel estimation strategy Example: FMRI experiment Level 1 Estimate coefficients & variances for each individual, including mediation (ab) effect Level 2 Precision (1/variance)- weighted estimates of fixed and random coefficients (weighted least squares) Y ij d 0j c j ij q 1j Q 1ij... q nj Q nij r ij Z j j r ij Y ij d 2j c j ' ij b i M ij q 1j Q 1ij... q nj Q nij f ij M ij d 1j a j ij q 1j Q 1ij... q nj Q nij e ij Path coefficient for subject j Covariates Population effect Subject effect (random) a j Z a g u aj a j Between-subjects predictor(s) Which brain pathways mediate expectancy effects on pain? Update estimates of random effects (between subject) variance using Empirical Bayes coefficient estimates Update estimates of coefficients. For classical inference: calculate p- values * Rapid estimation compared to full iterative approach Slide from Tor Wager Atlas, Bolger, Lindquist, and Wager, 2010, JNeurosci PAIN The Pain Matrix Subjective perception Expectancy, Attention, Emotion Report biases/ Change in criteria? (Allan & Siegel, 2002; Clark 2003) SI SII Posterior Insula Posterior cingulate dacc Thalamus Anterior insula High vs Low pain Four studies N = 75 FWE, p<.05 8

9 Average expectancy effect on ACC response to pain 10/3/2011 Expectancy effects on pain Expectancy effects on pain Expectations? Expectations Pain? No Effects Wager et al., 2004, Science (p) Koyama Kong et al., et al., 2006, 2005, JNeuro PNAS (p) (c) Bingel Keltner et et al., al., 2006, 2006, Pain JNeuro (p) (c) Price et al., 2007, Pain (p) Eippert et al., 2009, Neuron (p) Koyama Kong et al., et al., 2008, 2005, Jneuro PNAS (n) (c) Keltner et al., 2006, JNeuro (c) (c): cues (p): placebo (n): nocebo Experience Whalen et al., 1998 Bornhovd et al., 2002 Individual differences in expectancy effects on pain Expectations Pain? Individual differences in expectancy effects on pain Average expectancy effect on pain (Control placebo) Wager et al., 2004, Science Kong et al., 2008, JNeuro 9

10 Individual differences in expectancy effects on pain Correlations may reflect individual differences in trait-level psychological factors Optimism (Morton et al., 2009) Suggestibility (De Pascalis et al., 2002, Morton et al., 2010) Neurochemistry (Zubieta et al., 2005, Scott et al., 2007) How do expectancies shape DYNAMIC affective experience? Expectations? Pain Mediation vs. conjunction analysis Conjunction analyses Relationships within subjects, over time Voxelwise G Voxelwise parametric regression S O O R Voxels with overlap 10

11 Conjunction analyses Relationships within subjects, over time CRITICAL ISSUE: Even if region shows overlap, it does not necessarily explain the effects of S on R S O? R Predictive cue Our approach Reported pain We used multi-level mediation to assess dynamic relationship between trial-by-trial cue-based expectancy, brain activity, and reported pain 2s 6s 10s Trial structure EPERIMENTAL CONDITIONING PHASE LL Analysis 1: Trial Pain-evoked structure responses EPERIMENTAL PHASE 10s 14s 4s 8s How Painful? CUE Anticipatory delay HH HEAT HEAT ISI ISI LL LOW PAIN (Level 2) HIGH PAIN (Level HH 8) LL Moderately painful stimulation (Level 5) HH Two Six Experimental Conditioning Runs Moderately painful stimulation (Level 5) 11

12 Perceived Pain 10/3/2011 Analysis 1: Trial Pain-evoked structure responses Do cues affect pain perception? HEAT How Painful? HEAT How Painful? Moderately painful stimulation (Level 5) **** RESULTS Cue-based stimulus expectancies strongly modulate pain experience. 4 3 Stimulus expectancies Brain response Subjective pain LE-Low LL LE-Medium HE-Medium HE-High HH Do cues shape PPN responses to noxious stimulation? Do changes within the PPN underlie expectancy effects on pain experience? -: t(17) = 8.59, p<.0001 N = 18 Atlas, Bolger, Lindquist, & Wager, JNeurosci,

13 Reported Pain LL HH 10/3/2011 Analysis 1: Trial Pain-evoked structure responses Mediation model 10s PREDICTIVE CUE (-) **** REPORTED PAIN How Painful? Y HEAT Moderately painful stimulation (Level 5) Does the pain matrix mediate cue effects on pain? BRAIN ACTIVITY DURING HEAT M Important! # of observations Voxelwise single trial analysis Within each subject, need equal observations of, M, and Y Easy if individual differences or 3 brain regions (connectivity) Here, each trial has: 1 cue () 1 rating (Y) ~10 seconds of pain, plus HRF! 1. Fit basis functions trial-by-trial 2. Estimate trial-by-trial height, width, delay, and area under the curve (AUC) 3. Use trial level parameters in subject level analyses and multi-level mediation 13

14 Cue Cue Reported Pain AUC LL HH Reported Pain Voxelwise AUC Pain > : Pain Regions Average % signal change Cue L. Ant. Insula % signal change AUC Pain 10/3/2011 Mediation model Mediation model PREDICTIVE CUE (-) REPORTED PAIN Y PREDICTIVE CUE PREDICTIVE CUE PREDICTIVE (-) CUE PREDICTIVE (-) CUE (-) (-) REPORTED PAIN REPORTED PAIN REPORTED PAIN REPORTED PAIN Y BRAIN ACTIVITY DURING HEAT (Trial-by-trial AUC) M BRAIN ACTIVITY BRAIN ACTIVITY DURING BRAIN ACTIVITY HEAT DURING BRAIN ACTIVITY HEAT (Trial-by-trial DURING HEAT AUC) (Trial-by-trial DURING HEAT AUC) (Trial-by-trial AUC) (Trial-by-trial AUC) M RESULTS Path a PREDICTIVE CUE (-) PAIN PERIOD ACTIVATION PREDICTIVE CUE (-) **** REPORTED PAIN Y Right SII Right SII Left Anterior Insula Medial Thalamus LL HH Right Pre-SMA Path a. Do cues affect the brain s response to pain? BRAIN ACTIVITY DURING HEAT M Cue Pain Rate 14

15 Reported Pain Reported Pain LL HH LL HH Report-related Pain Regions Left Anterior Insula Reported pain 10/3/2011 RESULTS Path b PAIN PERIOD ACTIVATION REPORTED PAIN PREDICTIVE CUE (-) **** REPORTED PAIN Y R. Ant. Insula rdacc Pre-SMA Cerebellum Path a. Do cues affect the brain s response to pain? BRAIN ACTIVITY DURING HEAT Path b. Do pain regions predict variations in report, controlling for cue? YES M PREDICTIVE CUE (-) RESULTS **** REPORTED PAIN Predictive cue (-) Direct effect (c ) 0.568(.079)*** 0.011(.003)** Perceived Pain (trial-by-trial report) Y a*b. Do pain regions mediate cue effects on perceived pain? BRAIN ACTIVITY DURING HEAT Path b. Do pain regions predict variations in report, controlling for cue? rdacc R. Thalamus L. Ant. Insula M YES 15

16 Covariance and multi-level mediation c-c = a*b cov(a,b) R=0.76 Positive functional pathway from to Y But individual differences within paths! Y - - M See Kenny, Korchmoros, & Bolger 2003 M Y Predictive cue Expectancies affect PPN responses. Summary Cue-based expectations strongly modulate dynamic pain experience. Expectancy effects on PPN responses mediate expectancy effects on pain Reported pain PPN responses predict variations in report. Atlas, Bolger, Lindquist, & Wager, JNeurosci, 2010 Summary NOTE: Pain-evoked responses in other regions also mediated cue effects on reported pain, including Right DMPFC, left amygdala, striatum, pgacc and DLPFC. This suggests Regulation that expectancy effects on subjective Affective / Cognitive value control experience are determined by multiple sources. Overview Introduction, Single level mediation Multi-level mediation: Identifying brain regions that link independent and dependent variables Connectivity analysis Level 2 moderators Practical aspects Matlab code, M3 toolbox 16

17 Connectivity Connectivity So far: Testing relationships between psychological manipulations, brain, and behavior and Y are IV and DV Now: Connectivity analysis, M, Y = activity in a voxel or betas from a region Data reduction approaches: identify distributed patterns E.g. PCA, ICA, PLS Path modeling approaches: inferences on specific connections Path models, PPI, SEM, DCM, Granger causality Multilevel mediation and functional connectivity VMPFC response to SET Wager et al., Neuroimage 2009 pstc interaction with picture presentation Hare et al., JNeuro PAG response to SET - IFG interaction with picture presentation HR during SET VMPFC interaction with picture presentation Right amygdala single trial response Pain predictive cue during medium heat [ ] - Parahippocampal single trial response - Cue-evoked response in R VS Cue-evoked response in mofc Visual perception (hit / miss decision) Lim et al., PNAS 2009 Pain-evoked response in PPN mediators Atlas et al., JNeuro 2010 How do expectancy effects on the PPN emerge? Predictive cue Anticipation VS? DLPFC mofc VLPFC pgacc Amyg. 1. Expectations change pain value (Affective value model) Fields 2007, Leknes & Tracey 2008 Heat Reported pain 2. Expectations inhibit responses (Regulation model) Lieberman 2004, Wager 2005, Wiech Ploner & Tracey

18 Cue Anticipatory AUC L. Ant. Insula AUC Reported Pain Cue Cue L. Ant. Insula AUC Reported Pain Reported Pain 10/3/2011 Analysis 1: 2: Pain-evoked Cue-evoked responses Independent variable Dependent variable 10s How Painful? Expectancy (-) Perceived pain HEAT Brain activity during pain Pain period Mediator Independent variable Dependent variable Independent variable Dependent variable Expectancy (-) Perceived pain Expectancy (-) Perceived pain M, voxelwise search Cue-evoked response Brain activity during pain Y Cue-evoked response Brain activity during pain rdacc L. Ant. Ins R. Thalamus Additional region Pain period Mediator 18

19 Analysis 2: Results Develop predictions Update value based on deviations between expectations and experience. mofc = appetitive PE VS = aversive PE Gottfried et al., 2003 Saddoris et al., 2005 Schoenbaum et al., 2007 Consistent with affective value model mofc LL HH Predictive cue mofc VS Anticipation Summary Heat Reported pain This suggests that regions involved in evaluating predictive cues and generating value shape PPN responses, which in turn shape subjective experience. Overview Level 2 moderation Introduction, Single level mediation Multi-level mediation: Identifying brain regions that link independent and dependent variables Connectivity analysis Level 2 moderators Practical aspects Matlab code, M3 toolbox Observations nested in subjects; ind diffs might explain meaningful differences in pathway strength NOTE: Bootstrapping is not implemented for L2Ms within-subjs effects will be estimated with ordinary least squares, Sobel test c-c = a*b cov(a,b) 19

20 Path a effect Path b effect 10/3/2011 Example 3: L2Ms Do beliefs about cues, prior to experience, influence expectancy effects on brain responses during the task? Pre-task expectancy ratings Moderation by pre-task expectancy PREDICTIVE CUE (-) REPORTED PAIN Y Pre-task expectancy score = High cue rating Low cue rating BRAIN ACTIVITY DURING HEAT M Moderation by pre-task expectancy Moderation by pre-task expectancy PREDICTIVE CUE (-) REPORTED PAIN Y PREDICTIVE CUE (-) REPORTED PAIN Y Pre-task exp [H-L] BRAIN ACTIVITY DURING HEAT M BRAIN ACTIVITY DURING HEAT M Pre-task exp [H-L] 20

21 Summary Why use multilevel mediation: 1. Relate independent and dependent variables 2. Test hypothesized pathways c-c = a*b cov(a,b) 3. Relate individual differences to within-subjects pathway strength Summary Resources Consider inferences: Stronger inferences about directionality if variables are separated in time E.g. Cue -> Anticipation -> Pain -> Report Strongest inference when you can experimentally manipulate AND M (e.g. using TMS) see Holland, Rubin Mediation analysis: Baron & Kenny, 1986, JPSP Shrout & Bolger, 2002, Psychological Methods Kenny, Korchmaros & Bolger, 2003, Psychological Methods MEPM: Wager et al., 2008, Neuron Wager et al., 2009, Neuroimage Atlas et al., 2010, JNeuro 21

22 Midbrain activity (fixed) 10/3/2011 Part 2. Practical aspects Additional slides Break! Technique Group ICA, tensor ICA Seed Analysis PPI Granger causality Advantages Distributed patterns Bivariate interactions w/ 1 area Single moderator of biv connectivity Bivariate interaction w/ time lag/diff HRFs Search for brain regions Identify mediators Handle HRF diffs Multilevel Nonparam options Y N N N N Y N N N N Y N N* N N Y N Y N N DCM Powerful N Y Y N N SEM modeling of multi-region activity N Y N N N Multilevel mediation Exploratory and confirmatory Y Y Y Y Y Implications of mixed effects modeling Separate within-subjects and between-subjects effects Generalize to new subjects (population inference) by taking into account sampling variability Tests are based on interaction of fixed factors (predictors) with subject (random) Repeated measures: special case One observation per subject per measure. Random intercept, fixed slope Error is based on conditions x subjects interaction Assumes all subjects have same variance ology/tor/ Hypothetical Data for ->M Medial prefrontal activity (fixed) Error terms for Inference: Subject x intercept Subject x slope 22

23 Beyond repeated measures G: benefits of full mixed effects estimation Multi-level model: conceptualize sources of variation in mixed effects model as belonging to 2 levels of analysis Within-subject, between-subject, subject is random effect With more observations within subjects, possible to estimate variance components (within, between), usually using iterative algorithm and ReML estimator Two benefits: If error variance or predictor 1) Retain validity and power with variance (design) are unbalanced designs/unequal variance heterogeneous, a multi-level across subjects model can weight appropriately 2) Provide tests of significance for interindividual variability based on precision. ology/tor/ Multilevel estimation strategy Level 1 Estimate coefficients & variances for each individual, including mediation (ab) effect Level 2 Precision (1/variance)- weighted estimates of fixed and random coefficients (weighted least squares) Update estimates of random effects (between subject) variance using Empirical Bayes coefficient estimates Y ij d 0j c j ij q 1j Q 1ij... q nj Q nij r ij Z j j r ij Y ij d 2j c j ' ij b i M ij q 1j Q 1ij... q nj Q nij f ij M ij d 1j a j ij q 1j Q 1ij... q nj Q nij e ij Path coefficient for subject j Update estimates of coefficients. For classical inference: calculate p- values ology/tor/ Covariates Population effect Subject effect (random) a j Z a g u aj a j Between-subjects predictor(s) * Rapid estimation compared to full iterative approach Analysis 2: Results Develop predictions Update value based on deviations between expectations and experience. Consistent with affective value model mofc QUESTION 1. Do pain matrix regions mediate expectancy effects on pain? 1. Which processes give rise to expectancy effects on pain matrix mediators? ANSWER YES Left insula, rdacc, and right thalamus Anticipatory responses in mofc and right ventral striatum Value and PE? mofc = appetitive PE VS = aversive PE Gottfried et al., 2003 Saddoris et al., 2005 Schoenbaum et al., 2007 LL HH 1. Why use mediation? 23

24 Expectancy Low freq. rtms to L DLPFC Pain Perceptio n a mediator of expectancy effects on pain implicated in cognitive control LDLPFC causes decreases with low pain expectancy (placebo) N=5 p>.1 24