PSY Paper

Original Article

Identifying Patterns in Complex Field Data Clustering Heart Rate Responses of Agoraphobic Patients Undertaking Situational Exposure

Andrew J. White,1 Dieter Kleinböhl,2,a Thomas Lang,3,4 Alfons O. Hamm,5

Alexander L. Gerlach,6 and Georg W. Alpers1,2

1Department of Psychology, School of Social Sciences, University of Mannheim, Germany 2Otto Selz Institute for Applied Psychology – Mannheim Centre for Work and Health, University of Mannheim, Germany 3Christoph-Dornier Foundation for Clinical Psychology, Bremen, Germany 4Department of Clinical Psychology and Psychotherapy, University of Hamburg, Germany 5Department of Psychology, University of Greifswald, Germany 6Department of Psychology, University of Cologne, Germany

Abstract: Ambulatory assessment methods are well suited to examine how patients with panic disorder and agoraphobia (PD/A) undertake situational exposure. But under complex field conditions of a complex treatment protocol, the variability of data can be so high that conventional analytic approaches based on group averages inadequately describe individual variability. To understand how fear responses change throughout exposure, we aimed to demonstrate the incremental value of sorting HR responses (an index of fear) prior to applying averaging procedures. As part of their panic treatment, 85 patients with PD/A completed a total of 233 bus exposure exercises. Heart rate (HR), global positioning system (GPS) location, and self-report data were collected. Patients were randomized to one of two active treatment conditions (standard exposure or fear-augmented exposure) and completed multiple exposures in four consecutive exposure sessions. We used latent class cluster analysis (CA) to cluster heart rate (HR) responses collected at the start of bus exposure exercises (5 min long, centered on bus boarding). Intra-individual patterns of assignment across exposure repetitions were examined to explore the relative influence of individual and situational factors on HR responses. The association between response types and panic disorder symptoms was determined by examining how clusters were related to self-reported anxiety, concordance between HR and self-report measures, and bodily symptom tolerance. These analyses were contrasted with a conventional analysis based on averages across experimental conditions. HR responses were sorted according to form and level criteria and yielded nine clusters, seven of which were interpretable. Cluster assignment was not stable across sessions or treatment condition. Clusters characterized by a low absolute HR level that slowly decayed corresponded with low self-reported anxiety and greater self-rated tolerance of bodily symptoms. Inconsistent individual factors influenced HR responses less than situational factors. Applying clustering can help to extend the conventional analysis of highly variable data collected in the field. We discuss the merits of this approach and reasons for the non-stereotypical pattern of cluster assignment across exposures.

Keywords: ambulatory assessment, heart rate response, agoraphobia, cluster analysis, situational exposure

Research evidence supports the inclusion of exposure therapy as a central treatment component for panic disor- der (PD) and agoraphobia (AG). However, since a sizable minority of patients do not respond to exposure therapy or experience relapse (Boschen, Neumann, & Waters, 2009), it is important to learn more about how symptoms change throughout treatment. Ambulatory assessment approaches are well suited for examining dynamic processes such as physiological and self-report measures across time (Carpenter, Wycoff, & Trull, 2016), and can be applied to

document symptom changes during exposure sessions for patients with PD (Alpers, 2009).

As sample sizes grow and the assessment context becomes more complex, researchers often face a challenge – the variability of data can be so high that conventional analytic approaches based on group averages fail to ade- quately describe individual change. To address this chal- lenge, we outline an approach that relates the structure of variable, dynamic responses to disorder-relevant symptoms, and that supplements conventional analytic approaches.

a Dieter Kleinböhl now works at the Central Institute of Mental Health, University of Heidelberg, Mannheim, Germany.

Zeitschrift für Psychologie (2017), 225(3), 268–284 �2017 Hogrefe Publishing https://doi.org/10.1027/2151-2604/a000310

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Fear Activation

The heart rate response of patients with PD and AG under- taking repeated exposure is dynamic, and is often used to examine fear activation – a hotly debated mechanism thought to underlie exposure therapy. Fear activation refers to the extent to which a patient experiences fear during the confrontation of an exposure area. As a central component of Emotional Processing Theory (EPT), activation of a fear network is regarded as a prerequisite for successful integra- tion of corrective, incompatible information (Foa & Kozak, 1986). Researchers have sought to clarify the association between the degree of fear activation and treatment out- come, yet results remain divergent. On the one hand, some findings have suggested that exposure which elicits greater fear activation is associated with more successful treatment outcomes (Foa, Hembree, & Rothbaum, 2007; Hope, Heimberg, & Turk, 2006). In contrast, other researchers have been unable to replicate this effect (Baker et al., 2010; Craske et al., 2008; Craske, Treanor, Conway, Zbozinek, & Vervliet, 2014; Meuret, Seidel, Rosenfield, Hofmann, & Rosenfield, 2012). We used this debate as a starting point to demonstrate a novel analytic approach that describes how fear responses vary across repeated expo- sure, and are related to other disorder-relevant symptoms. We contended that this helps to extend conventional analytic approaches, which are largely based on averaging across experimental groups. Our overarching aim was thus to examine the variability of patients’ fear responses across repeated exposure with a view to understanding how response types relate to disorder-relevant symptoms.

Heart Rate as an Index of Fear Activation

In the current study, we examined the HR responses of patients with PD and AG. HR has been used to index fear during Behavioral Approach Tests (BATs) and has proven useful in distinguishing between agoraphobic and control participants (Roth, Telch, & Taylor, 1986). Specifically, before and during a BAT at a large shopping mall, the HR levels of agoraphobics were elevated compared to control participants, during both baseline sitting and walking tasks. Moreover, compared to other symptoms, cardiovascular disturbances are central to panic (Cohen et al., 2000; Friedman & Thayer, 1998) and greatest during situational exposure (Alpers, Wilhelm, & Roth, 2005).

Fear activation during exposure therapy is commonly indexed by the maximum fear levels at the start of the exer- cise (Craske et al., 2008; Meuret et al., 2012). For example, initial fear activation was operationalized in one study as the peak (maximum) HR or self-reported levels of distress within the initial stages of the first exposure session (Baker et al., 2010). Similarly, as part of a study on fear reactivity

(activation and reduction of fear responses), peak physio- logical measures were used to calculate within-session acti- vation – baseline values were subtracted from maximum HR values during exposure and averaged across three exposure sessions (Meuret et al., 2012). Although these operationalizations are in line with EPT, they view activa- tion as largely dependent on response magnitude, and do not consider the form or temporal characteristics of responses (i.e., the pattern of activation). Assessing the form and temporal stability of fear responses during expo- sure, particularly within the physiological response domain, may help to shed light on previous divergent findings.

Sources of Response Variation

There are good reasons to expect that the initial HR responses of patients with panic disorder with agoraphobia (PD/A) who undertake situational exposure will exhibit substantial intra- and inter-individual variability. First, the heterogeneous nature of PD/A can contribute to response variability. PD is a disorder comprised of somatic, physiolog- ical, and cognitive symptoms, with some research suggesting that disorder subtypes exist. Respiratory and non-respiratory panic subtypes have been identified using self-report data (Andor, Glöckner-Rist, Gerlach, & Rist, 2008; Drenckhan et al., 2014; Roberson-Nay, Latendresse, & Kendler, 2012), and using physiological parameters such as HR variability (Sullivan et al., 2004). In contrast, authors of a large review of the panic subtype literature concluded that previously identified PD subtypes were not adequately validated and thus lacked predictive validity (Kircanski, Craske, Epstein, & Wittchen, 2009). Nonetheless, studying the associations between panic symptoms, and particularly how they unfold across time, represents a promising approach to explore the organization of disorders (Borsboom & Cramer, 2013).

Another reason to expect large response variance is that the environments in which situational exposure is con- ducted are complex and not all features can be standardized (cf. controlled laboratory studies). The extent to which environmental features covary with psychophysiological activity is an important dimension which shapes individual responses (Cacioppo, Berntson, & Andersen, 1991). At one extreme, psychophysiological activity can vary as a function of a discrete environmental feature (e.g., when a dog is pre- sented to a person with a dog phobia). At the other extreme, activity can vary as a function of multiple environmental features (contextual features), as can be expected under complex field conditions (Fahrenberg, 1996). Because patients may confront a diverse range of threatening envi- ronmental features across repeated exposure, even when situational exposure tasks are standardized, it remains likely that accompanying psychophysiological responses vary as a function of contextual events.

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In sum, the heterogeneous nature of PD/A, as well as the influence of contextual factors inherent in field studies, suggest that initial fear responses will be variable. This calls for an analytic approach that puts the focus on individual responses in order to determine the temporal stability of characteristic physiological profiles. We argue that this has important implications for how specific research ques- tions are addressed.

Reasons for Extending Conventional Analytic Approaches

Complex field conditions play a central role in increasing the variability of responses, which has implications for how aggregation should proceed. Averaging responses is often justified under laboratory conditions, where tight experimental control helps to minimize response variation attributable to uncontrolled contextual variables (Stemmler, 1996). But under variable field conditions, it is too restric- tive to assume that a response is only driven by individual factors and experimental conditions. Since two core assumptions of averaging procedures are that responses have a stable form and time course, we maintain that responses should initially be sorted according to these crite- ria. Sorting by form and level provides an opportunity to determine whether averaging an individual’s responses is justified. In sum, by focusing on individual responses, we think it is possible to extend conventional analytic methods. At the very least, such an approach can promote a better understanding of how disorder-relevant responses (e.g., heart rate and self-reported anxiety) change across time.

Sorting Responses Using Cluster Analysis

Cluster analysis is a structure-revealing procedure used to identify groups of observations that are cohesive and dis- tinct (Fraley & Raftery, 2002). There are several types of cluster analyses, each with their own similarity criteria that are used to estimate the probability that a data point belongs to a particular cluster (Kaufman & Rousseeuw, 1990). Under complex field conditions, it is advantageous to choose a method of clustering that makes few assump- tions about the structure of data. Model-based clustering is suitable for this purpose, does not require the number of clusters to be prespecified, and data are sorted using a combination of hierarchical agglomeration, Expectation Maximization (EM), and Bayes Factors (Fraley & Raftery, 2002). A central assumption of this method is that objects belong to one of several latent, unobserved subgroups. Several successful applications of model-based clustering have been reported. For example, it has been used to group personality traits, which helped reveal distinct pathological

gambling (Vachon & Bagby, 2009) and psychopathy subtypes (Hicks, Markon, Patrick, Krueger, & Newman, 2004).

After assigning data to clusters and assessing the stability of these groupings, it is necessary to validate clusters to explore the meaningfulness of the sorting. The predictive validity of clusters can be demonstrated by comparing responses assigned to clusters with variables external to the sorting procedure (Clatworthy, Buick, Hankins, Weinman, & Horne, 2005), and ideally using measures from multiple response domains (e.g., psychophysiological, verbal, behavioral). In the current study, we validated the cluster solution with three external variables. First, for each cluster, we examined the corresponding momentary ratings of self-reported anxiety collected during (at pre-, peri-, and post-boarding epochs) exposure. The benefits of experience sampling methods are well grounded in theory (for a review, see Santangelo, Ebner-Priemer, & Trull, 2013). In addition, we assessed the concordance between self- report and physiological measures of anxiety (Hodgson & Rachman, 1974). Concordance has been effective in assess- ing change during repeated situational exposure (Alpers & Sell, 2008; Lewis & Drewett, 2006). Finally, we examined distress tolerance, which is a central goal of many psycho- logical interventions. Distress tolerance refers to “the perceived capacity to withstand negative emotional and/ or other aversive states (e.g., physical discomfort)” and also encompasses “the behavioural act of withstanding distress- ing internal states elicited by some type of stressor” (Leyro, Zvolensky, & Bernstein, 2011, p. 4). We were specifically interested in bodily symptom tolerance, which we expected to improve across sessions due to the ameliorative effects of exposure. In sum, we examined the external validity, and thus the substantive meaning, of clusters by examining the correspondence between specific HR groupings and factors derived from other response modalities.

Our Strategy

We applied model-based clustering to heart rate data collected from patients with PD/A who undertook repeated situational exposure. Data were obtained in the context of a multicenter clinical study, in which two active treatments were compared: standard situational exposure and fear- augmented exposure (standard exposure combined with interoceptive exposure) (Hamm et al., 2016). Patients were randomly assigned to conditions and engaged in a fixed sequence of exposures that included therapist-accompanied and unaccompanied exposure. Exposure involved riding on a bus, which was suitable for the collection of psychophys- iological data because there was relatively little bodily movement and thus exercise activation (see Alpers et al., 2005). We assessed the stability of the cluster solution,

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described cluster characteristics, and examined the extent to which patterns of intra-individual transitions between clusters could be explained by several factors relevant to the experimental design and the disorder (e.g., treatment group, session number, sex, age, and bodily symptom tolerance).

In addition, we presented results from a conventional analysis in which unclustered HR responses were examined with respect to treatment condition, exposure session, as well as throughout individual exposures. We were inter- ested in whether level differences or temporal trends distin- guished between treatment conditions and across exposure repetitions. Specifically, we expected a higher average HR among those in the augmented exposure condition, who provoked bodily symptoms with interoceptive exercises during situational exposure. As symptom reductions for PD/A patients are usually observed within several exposure sessions (e.g., Meuret et al., 2012), we expected to see a decrease in absolute response level across sessions.

In summary, we aimed to demonstrate the incremental value of sorting psychophysiological responses to assess the stability of HR responses across repeated exposure. To achieve this, we examined the variability of patient’s fear responses across exposure repetitions to understand how response types relate to panic disorder symptoms.

Method

Participants

As part of the second phase of a multicenter treatment study (Gloster et al., 2011) conducted in Germany across five outpatient treatment centers, participants were ran- domized to one of two treatment groups after they had been recruited through physician referral and via additional advertisements in various media outlets. Inclusion criteria consisted of: (a) age 18–65 years; (b) a current primary diag- nosis of panic disorder with agoraphobia (PD/A) according to DSM-IV-TR criteria; (c) Clinical Global Impressions scale (CGI) score � 4; (d) ability and availability to regularly attend therapy sessions. Exclusion criteria were: (a) current suicide intent; (b) comorbid psychotic or bipolar I disorder; (c) current dependence on alcohol, benzodiazepine, or other psychoactive substance; (d) current psychotherapeu- tic or psychopharmacological treatment for another Axis I disorder; (e) serious medical illness that excluded expo- sure-based cognitive-behavioral therapy (CBT) (e.g., renal, cardiovascular, or neurological disease).

Psychotherapists at each of the cooperating treatment centers coordinated recruitment, delivered treatment, and collected data. At the time of data analysis, data from 98 patients were available, which comprised a total of

298 distinct exposure trials. From these, we excluded 65 trials – 27 contained no HR data; 26 had insufficient pre-boarding HR data; 9, on inspection of global positioning system paths, did not appear to be bus journeys; three could not be correctly aligned due to timestamp or marker prob- lems. The final sample used in the cluster analysis consisted of 85 patients (age:M = 33.89; SD = 10.51; 50 females; 41 in the augmented exposure condition) who had completed 233 exposure exercises. The local Ethics Committees approved all data assessment procedures (for further details, see Gloster et al., 2011).

Materials

Physiological activation (heart rate, HR) and location (GPS coordinates) were collected during exposure using a commercial sports monitor (Garmin Forerunner 310XT, Garmin Ltd., Southampton, UK). Devices from the same product line (“Forerunner” series) have been successfully used to record the HR of participants during laboratory (Polheber & Matchock, 2013; Reid, McMillan, & Harrison, 2011) and field (Avila, Goetschalckx, Vanhees, & Conrelissen, 2014; White, Umpfenbach, & Alpers, 2014) assessments.

Ecological Momentary Assessment (EMA) of self- reported anxiety was conducted with a handheld computer (Apple iPod Touch) and customized software (iDialogPad, Mutz, University of Cologne, Germany). Responses to self-report EMA items were provided on an 11-point Lik- ert-type scale ranging from 0 (= none) to 10 (= very anxious). Prior to bus boarding, patients were asked “How anxious are you now when you think about confronting this situa- tion?”. During bus exposure, patients were prompted to answer the question, “How much anxiety are you experi- encing now?” (post-boarding), every 3 min. Those in the augmented exposure condition were also asked, “Have you tried to augment your anxiety?” After exiting the bus, patients were asked to provide responses to the following questions: “During the exercise, what was the highest level of anxiety you experienced?” and “How well did you manage to tolerate the emergence of physical symptoms?”

To describe patients prior to the commencement of therapy, we reported scores from several measures. The Mobility Inventory (MI; Chambless, Caputo, Jasin, Gracely, &Williams, 1985) was used to assess agoraphobic avoidance across a range of situations. We also include a specific item that describes avoidance of buses. The inventory comprises 27 items, which include specific locations (e.g., theaters), several forms of public transport, and numerous situations (e.g., being far away fromhome). Items are rated on a 5-point Likert-type scale from 1 (= never avoid) to 5 (= always avoid). The MI has demonstrated good internal consistency and discriminant validity (Chambless et al., 2011). The Bodily

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Sensations Questionnaire (BSQ; Chambless, Caputo, Bright, & Gallagher, 1984) assessed the extent to which various bodily sensations elicit anxiety. The BSQ is rated on a 5-point scale ranging from 1 (= not at all) to 5 (= extremely). The Agoraphobic Cognitions Questionnaire (ACQ; Chambless et al., 1984) was used to assess the severity of maladaptive thoughts when anxiety is experienced. It consists of 15 items that are scored on a 5-point Likert-type scale ranging from 1 (= thought never occurs) to 5 (= thought always occurs).

Procedure

The entire treatment comprised 12 sessions and two follow- up booster sessions (two and four months following the last session). Therapy was delivered by advanced-level clinical psychology graduates who received extensive training in the treatment protocol and who were experienced in CBT. Following the screening, informed consent, and initial assessment, patients were randomized to one of two treat- ment conditions: Standard in vivo exposure (standard exposure) or fear-augmented exposure (augmented expo- sure). Those in the augmented exposure condition were instructed to additionally focus their attention toward cues that induced fear, such as bodily symptoms or specific situational aspects, and to perform interoceptive exposure exercises (these were individually tailored to patients) if fear did not occur spontaneously. For both conditions, therapy sessions were 100 min in duration and topics covered in the initial six sessions included psychoeducation; rationale for exposure therapy; behavioral analysis; role of avoidance behavior; interoceptive exposure; and relapse prevention. A bus ride was chosen as a standardized expo- sure task as public transport is frequently avoided by PD/A patients. Patients were instructed to remain on a bus until their fear declined, and to assume a seated position in order to minimize artifacts due to exercise activation (see Alpers et al., 2005).

Session number (within-subjects) represented four possi- ble exposure timings: A therapist-accompanied exposure in Session 7 of therapy (Exposure 1), an unaccompanied homework exposure following Session 7 (Exposure 2), an accompanied exposure in Session 11 (Exposure 3), and an unaccompanied homework exposure following Session 11 (Exposure 4). Since session type (in-session accompanied exposure/unaccompanied homework exposure) and expo- sure timing (Session 7/11) were conflated, we opted to focus on change across session number as the advantages of ther- apist-accompanied exposure were recently demonstrated

(Gloster et al., 2011). We included data from all patients, irrespective of whether they had completed all or only some of these sessions. Of the 85 patients in the final sample, most of them repeated homework exposure (number of completed exposure sessions per patient: min = 1, max = 8, M = 2.74, Mdn = 2, SD = 1.47).

The exposure task was conducted according to a standardized protocol which outlined: The exposure task instructions; device setup (method of connecting the watch to the heart rate belt and GPS satellites), and recording instructions. Recording instructions described how to set an event marker using the watch’s “lap” button at the start and end of exposure, and when to use the EMA device – before, during (every 3 min), and after exposure. Before and during the bus ride, the EMA device prompted patients to rate their current anxiety level. Following bus exposure, it prompted patients to rate how well they tolerated their bodily symptoms.

Homework exposure consisted of a bus exposure task that was carried out without therapists. Patients were instructed to repeat the homework exposure twice between sessions and were provided with worksheets outlining the required monitoring steps. Neither patients nor therapists were blind to group assignment, however patients were not informed about the research hypotheses.

Preprocessing of HR Data

The sample whose data were subjected to cluster analysis consisted of 85 patients who had completed 233 exposure exercises. The mean missing data rate, calculated from the uncompressed1 (1 Hz) recordings, was 0.42% (SD = 1.6%).

We used a baseline concept that capitalized on the standardized start to bus exposure (i.e., waiting for the bus). Baseline was defined as the tonic, pre-boarding HR level.

Selection of a Salient Event and Segmentation

We analyzed an assumed salient event at the beginning of each exposure, which was marked by bus boarding. We argued that it (i) was preferable to analyze intra- individual variability during a fixed interval compared to across an entire exposure, and (ii) made sense to examine HR during this circumscribed event as it allowed us to examine patterns of initial fear activation (cf. Alpers & Sell, 2008; Baker et al., 2010; Meuret et al., 2012).

1 The HR device relied on a data compression algorithm (“smart recording”), where data points were recorded only when parameters (speed, direction, or HR) changed. We found that this algorithm produced a compression ratio of about 3:1 [uncompressed:compressed, 300:300 � (.69 � 300)]. During the study, a software update released by Garmin enabled equidistant sampling of parameters (1 Hz). HR data from 185 trials were decompressed to a common 1 Hz grid.

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Following data extraction from both devices, HR and EMA data were segmented into three epochs (before, during, and after situational exposure exercise). We focused on the interval 2.5min before to 2.5min after bus boarding, and visually inspected data to control for gross artifacts. Our analysis was limited to the first boarding occasion per exposure; patients sometimes had to change buses to reach their desired destination.

Alignment of HR Responses

To identify boarding time, we capitalized on the redun- dancy of information across multiple signals (for a discus- sion of this approach, see Wilhelm & Grossman, 2010). We aligned GPS-derived position changes, speed, and manually-set boarding markers. This involved verifying when the movement speed exceeded 10 km/hr (walking speed does not typically exceed this), when markers had been pressed on the watch and/or EMA device, and when position changes could be construed as bus travel (i.e., on a road, along a bus route).

Statistical Analyses

Cluster Analysis and Stability Assessment Response typologies were identified by applying latent class cluster analysis on the individual raw HR time series data (R-package mclust, Fraley, Raftery, Murphy, & Scrucca, 2012). RawHR data were stored in a wide-format dataframe (233 rows� 300 columns), where rows represented individ- ual exposure exercises, and columns contained HR across each of the 300 s segments. Clustering provided a data- driven sorting of the individual (300� 1 s samples) HR time series into a set of a posteriori groups, minimized within- group variance, and concurrently maximized between- group variance. Similar HR time courses were grouped together in clusters assumed to represent a set of latent class distributions underlying the empirical data. Averaging the HR responses within a given cluster yielded a HR time course, which we considered prototypical for that group.

Two methods were used to assess cluster stability. First, we compared the cluster solution based on the complete data set to those based on data sets reduced consecutively by single HR series. Here, we compared our model-based (latent class) method with k-means and hierarchical (using Ward’s minimum variance criterion) clustering algorithms (R-package clvalid, Brock, Pihur, Datta, & Datta, 2008). Several metrics were inspected: Average Proportion of Non-overlap (APN), the average proportion of observations not placed in the same cluster; Average Distance (AD), the average distance between observations; and Average Distance between Means (ADM), the average distance

between cluster centers. Lower values for each measure reflect improved stability.

Second, we compared a cluster solution based on the entire sample of HR time series to a solution based on a reduced, randomsample (50%of the entire data set, without replacement). To deal with the arbitrary numbering of clus- ters across the two cluster solutions (HR from one trial may be placed in cluster 1 in one solution and in cluster 4 in the next), we compared solutions using the Kappa Max (κmax) statistic (Reilly, Wang, & Rutherford, 2005). This method is an extension of Cohen’s κ, which is commonly used to measure pairwise agreement between a set of raters.

Effectiveness of Clustering and Conventional Analysis We assessed the effectiveness of the clustering procedure by comparing a model with and without a cluster term included as a random effect. To establish the degree to which the cluster solution accounted for nonsystematic variance, we conducted a repeated-measures analysis, in which cluster assignment was included as an additional categorical model term.

Linear mixed models (LMMs) were used to assess the effectiveness of clustering and to examine the effects of a priori experimental conditions (treatment condition, and session number) across time. LMMs are well suited to deal with violations of multisample sphericity and can handle missing data (Magezi, 2015). Main and interaction effects of conditions and time on HR were computed as a linear mixed effects model (R-package nlme, Pinheiro, Bates, DebRoy, Sarkar, & R Core Team, 2015). The HR time series were first collapsed into six 50 s segments (3 � 50 s before and 3� 50 s after bus entry). Two random intercept models were specified to facilitatemodel comparison and to account for nonsystematic variance due to individual differences. In the first model, trials were nested within the participant term to account for nonsystematic variance due to individual differences of subjects (at the trial level). In the second model, the participant term was replaced with a cluster assignment term, which represented the result of the cluster solution. Since the fixed-effects structure was the same in both models, the Akaike Information Criterion (AIC; Sakamoto, Ishiguro, & Kitagawa, 1986) and likelihood ratio (LR) tests were used as model comparison criteria – models with lower AIC statistics and statistically significant LR tests were preferred.

In the conventional analysis of HR, we examined the fixed effects that were based on the a priori design struc- ture – treatment (standard exposure vs. augmented expo- sure) was a between-subjects factor; session number (Exposure 1–4) and timewere within-subjects repeatedmea- sures. HR changes across the six 50 s segments were tested for linear, quadratic, and cubic trends as these encompassed the most plausible HR time courses. Contrasts between

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factor levels were assessed using t-tests, and corrected for multiple comparisons where necessary, using the false discovery rate (FDR; Benjamini &Hochberg, 1995). The sig- nificance level was set at 5% and, where applicable, 95% confidence intervals (CI) are presented.

Cluster Transitions and Assignment To examine changes in intra-individual HR cluster member- ship (transitions) across sessions, we identified frequent and discriminant subsequences on the basis of treatment group and bodily symptom tolerance (R-package TraMineR; Gabadinho, Ritschard,Müller, &Studer, 2011).We also stud- ied the effect of experimental conditions and a postexposure rating of bodily symptom tolerance on cluster transitions. We expected patients who better tolerated their physiologi- cal arousal to have HR responses that remained in HR clus- ters characterized by low physiological arousal (i.e., clusters where HR was less than 100 bpm). Fisher’s exact tests were used to explore the association between overall cluster assignment and experimental conditions (treatment group and session number), sex, and age.

Cluster Validation We assessed the external validity of clusters by examining the association between cluster assignment and three vari- ables external to the clustering procedure. First, for each HR cluster, we examined the corresponding changes in self-reported anxiety collected during (at pre-, peri-, and post-boarding epochs) exposure. Second, we examined con- cordance between HR and self-reported anxiety across treatment conditions, session number, and clusters. Concordance was calculated using interindividual Pearson correlations between HR, averaged across pre-, peri-, and post-boarding epochs, and momentary anxiety ratings (for the same epochs). These correlation coefficients were converted to Z-scores to allow average measures of concor- dance to be computed for treatment group, session number, and cluster. Z-scores were converted back to Pearson’s correlations before the difference between the two correla- tions was calculated. Third, to examine variations in dis- tress tolerance, we calculated Pearson’s correlations between self-rated tolerance of bodily symptoms (reported following each exposure session), and treatment, session number, and cluster. All preprocessing of the physiological data as well as statistical analyses were conducted with the free software R (R Core Team, 2017).

Results

Pretreatment Patient Descriptions

Pretreatment scale scores indicated that patients experi- enced moderately severe symptoms. The mean score from

the MI item that specifically refers to buses suggested that patients avoided buses about 50% of time when alone, M = 3.12, SD = 1.44, and infrequently when accompanied, M = 2.00, SD = 1.33. The Bodily Sensations Questionnaire (BSQ) scores indicated that bodily symptoms (e.g., heart palpitations, dizziness) elicited a moderate amount of anxiety in patients,M = 2.85, SD = 1.87. Agoraphobic Cogni- tions Questionnaire (ACQ) scores suggested that patients occasionally had catastrophic beliefs about the conse- quences of experiencing anxiety and panic, M = 2.09, SD = 0.23.

Cluster Stability

The clustering procedure yielded a stable cluster solution, as evidenced by the convergence of several cluster stability measures (APN, AD, ADM) for three clustering methods (latent class model-based, hierarchical, k-means). APN scores supported an 8-cluster solution (8, 8, and 9 clusters, respectively), AD scores supported a 9-cluster solution (9, 9, and 8 clusters, respectively), and ADM scores an 8-cluster solution (6, 8, and 8 clusters, respectively).

We compared the cluster solution based on the full sample to a solution based on a reduced (50%) sample (κmax = .75). This result indicated good agreement between the solutions. Although the cluster analysis yielded nine clusters, the two smallest clusters (n = 2 and n = 6 trials) were not included in subsequent analyses. These excluded trials were from six patients (Exposure 1 = 4 trials; Exposure 2 = 2 trials; Exposure 4 = 2 trials).

Cluster Characteristics

The average HR time course of trials within the seven clusters showed that individual trials were grouped accord- ing to form and level characteristics and had reduced variability within response clusters (see Figure 1). In all clusters, there was a discontinuity at the estimated time of bus boarding, at time point zero, which reflected the saliency of the event.

Individual waveforms within clusters showed high vari- ability before the event and reduced variability thereafter. This indicated that individual differences in respondingwere most pronounced during the anticipation of bus exposure.

Two cluster sets could be distinguished – three low-level clusters (3, 4, 6), which had a median HR less than 91 bpm, and four high-level clusters (1, 2, 5, 7), which had amedian HR greater than 97 bpm. Although the sample size interfered with the smoothness of average responses, proto- types from Cluster 5 followed an arousal pattern – this typi- cally involved a marked HR increase before the salient event, followed by a decrease. Furthermore, both Clusters 5

Zeitschrift für Psychologie (2017), 225(3), 268–284 �2017 Hogrefe Publishing

274 A. J. White et al., Fear Is Not Uniform

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and 7 showed increased variability, in contrast to other clusters, whose trials had more restricted HR variations. Cluster 7 showed a variable response which started at extre- mely high levels,M = 166 bpm, and decreased to a still high 107 bpm.

Higher HR levels were associated with larger response amplitudes. Concerning the association of response

amplitude and overall HR level per cluster, the law of initial values would only partly explain the distribution of ampli- tudes. The largest response change was approximately 60 bpm and occurred in Cluster 7, which had the highest overall HR level. In Cluster 5, HR increased by about 20 bpm between the pre- and peri-boarding epochs, before decreasing to approximately 100 bpm. In Clusters 1–4,

Figure 1. HR responses across clusters. Clusters were sorted by increasing absolute HR level. Individual trials in each cluster were first centered by removing the mean HR level. The corresponding level information for three consecutive blocks of 100 s time spans is given in the insets as mean HR level (bpm). The variability and the average time course within each cluster are given by the interquartile range (Q1–Q3) which is the area shaded in gray, and the mean, which is indicated by a white line. Single HR responses within each cluster are superpositioned in the background (light gray lines).

�2017 Hogrefe Publishing Zeitschrift für Psychologie (2017), 225(3), 268–284

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and 6, the pre-boarding HR level was elevated and there- after decayed by approximately 10 bpm.

Two clusters (Clusters 5 and 7) contained more variable responses and were characterized by comparatively large peri-boarding HR changes. Cluster 5 was characterized by a phasic HR increase that commenced shortly before (ca. 25 s) bus boarding and returned to pre-boarding levels approximately 75 s post-boarding. In contrast, Cluster 7 was characterized by an initial, elevated HR level that decayed, but which remained unstable at the end of the recording segment. Particularly in the case of Cluster 5, these HR increases likely reflected emotional activation due to bus exposure context. Alternate explanations are also possible. For instance, some patients may have been unable to find a seat before the bus started moving; the traffic conditions may have allowed the bus to travel at a higher speed; the bus may have been more (or less) crowded than on previous exposure. Any of these factors may have placed an additional load on the cardiovascular system.

Effectiveness of Clustering

We assessed the effectiveness of the clustering procedure by comparing unclustered to clustered HR responses. Results showed that inclusion of cluster assignment as a random effects term markedly improved model fit, as indicated by a statistically significant drop in the AIC (AICunclustered = 11,365.56; AICclustered = 10,978.94), and a significant likelihood ratio test, w2(1:2) = 406.42, p < .001.