On the Predictive Value of Network
Characteristics
Marie Katharina Deserno
A thesis presented for the degree of Master of Science
Psychological Methods University of Amsterdam
The Netherlands August 15th, 2014
Name : Marie Katharina Deserno Student ID number : 5996147 Address : Egidiusstraat 81-II
Postal code and residence : 1055 GP Amsterdam Telephone number : +31(0)6 53595632
Email address : marie.deserno@gmail.com
Supervisors
Within ResMas : Prof Dr. Denny Borsboom
Specialization : Psychological Methods / Clinical Psychology External supervisor : Dr. Marieke Wichers
Second assessor : Sacha Epskamp
Research center / location : University of Amsterdam / Maastricht University
Number of credits : 29ec
Abstract
Previous studies have suggested that a dynamic network approach to psychopathology o↵ers a promising framework to study major depression (Bringmann et al., 2013; A. Cramer et al., 2012; A. O. Cramer et al., 2010; Van de Leemput et al., 2014). To consolidate the clinical utility of the network paradigm, we need to overcome several methodological obstacles. In this project, we aimed to explore (i) how well individual network characteristics at one stage can predict the individual’s chance to recover at a later stage, and (ii) what specific network characteristics play an important role in this. We aimed to establish a testing framework including (i) a method that enables us to structurally di↵erentiate between healthy networks and depressed networks based on their network parameters and (ii) a method to investigate the predictive value of these network characteristics for an individuals’ chance to recover. For this task, we used the baseline ESM data and the post-treatment measurements regarding
depressive symptomatology of 102 individuals with major depression. However, our results did not expose meaningful di↵erences in network characteristics between
recovered (responders) and not-recovered (non-responders) individuals. Thus, based on this study we cannot conclude that (i) healthy networks and pathological networks actually di↵er from each other with respect to network characteristics at baseline and (ii) that specific characteristics show predictive value for an individual’s risk to relapse or recover.
Introduction
In the past two decades, scientists witnessed an epidemic-like spread of interest in system-level approaches instead of reductionist approaches to objects of scientific interest (Barab´asi, 2011). The driving force behind this shift is inevitably related to high-throughput technologies (e.g., momentary assessment technology) that o↵er unparalleled opportunities to gather data on complex systems. In psychometrics, the issue of how to measure and model inter- and intra-individual variability is a topic of ongoing discussion (Chow et al., 2005; Wang et al., 2012). To date, the most
commonly used approach is based on the common cause hypothesis as it is
implemented in latent variable models. Often, latent variables are assumed to be the underlying cause of the covariance between observed variables, such as an individual’s answers to items on a mood questionnaire (Borsboom et al., 2003). Consequently, individuals are assigned to the same diagnostic categories while their
psychopathological profiles in fact have little in common. The level of heterogeneity in individuals’ symptom display, illness course, need for therapy, and treatment response is so prominent that researchers and clinicians doubt whether common labels can provide much clinical utility (Van de Leemput et al., 2014).
A Dynamic Network Approach to Psychopathology
Recent developments on the matter of system-level approaches in psychopathology have been pointing towards a dynamic network approach for the analysis of
psychological constructs (Bringmann et al., 2013; A. O. Cramer et al., 2010). The network perspective (Borsboom, 2008; A. O. Cramer et al., 2010) is a relatively new psychometric conceptualization in which psychological phenomena are seen as a dynamic set of causally intertwined properties (e.g., insomnia ! fatigue !
concentration problems). Instead of seeing observed variables as indicators of a latent variable, this novel approach suggests that these observables are tightly related by causal and functional mechanisms. This conceptualization combined with momentary assessment technology provides us with a new psychometric toolbox to study the complex (time-)dynamics of psychopathology with a much more individualized approach. Uncovering the architecture of complex psychological processes, such as a↵ective experiences, would require time series data. This type of data can be obtained with the experience sampling method where data are collected repeatedly over
di↵erent time points, for example, on a↵ective experiences of patients in their daily lives (Csikszentmihalyi & Larson, 1987).
Figure 1. Example of a Network Visualization with R-packageqgraph(Epskamp et al., 2012)
Items or symptoms are represented as nodes and their interrelations as red (inhibitory) or green (enhancing) edges. The strength of the connection is visualized by the thickness of the edge: the stronger the connection, the thicker the edge. Self-loops are represented by autoregressive arrows from a node to itself.
Recent empirical evidence suggests that the network perspective, indeed, provides an adequate and promising approach to study several psychological disorders (Wichers, 2013) such as major depression. First, intra-individual analyses of multivariate time series data have demonstrated direct relations between variables that are related to psychopathology (Bringmann et al., 2013). Also, symptoms of major depression display distinct responses as a consequence of major life events (such as the loss of a loved one; (A. Cramer et al., 2012)) and show di↵erent relations to other external variables and to other (distinct) disorders (Lux et al., 2010). Furthermore, clinical experts themselves report a dense set of causal relations between symptoms of various psychopathology (Borsboom & Cramer, 2013; Kim & Ahn, 2002). Finally, using recently developed self-report methods, individuals with elevated symptom levels typically report causal interactions between their symptoms of anxiety, posttraumatic stress and major depression (Frewen et al., 2012).
The Predictive Value of Network Characteristics
After the theoretical consolidation of the network paradigm, an inevitable next step lies in the challenge to overcome some methodological obstacles. In order to investigate the clinical utility of network analysis and representation we need to investigate the
predictive value of network characteristics and define a range of network parameter values (i.e., connection strength, number of connections, self-loops, number of feedback loops) for which the behavior of a system becomes pathological. Additionally, we need to establish a method to quantify similarity, change, and di↵erence of networks to gain extremely relevant insights: Can we predict critical transitions from being healthy to being depressed? Research on dynamical systems has shown, for example, that positive feedback loops among causal relations can cause a system to have alternative stable states separated by tipping points (Sche↵er et al., 2009). Earlier research in ecosystems has shown that a large perturbation of the system (i.e., a treatment intervention in our case) might have more impact if timed very near a tipping point instead of further away from that point. Based on this finding, Van de Leemput et al. (2014) have shown that the mood system also displays signals of critical slowing down, a phenomenon that emerges when a dynamic system approaches a tipping point: elevated temporal autocorrelation, variance and cross-correlation between a↵ective experiences. This suggests that studying the mood regulation system on system-level can provide promising insights to improve treatment strategies for patients with major depression.
Key Questions
In this study, we aimed to examine whether specific characteristics of depressed networks at baseline predict whether a planned intervention will be e↵ective or not: Can we translate individual network architecture into individual predictions of risk for relapse or recovery? To answer this question, we need to establish a testing framework, including (i) a method that enables us to structurally di↵erentiate between healthy networks and depressed networks based on their network parameters (e.g., do healthy networks and pathological networks actually di↵er from each other with respect to specific parameters?) and (ii) a method to investigate the predictive value of these characteristics for the risk to relapse or recover.
Since this research project mainly focusses on the enrichment of a new psychometric toolkit, we want to be clear about the fact that the research is conducted in an exploratory fashion: We did not test specific hypotheses. Generally, we expected to find that patients with a highly connected network of symptomsand many feedback loops are less likely to recover. Here, we translate this expectation in terms of, amongst others, the number of connections between symptoms, self-loops, connection strength and feedback loops. This is based on the idea that the probability of a symptom being present, depends solely on the activation of its neighbors and its autocorrelations (Van de Leemput et al., 2014). We may expect the following network characteristics to be relevant to an individuals’ risk for recovery/relapse: (i) high connectivity between indicators of negative a↵ect, especially in combination with low connectivity between indicators of positive a↵ect and high cross-connectivity between indicators of opposite
valence, (ii) signs of violated stationarity in the network (e.g., the adjacency matrix’ eigenvalue is higher than one (1)) and (iii) strong presence of indicators for critical slowing down (as specified above). We aim to investigate the di↵erences in (latent) network architecture between di↵erent groups and shed some light on the predictive value of these characteristics for an individual’s risk of relapse or recovery.
Method Participants
This study is based on clinical data1 from the Institute of Mental Health Care Eindhoven and the Kempen and Maastricht University Medical Centre obtained with palmtop-based experience sampling. A total of 124 participants aged 18 to 65 were recruited from mental health care facilities in the cities of Eindhoven and Maastricht by their health care professionals and by distributing posters and flyers in health care facilities and local media. Inclusion criteria were (i) a DSM-IV-TR diagnosis of a depressive episode with a current symptom score on the Hamilton Depression Rating Scale -17 (HDRS) above remission cut-o↵, i.e. a score that is equal to or above 8, (ii) receiving pharmacological treatment with antidepressants or mood stabilizers, (iii) adequate vision, (iv) sufficient Dutch language skills, (v) no current or lifetime diagnosis of non-a↵ective psychotic disorder, and (vi) no (hypo) manic or mixed episode within the past month.
Procedure
Participants were provided with a palmtop (PsyMate; (Wichers et al., 2012)) that followed a programmed assessment schedule. They carried the palmtop with them during a 5-day experience sampling (ESM) baseline assessment period, a 6-week intervention period and the 5-day ESM post assessment. On each experience sampling day, there were up to ten assessments, within a 14-hour time frame, during which the questionnaire items were presented to the participant. Responses were uploaded to a central server. At each assessment occasion, the participants used the PsyMate to digitally complete a brief questionnaire on their current a↵ective and physical experiences, their current context (i.e., location, social environment et cetera) and their activities.
After baseline, patients were randomly assigned to three treatment arms: the experimental, pseudo-experimental or the control group. The randomization to the di↵erent conditions was stratified in terms of (i) duration of antidepressant
pharmacotherapy, and (ii) whether one currently receives psychotherapy. The
experimental group participated in a longitudinal ESM measurement phase of 3 days a
1This data set has been previously used in published articles, however the predictive value of network
week over a 6-week period in addition to treatment as usual. This also included weekly (standardized) feedback on individual patterns of positive a↵ect. The
pseudo-experimental group also participated in this ESM procedure in addition to treatment as usual but without the feedback component. The control group did not participate in the ESM procedure in addition to treatment as usual.
There were four items serving as indicators of positive a↵ect (cheerful, content, enthusiastic and relaxed) and six items serving as indicators of negative a↵ect (down, suspicious, guilty irritated, lonely and anxious). At each assessment occasion
participants were instructed to indicate how much they were experiencing each of the ten a↵ective experiences at that very moment. The answering scale ranged from 1 (not at all) to 7 (very). Participants were instructed to complete the questionnaire as fast as possible after they received a beep.
Material
The palmtops that have been used to collect the ESM data belong to the Department of Psychiatry and Psychology, Maastricht University. The palmtops have been
programmed with software to control the schedule, present the items and upload the participants’ responses to a central server. As noted above, the PsyMate questionnaire that has been used in this study consisted of ten mood items.
Measures
Numerous recent studies (Geschwind et al., 2011; Os et al., 2013; Wichers, 2013) have shown clear e↵ects of experimental modification of the dynamic a↵ective network on the increase or decrease in depressive symptomatology, as assessed by the HDRS. Given our research question, we selected six of the momentary assessment items as prototypical representations of pleasant and unpleasant a↵ective and physical experiences that are variable in the daily lives of individuals with major depression. The items serve as indicators of depressive symptoms (physically tired, worrying), high- and low-arousal positive a↵ect (cheerful, satisfied ) and high- and low-arousal negative a↵ect (agitated, feeling lonely).
Analysis
Power calculations for previous work (Kramer et al., 2014) led to the initial sample size of 120 with a power of 84% to detect a 3-point di↵erence in HDRS score. However, forty-six participants were excluded for this study because they did not complete enough assessment beeps (i.e., less than 30 % of the possible beeps) for the baseline ESM period (n = 27) or did not complete the Hamilton Depression Rating Scale at the follow-up measurements (n = 19). Included participants varied in their number of completed beep questionnaires between 17 and 50 completed assessments.
Since we are interested in decrease of depressive symptoms over time, we defined a priori that a clinically relevant cuto↵ would be 3 or more points decrease in Hamilton Depression Rating Scale -17 (HDRS) scores (Hegerl & Mergl, 2010; Kramer et al., 2014). Forty-two people met this criterium and were labeled as responders, while thirty-two people did not meet this criterium and were labeled as non-responders. In order to test whether an individual’s a↵ective system can be labeled as ’recovered’ or not we aim to develop a testing framework including ranges of network parameter values that identify the a↵ective system as depressed or healthy. First, we want to test whether depressed networks di↵er from healthy networks with respect to their network parameters. For this task, we will only use the baseline ESM data and the post
measurements regarding depressive symptomatology of all three groups (the
experimental group, the pseudo-experimental and the control group in the study). We aim to extract individual baseline networks to investigate whether certain network characteristics at baseline can predict an individual’s risk of recovery from (or relapse into) a depressive episode at post measurement. These network characteristics are translated in terms of, for example, (i) the number of connections in an individual’s a↵ective network, (ii) the number of feedback loops in the a↵ective network, (iii) connection strengths between symptoms and connection strengths of self-loops, and (iv) centrality measures in the network.
Results
Responders and non-responders did not significantly di↵er in sociodemographic characteristics. In addition, we found no significant di↵erence in baseline depressive symptoms between patients who completed the full intervention period and those who did not (HDRS; B=.76, p=.73).
A Vector Autoregressive Model for Multiple Time Series
We started our analytical path with a new approach to time series data to extract individual network dynamics: we estimated a multilevel vector autoregression model on the baseline data that models the time dynamics of the selected variables both within an individual and on group level (Bringmann et al., 2013). With this
multivariate extension of an autoregressive model each variable (node in the network) is regressed at time point t to a lagged version of itself at time point t 1 and all other variables at time point t 1. Since we have six items, there are six such regression equations in our analysis. In other words, this analysis allows us to relate the dynamics of all six symptoms on one day to the dynamics of these symptoms on the consecutive day and so forth.
Figure 2. Baseline Average Population Network.
The six items are: physically tired, worrying, feeling cheerful, feeling lonely, feeling agitated and feeling satisfied. The edges indicate either an inhibitory relationship (red, i.e., beta smaller than zero) between the (a↵ective) experiences or an enhancing relationship (green, i.e., beta is larger than zero).
By applying the multilevel VAR method to the baseline measures we can not only estimate the average connection strengths between all variables (e.g., symptoms) in the population but also infer separate networks based on each individual’s variability. To construct these individual networks, Bringmann et al. [2013] suggest to take the estimate of the population standard deviation of the person-specific (random) e↵ects and add it to the fixed e↵ect of the respective connection in the network. Each slope then represents the strength of the temporal connection between the respective nodes in the depressed network. In the constructed networks, both individual and on group-level, we see that a↵ective experiences of the same valence cluster together (see Figure 2). The positive mood items are connected through green edges among each other, representing enhancing relationships. The same patterns goes for the negative mood items among each other. Between a↵ective experiences of the opposite valence there are mostly red edges, representing inhibitory relationships. These self-sustaining clusters of a↵ective experiences and high cross-connectivity between indicators of opposite valence can bet interpreted as in line with a dynamic perspective on a↵ect (Fredrickson & Joiner, 2002). We could not identify a particular pattern regarding the connectivity between a↵ective experiences, as suggested in the introduction: we did not find a particular high connectivity between indicators of negative a↵ect in combination with low connectivity between indicators of positive a↵ect.
The created networks allow for the identification of the focal points of the network (Opsahl et al., 2010) by looking at measures of node centrality. To gain information about the relative centrality of the di↵erent nodes in the network, we conducted a global network analysis (Bringmann et al., 2013) based on the networks extracted with the implemented VAR-model. This analysis enables us to investigate di↵erences in the global structure of the network for di↵erent groups. We studied the di↵erences in the relative betweenness, closeness and degree centrality (for an elaborate definition of these concepts, see (Costantini et al., 2014)) between two groups: patients that showed clinically relevant improvement on the HDRS (a change of > +3,“responders”) and patients that did not show significant improvement on the HDRS (a change of < +3, e.g.,“non-responders”). We illustrate these findings in Figure 3 by graphically
displaying some of the centralities of the nodes for both, the responders and the non-responders.
Figure 3. Centrality Measures for the Responders and the Non-Responders.
This figure shows three centrality measure for all six items: betweenness, closeness and node strength (or degree). The red lines refer to the individuals that did not recover (non-responders) while the blue lines refer to the recovered individuals (responders).
Given our research question, we added the individual’s relative change score on the HDRS, i.e. the di↵erence between the individuals’ baseline score on depressive symptoms and their follow up score (after 32 weeks), as a covariate to the multilevel VAR model. For none of the variables in our model, the change score covariate was significant. Thus, we cannot conclude that the responders di↵ered from the
non-responders in terms of their network structure of the six selected variables. Consequently, focusing on patterns in specific item connections might not be the right approach to structurally di↵erentiate between healthy networks and depressed
networks. People may di↵er qualitatively with regard to (i) associations between specific symptoms and (ii) the directionality of this association, but they might be similar in the e↵ects amongst their a↵ective experiences (i.e. predictability of their symptoms).
Latent Networks for Responders and Non-Responders
To explore this idea in depth we took a next analytic step focusing on shared
time-lagged e↵ects in the patients groups (responders/non-responders): a latent vector autoregressive model (Epskamp et al., n.d., in preparation). This VAR model is extended by modeling each personal network as a mixture of constant latent networks. In other words, this model enables us to check whether responders and non-responders
can be identified at baseline by two structurally di↵erent latent networks. The authors suggest that these common patterns in the personal networks could then be identified by estimating mixing parameters using the population estimates of latent networks. In our study, we translated this novel idea as follows: We split the data in two equal parts. First, we aimed to identify two distinct latent networks within the first part of the data. Following the suggested procedure in Epskamp et al. (n.d., in preparation), we then estimated the mixing parameters within the second part of the data to identify patients whose network structure resembles either the responders’ or the non-responders’ latent network. However, conventional model selection methods (read: RMSEA, CFI, Chi-Square, et cetera) did not suggest the presence of two latent networks to be eligible in our sample. We were therefore not able to identify a
di↵erence in shared patterns in the a↵ective network of responders and non-responders.
Network Connectivity and Feedback Loops of Responders and Non-Responders
To examine di↵erences in network connectivity between the two groups, we extracted all the individual’s slopes from the multilevel model (Pe et al., 2014) and conducted an independent samples t-test comparing the responders and the non-responders
regarding the density of their depressed network. Since we were mainly interested in the strength of the connections in the network, we calculated the average of the absolute value of the slopes to represent the network connectivity for each individual (Pe et al., 2014). Again, we did not find a substantial di↵erence in the connectivity of the depressed networks at baseline between responders and non-responders.
Additionally, there was no di↵erence in the strength of self-loops between the two groups. Thus, the groups did not di↵er in the extent to which the activation of a symptom in their a↵ective network on one day predicts its activation on the next. Finally, we examined a third network characteristic relevant to the vulnerability of an individual’s network: the number of feedback loops that create self-sustaining clusters of symptoms in the network. For this purpose, we identified the feedback loops in each individual’s network of symptoms, using the R-package LoopAnalyst (Frewen et al., 2012, Dinno, 2009). The analysis of feedback loops in each individual’s network revealed that the number of feedback loops ranged from 0 to 40 amongst the
participants. However, we did not find a di↵erence in the number of feedback loops in the depressive networks of responders and non-responders.
Discussion
To our knowledge, this study is the first attempt to elucidate the predictiveness of specific network characteristics for an individual’s risk to recover or not. However, our results did not expose meaningful di↵erences in network characteristics between recovered (responders) and not-recovered (non-responders) individuals in our sample. This was not in line with the general hypothesis underlying this exploratory study. Although we looked into di↵erent characteristics and parameters of the groups’ networks, we did not find support for the idea of di↵erent shared patterns in the networks of responders and non-responders at baseline. Thus, based on this study we cannot conclude that (i) healthy networks and pathological networks actually di↵er from each other with respect to network characteristics at baseline and (ii) that specific characteristics show predictive value for an individual’s risk to relapse or recover. Methodological Limitations
However, the lack of meaningful results of this study might also be related to some methodological obstacles that need to be overcome before we can elucidate di↵erences in network architecture. First, we should make sure that the extracted networks based on regression weights are una↵ected by our sample size and the variance of the
symptoms (i.e. nodes in the network). This is particularly important for all endeavors that aim to delineate di↵erences in network architecture between two groups. Previous power calculations suggest that our sample size (n=78) is rather small for the research we conducted (Kramer et al., 2014). When we, as in this study, attempt to compare the network of recovered (or healthy) and pathological networks, we should be able to verify that di↵erences in network parameters can be attributed to di↵erences in architecture instead of di↵erences in sample size between the groups. This remains difficult when considering networks with edges based on significant regression coefficients: the larger the sample size the more edges the network contains. In addition, the number of variables (nodes) that we could include in the multilevel extension of the vector autoregressive model (Bringmann et al., 2013) is limited to six. The architecture of the networks is therefore unlikely to be definitive. With the choices we made regarding the inclusion of items we aimed to cover most important
components of the average depressive network. Undoubtedly, this does not delineate a complete picture of the temporal dynamics in depressive symptomatology. Currently, di↵erent research groups focus on the extension and validation of the multilevel VAR model (Bringmann et al., in preparation) with more than six variables. Thus, future endeavors using this model approach might already have the opportunity to benefit from their work in progress. Another issue could be that participants varied in the number of assessment time points they completed. For example, some participants’
networks are based on only 40% of the possible assessment points, others completed up to 80%. Hence, before we can start future e↵orts focusing on similar research
questions, we should make sure that these methodological issues are solved.
Additionally, the potential of other techniques for determining structural di↵erences in network architecture should be investigated. The approach of Pe et al. (2014) to investigate network connectivity suggests to calculate the absolute slope values of the temporal relations between the various nodes in the network. Thus, the directionality of the associations among the nodes is not taken into account. Generally, this is less important when focusing on the quantification of network connectivity only. However, when interested in qualitative di↵erences (e.g., feeling more sad after feeling angry vs. feeling less sad after feeling angry), we need to take the directionality of the
associations into account.
Predicting Categorical Change from Micro-Level Information
Finally, it might be worth to take a step back and consider a more theoretical discussion point. Does micro-level information on an individuals’ dynamic mental system, as gathered with ESM technology, really predict an individuals’ change in their sum score on a diagnostic questionnaire like the HDRS? One could argue that
structural changes in ESM data collected for the purpose of elucidating a↵ective day-to-day dynamics, might only be predictive of recovery right before a substantial switch (e.g., phase transition) in the network. In this study, however, we investigated whether the structure of day-to-day a↵ective dynamics at baseline, as assessed by momentary assessment technology, predict a clinically relevant change within diagnostic categories at a later stage. In other words, it might be more insightful to investigate a shared pattern in networks while they approach a point of relevant change (e.g., tipping points, as suggested by Van de Leemput et al. (2014)). Future e↵orts might benefit more from following that line of thought when further developing a network approach to predict whether someone recovers or relapses.
In general, it might also be important to discuss the plausibility of the idea of shared network architecture of responders and non-responders at baseline, as assessed with ESM technology. Do people with major depression that recover within a certain timeframe really share similar network parameters in such an early stage? As suggested before, it might be more insightful to focus on shared patterns in network connectivity right before one can observe a categorical change. This is mainly because it seems more plausible that all individuals have di↵erent network parameters but that specific circumstances combined with individual network reactivity can lead to a phase transition in the network.
As this particular project is a subproject of the PsychoSystems project of the
Psychological Methods department of the University of Amsterdam, this study should be considered a first exploration of the predictive value of network characteristics. In terms of intended results, we aimed to overcome the previously specified
methodological obstacles and be able to predict depressive patients’ clinical risks based on their network characteristics. We intended to define network characteristics at baseline that di↵er between the recovered and the relapsed patients. Our goal was to be able to report network characteristics that contribute to a depressed patient’s risk to relapse or recover after a planned intervention. The investigation of a network approach to patient’s recovery could have important implications for the development of more personalized treatment schedules based on an individual’s a↵ective system characteristics. Given the fact that depression ranks among the most wide-spread mental health problems, to be able to assess the likelihood of recovery/relapse based on individuals’ networks would facilitate in reducing the immense societal costs of major depression. In addition, if characteristics of networks vulnerable to develop major depression are known, then this might aid in developing preventive strategies. Finally, other scientific disciplines, such as the study of genetic correlates of major depression, might benefit from future e↵orts in this direction by being o↵ered an alternative research path. Usually, genetic variants are conceptualized as potential predictors of sum scores for a specific phenotype. The network paradigm could o↵er a more fruitful approach to conceptualize genetic variants as potential predictors of certain symptoms and relations between these symptoms.
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