Is the Looming Maladaptive Cognitive Style a Central Mechanism in the
(Generalized) Anxiety – (Major) Depression Comorbidity:
An Intra-Individual, Time Series Study
Thesis submitted in partial fulfillment of the requirements for the degree of “DOCTOR OF PHILOSOPHY”
by
Dana Tzur-Bitan
Submitted to the Senate of Ben-Gurion University of the Negev
May 2011
Beer-Sheva
Is the Looming Maladaptive Cognitive Style a Central Mechanism in the
(Generalized) Anxiety – (Major) Depression Comorbidity:
An Intra-Individual, Time Series Study
Thesis submitted in partial fulfillment of the requirements for the degree of “DOCTOR OF PHILOSOPHY”
by
Dana Tzur-Bitan
Submitted to the Senate of Ben-Gurion University of the Negev
Approved by the advisor Approved by the Dean of the Kreitman School of Advanced Graduate Studies
May 2011
Beer-Sheva
ii
This work was carried out under the supervision of Prof. Nachshon Meiran and Prof. Golan Shahar
In the Department of psychology Faculty of Humanities and Social Sciences.
iii
Acknowledgments
First and foremost, I would like to thank my advisors, Professor Nachshon Meiran and Professor Golan Shahar, for their guidance and support throughout the past six years. To
Proffesor Meiran, who has constantly challenged me to critical thinking and encouraged me to experiment, for carrying a positive and optimistic view, and for balancing my emotionality with a rationale and professional attitude. To professor Shahar, for mentoring my development as a psychologist and encouraging me to peruse my inner passions, for being genuinely interested in my success, and for taking an active part in my professional and personal growth. Thank you both for fruitful discussions, financial and moral support, and for sharing your knowledge and skills with me.
I would like to deeply thank Professor David Steinberg, the head of school of mathematics in Tel Aviv University, for providing statistical and mathematical consultation. I would like to express my gratitude to the ISEF foundation, for providing me with financial support through 4 years of my phd studies. Not less important, I would like to thank the longitudinal phase participants, RG, RS, and HB, for letting me into their world and sharing their thoughts, feelings and experiences with me. To my dearest Colleagues, who are in essence my friends, for truly being there for me when I needed the most.
Last but not least, I would like to thank my family: my mother, for baring the anxiety of my long distance travelling and for constantly praying, literally, for my health and success; to my mother and father in law, for countless hours of babysitting. To my wonderful husband, Daniel, for providing me with everything I need, and not a thing less. You have been the most stable and closest comfort, a true partner, and I love you. And for my beautiful, intelligent sons, Har’el and Yali, for making this journey a challenge at which I am especially proud to surmount.
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To the men in my life: Daniel, Har’el and Yali
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Contents
Abstract …………………………………………………………….……….………1
1. Introduction …………………………………………………………….……....……5
1.1 The Co occurrence of Anxiety and Depression Disorders……………...... ……5
1.2 The need for multidimentional assessment of anxiety and depression….....……6
1.3 Explanatory models for the study of anxiety and depression comorbidity…...…8
1.4 The dynamic nature of anxiety and depression…………………………..…..…10
1.5 Exploring intra-individual dynamics using time series analysis…………..……11
1.6 Application of TS analysis in human behavioral sciences………….…....……..12
1.7 Summary of study objectives…………………………………….……………..15
2. Methods …………………………………………………………………….……….. 16
2.1 Participants………………………………………………………………..…….16
2.2 Procedure……………………………………………………………….….……17
2.3 Assessment…………………………………………………………...…..….….17
2.4 Data Analysis………………………………………………………………..….19
2.4.1 General overview of statistical methodology……………...... …...19
2.4.2 Statistical analysis and mathematical procedure………….….…..22
2.4.2.1 Stationarity examination and pre-transformations……….….…...24
2.4.2.2 ARIMA(p,d,q) modeling…………………………………...……27
2.4.2.3 Granger Causality Test……………………………………..…….33
2.4.2.4 Transfer Function Modeling……………………………….....….34
3. Results ………………………………………………………………………..…...…38
3.1 Step 1: Modeling each series separately………………………………..……....38
(how past levels of the series determine its current levels)…………………..…….38
3.2 Step 2: Granger Causality Tests…………………………………………...……40
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3.3 Step 3: TFM……………………………………………………………..….....…43
Estimating the size and positive/negative directionality of the causal influences...... 43
3.3.1 Within disorders…………………………………………….…...45
3.3.1.1 Within depression………………………………...…...45
3.3.1.2 Within anxiety…………………………………...……46
3.3.2 Between disorders………………………………………….……47
4. Discussion ……………………………………….……………………………...……. 48
5. Limitations ...... 51
6. Conclusions ...... 53
7. References ……………………………………………………………………....……. 55
8. Appendixes ……………………………………………………………………………………..……..67
- Appendix I……………………………………………………………………..……68
Summary of ARIMA models fitted to 8 collected series of each participant …. ……...…….68
-Appendix II…………………………………………………………………….…….70
Final transfer and noise function for between anxiety and depression components…….…. …70
-Appendix III………………………………………………………………...... 71
Final transfer and noise function within anxiety and depression components ...... 71
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List of Tables
Table 1. Summary of collected series in each data set…………………...... ….………22
Table 2. Mathematical formulation of MA, AR, and ARMA processes….…...... ……29
Table 3. Parameter Estimates and diagnostics statistics for Hopelessness in Participant
RS……………………………………………………………...... …...... ……30
Table 4. Estimated models, parameter diagnostics and correlations for the series
Hopelessness in Participant RS………………………………………....…...... ……..32
Table 5. Mathematical formulation of the Granger Causality Test…………...... ……34
Table 6. Mathematical formulation of the transfer and noise function……...... ………35
Table 7. Model Testing in of “Helplessness” as input and “Depression Symptoms”
as output in participant HB………………………………………………...... …..……38
Table 8. Summary of ARIMA models fitted to 8 collected series of each participant……………………………………………………………………...... …….39
Table 9. Significant and marginal Granger’s causality (F-tests)………….…...... …….41
Table 10. Transfer and Noise Function Models of pairs showing Granger
Causality within each disorder construct……………………………………...... …….44
Table 11. Transfer and Noise Function Models of pairs showing Granger Causality between anxiety components and depression components……………………...... …..45
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List of Figures
Figure 1. Flow chart of overall Analytic procedure in the current study…...……….23
Figure 2. Plots of the original series of participant RS, for evaluation of
Stationarity………………………………………………………………….………..24
Figure 3. Autocorrelation and Partial autocorrelation plots for series Hopelessness
in participant RS……………………………………………………………...……..25
Figure 4. Hopelessness series pre and post first order differencing and stationarity tests of the series after differencing……………………………....….….26
Figure 5. Cross Correlation Function of series “helplessness” as input and series “depression symptoms” as output in participant HB…………………………..37
Figure 6-8. Visual representation of causal network as detected by Granger
Causality Test in participants RS, HB, RG, respectively………….…………………42
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Abstract
The high prevalence of anxiety and depression co occurrence has been investigated and documented extensively in the past two decades. The disabling nature and poor prognosis in comparison to its pure presentation, along with the familial and financial burden associated with it, has caused the question of etiology to be a topic for ongoing research. Yet, in spite of ongoing and persistent clinical and empirical search, it seems that the underlying mechanisms of anxiety and depression comorbidity are still poorly understood.
Integrating the various findings related to this complex and multi dimentional phenomena, explanatory models focus on the exploration of the underlying mechanism causing these two clusters of disorder to co appear. The more traditional approach is based on the shared factor hypothesis, which pertains to the possibility that a higher order psychopathological factor underlies both disorders. Yet, recent approaches suggest the exploration of causation models, which targets one disorder
(or one of its components) as the cause of the other, or, alternatively, suggest reciprocal causality. Such causal relations are usually established by the temporal precedence of one disorder relative to the other, yet longitudinal studies have yielded mixed results regarding the exact pattern of presentation and failed to give a clear answer regarding the causal trajectory of these two disorders.
Exploring such possible causal trajectories, I examined the dynamic unfolding of anxiety depression comorbidity while emphasizing its multifaceted and intraindividual nature. An intensive time series design was employed, whereby three young adult patients diagnosed as suffering from co morbid Generalized Anxiety
Disorder (GAD) and Major Depression Disorder (MDD) were followed daily for a
1
period of 6 months. Daily reports included affective states, cognitive vulnerability, and symptoms of depression and anxiety.
An experience sampling questionnaire included specific items from well known self report questionnaires in order to fit the daily measurement structure of the study. The affective component of anxiety and depression was assessed using items from the Positive and Negative Affect Scale – Expended Form (PANAS X, Watson &
Clark, 1994), and included adjective related mostly to fear and sadness. Symptoms of depression and anxiety were assessed using items from the Beck Depression Inventory
(BDI, Beck, Steer & Brown, 1996) and the Beck Anxiety Inventory (BAI, Beck,
Epstein, Brown & Steer, 1988), and included symptoms such as anhedonia, sleep disturbances, apatite and energy for depression, and fear of the worst happening, feelings of panic, and increased heartbeat for anxiety. Cognitive vulnerability to anxiety and depression was assesses on two cognitive continuums: the first is the helplessness hopelessness axis using items from the short version of the Hopelessness
Helplessness Questionnaire (Lester, 2001), and the second, through the continuum of looming rumination; Looming Maladaptive Style (LMS), pertaining to the individual’s tendency to generate mental scenarios of potentially threatening situations that are rapidly rising in risk or intensifying in danger, was assessed with items taken from the Looming Maladaptive Style Questionnaire (LMSQ, Riskind, Williams,
Gessner, Chrosniak, & Cortina, 2000). Rumination, a cognitive vulnerability factor for depression, was assessed using items from the Ruminative Response Scale of the
Response Style Questionnaire (RRS RSQ, Nolen Hoeksema & Morrow, 1991) and measured rumination in response to depressed mood such as focusing on either the meaning of rumination or the subjective feelings related to the depressed mood.
2
Overall, 8 components were assessed for each participant, and included sadness, fear, symptoms of depression, symptoms of anxiety, helplessness, hopelessness, looming and rumination.
The results of each of the three participants were analyzed and treated as a separate study, whereby each such study contained 8 time series constructed from 180 daily measurements collected during the 6 month assessment period. Time Series
Analyses (TSA) included three main stages: First, each series were evaluated separately in order to assess the influence of past observations on the current and future dynamics of the series (ARIMA modeling). Regression based causality tests
(Granger, 1969) were then employed within each two variables, and enabled the assessment of causality within each disorder components (such as between depression symptoms and sadness) and between the two disorders (such as between anxiety symptoms and hopelessness). Pairs showing significant causation were further analyzed to determine direction, intensity and duration of the causal relations, using
Transfer Function Modeling (Box, Jenkins & Reinsel, 1994).
The results of the TSAs showed that LMS was predictive of Depression
Symptoms in two participants, and predicted Hopelessness, a cognitive vulnerability marker of depression, in other two participants. Within each disorder components, causal relationships involving Hopelessness and Depression Symptoms were found across all three participants. In two participants, these relationships were unidirectional, leading from Hopelessness to Depression Symptoms. In the third participant, an opposite pattern, leading from Depression Symptoms to Hopelessness, was found. Within anxiety related constructs, I found evidence for causal relations involving Looming and Anxiety Symptoms, with a pattern leading from Anxiety
3
Symptoms to Looming in one participant, and a reversed pattern in another.
The above mentioned findings have important implication in terms of conceptualization, methodology and for treatment and assessment. First and foremost, they provide an intra individual support for the hopelessness theory of depression, as well as the role of LMS as a vulnerability factor for anxiety. Furthermore, they suggest a possible causal mechanism linking anxiety to depression through the cognitive mechanism of LMS. The uniqueness of the causal network per each participant bares important implications for the ability to infer from cross sectional design to the specific individual, and support previous notions regarding the need to develop individualized treatment programs based on such causal representations (Haynes &
O’Brien, 2000; Haynes, 1997; Haynes & Williams, 2003). Overall, these findings emphasize the need to include an intra individual analysis for the purpose of elucidating the nature of psychopathological comorbidity, as well as for prompting the inclusion of longitudinal assessment methods for therapeutic purposes.
Key words: Anxiety and Depression, Comorbidity, Time series analysis, intra individual variation, Looming Maladaptive Style.
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Is the Looming Maladaptive Cognitive Style a Central Mechanism in the
(Generalized) Anxiety – (Major) Depression Comorbidity: An Intra-Individual,
Time Series Study
1. Introduction
1.1 The Co-occurrence of Anxiety and Depression Disorders
Anxiety Depression comorbidity is usually considered to be the rule, rather than the exception, in psychopathology (Kessler et al., 1996; Maser & Cloninger,
1990; Mineka, Watson, & Clark, 1998; Zimmerman, Chelminski, & McDermut,
2002). Large scope epidemiological studies indicate that 58% of patients with lifetime major depressive disorder have at least one anxiety disorder (Kessler et al., 1996). Of patients with lifetime generalized anxiety disorder, it is estimated that up to 62% also have major depressive disorder and 40% of them have dysthymia (Wittchen, Zhao,
Kessler & Eaton, 1994). The WHO Collaborative Study found that depression was 9 times more likely to develop in patients with anxiety disorders compared with those of no mental illness, with 39% of patients with current depression also having an anxiety disorder and 44% with a current anxiety disorder having comorbid depression
(Goldberg & Lecrubier, 1995).
The high prevalence of anxiety and depression co occurrence is especially meaningful in light of the greater disability associated with comorbid psychiatric disorders. Specifically, anxiety and depression co occurrence has been documented to result in a more severe course of illness, elevated social, marital and occupational impairment, risk for suicide, and a poor treatment response (Weissman, Klerman,
Markowitz & Ouellette, 1989; Cox, Direnfeld, Swinson & Norton, 1994; Ormel,
5
Oldehinkel, Brilman & van den Brink, 1993; Coryell et al., 1988; Noyes et al., 1993).
In comparison to pure presentation of each disorder, anxiety and depression comorbidity creates significantly higher economic and social burden, with patients in this group consuming 10 20% higher costs of health care budget (McLaughlin,
Geissler & Wan, 2003). Such severe costs, coupled with high prevalence rate, have made the study of anxiety and depression co occurrence to be extremely relevant field of investigation in recent years.
1.2 The Need for Multidimensional Assessment of Anxiety and Depression
In spite of ongoing and persistent clinical and empirical search, it seems that the underlying mechanisms of anxiety and depression comorbidity are still poorly understood. Part of the inconsistency in nosologic conclusions is related to the fact that these psychopathological entities are complex and multifaceted; Both anxiety and depression are presumed to include mood states (e.g., fear, sadness), clinical symptoms (e.g., hypervigilance, anhedonia), and distinct cognitive vulnerability.
Therefore, a model striving for a full account of the anxiety depression relationship cannot be limited to the presence of symptoms, but also to the affective and cognitive components of each disorder.
Some theoretical frameworks addressing the affective component of anxiety and depression suggest anxiety to be mostly related to fear and depression as mostly related to sadness, whereas a range of negative affect states such as anger, guilt, shame, and shyness appear in both clinical conditions (Bartlett & Izard, 1972; Izard,
Blumberg, & Oyster, 1985). This common range of negative affect is often regarded as the basic etiological factor underlying anxiety depression comorbidity (Clark,
Watson, & Mineka, 1994). Building on these findings, Clark and Watson (1991) 6
propose the "Tripartite Model" as a theoretical model that identify the affective structure underlying clinical anxiety and depression. According to this model, depression and anxiety share a common negative affect factor, but are distinguishable by the fact that anxiety uniquely includes physiological hyperarousal, whereas depression is uniquely characterized by an absence of positive affect (i.e., anhedonia,
Clark & Watson, 1991; for empirical support, see Brown, Chorpita, & Barlow, 1998;
Watson, Clark, & Carey, 1988).
Suggestions for cognitive mechanisms underlying anxiety depression comorbidity are slightly more prevalent. Pioneering the quest for cognitive basis of depression and anxiety, Beck (1976) suggested that each psychopathological condition is characterized by a disorder specific cognitive content. As such, individuals experiencing emotional distress have automatic negative thoughts born out of a maladaptive belief system about themselves and the world. The schematic representation of depression revolves around schemas dealing with loss, personal deficiency, worthlessness, and hopelessness. Conversely, anxiety is founded on schemas dealing with danger, uncertainty, and future threat. Once activated, these automatic thoughts bias individuals to interpret events in a negative manner consistent with the underlying schema (Beck & Emery, 1985). Therefore, it has been suggested that the progression through a cognitive continuum of helplessness hopelessness might account for their frequent co occurrence. Empirical studies have found some evidence for Helplessness to be a vulnerability dimension shared by both anxiety and depression, while Hopelessness appears to be a distinct depressive vulnerability
(Alloy, Kelly, Mineka, & Clements, 1990).
Another possible cognitive continuum is along the axis of rumination
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looming. Rumination, a focal cognitive vulnerability, pertains to the tendency for self reflection and repetitive and passive focus on one’s negative emotions (Morrow &
Nolen Hoeksema, 1990; Nolen Hoeksema, 1991). While rumination was demonstrated to be implicated in depressive vulnerability, it was also shown to be involved in the co occurrence of depression and anxiety (Cox, Enns & Tylor, 2001). A distinct cognitive volunerbility factor related to anxiety is the Looming Maladaptive
Style (LMS), pertaining to individuals' tendency to generate mental scenarios of potentially threatening situations as rapidly rising in risk or intensifying in danger.
This style was shown to be a distinct dimension of cognitive vulnerability to anxiety disorders (Riskind et al., 2000; Riskind & Rector, 2007; Riskind, Tzur, Williams,
Mann & Shahar, 2007; Riskind & Williams, 2006; Williams, Shahar, Riskind &
Joiner, 2005). LMS was also proposed as a depressive vulnerability dimension, mainly through its derailment of perceived ability to cope with life problems, thereby generating helplessness and hopelessness (Rector, Kamkar & Riskind, 2008).
1.3 Explanatory Models for the study of Anxiety and Depression Comorbidity
Another important consideration for of anxiety depression comorbidity is related to methodological differences across studies. For example, when reviewing past literature, one has to distinguish between Mixed Anxiety and Depression disorder
(MAD) and Comorbid Anxiety and Depression, both currently part of the DSM IV.
Study population in such studies may also vary from diagnosed, to subthreshold, presentation of symptoms. In addition, cross sectional studies might vary in results from longitudinal studies. Different definitions of comorbidity in terms of lifetime versus current diagnosis also add to the complexity of the overall picture.
A possible way to disentangle the various aspects of these complex entities is 8
by being explicit about links between data and the derived conceptual and statistical models. Systematic characterization of different comorbidity models has been provided previously (Neal & Kendler, 1995; Klein & Riso, 1993; Krueger & Markon,
2006), and has offered a general conceptual framework for the organization of data relating to co occurrence of two, or more, pathological phenomena.
One of the most dominant groups of explanatory models for the study of anxiety and depression comorbidity is based on the shared factor hypothesis, which pertains to the possibility that a higher order psychopathological factor underlies both disorders. This group of models, also referred as “Associated Liabilities models” posits that each disorder is influenced by a latent liability factor, and that these liability factors are correlated. Theoretical models nested in this group include the negative affectability factor of the Tripartite Model (Clark & Watson, 1991), neurotism as a shared genetic predisposition (Gray & McNaughton, 2000) or behavioral inhibition as a common mechanism (Hirshfeld et al., 1992).
Conversely, the causal relationships explanation targets one disorder as the cause of the other, or, alternatively, suggests reciprocal causality. In this group of models, also referred to as “causation models”, comorbidity results from the direct influences of one disorder on the development of the other. Such causal relations are usually established by the temporal precedence of one disorder relative to the other, yet longitudinal studies have yielded different conclusions regarding the pathways leading from one disorder to the other. While most studies suggest that anxiety proceeds, and might even bring about, depression (Breslau, Schultz & Peterson, 1995;
Hettema, Prescott & Kendler, 2003; Kessler et al., 1996; Lewinsohn, Zinbarg, Seeley,
Lewinsohn & Sack, 1997), other studies are consistent with the supposition that both
9
disorders are equally likely to be the first in a co morbidity sequence (Moffit et al.,
2007). Recently, it has been offered to model causal relations between symptoms of anxiety and depression using a network approach (Cramer, Waldorp, van der Maas &
Borsboom., 2010), by which direct influences are measured between the manifest symptoms of each disorder. By using such approach, the authors suggested the existence of yet a different pathway, namely leading from depression to anxiety. Thus, should such causal relations exist, standard statistical methodologies have failed to clearly determine its directionality.
1.4 The Dynamic Nature of Anxiety and Depression
A possible theoretical explanation for the inconsistency of results relating to temporal precedence of anxiety and depression is the dynamic, time variant, nature of each disorder. Intra individual study conducted recently suggest the existence of intense daily fluctuations in symptoms, cognitions and affective variants of both disorders, unique to participants reporting elevated levels of both anxiety and depression. Such a pattern was found to be sharply contrasted with the relatively stable manifestation of anxiety and depression in participants exhibiting, to begin with, elevated levels of either, but not both, anxiety and depression (Tzur Bitan,
Meiran & Shahar, 2010). Therefore, it is possible that co occurrence of anxiety and depression results in a unique pattern of variation, and therefore more intense sampling is needed in order to capture its temporal rhythm.
Exploring the dynamic unfolding of depression and anxiety over time may enable the detection of causal relationships, not only with respect to disorders , but also in terms of components of each disorder, e.g., between a cognitive vulnerability dimension of anxiety and a mood component of depression .An analogy
10
demonstrating the promise of this approach comes from intelligence research. In this field, the dominant theory posits a general intelligence factor (Spearman, 1904).
According to this theory, the abilities that are measured in individual tests indicate this general ability to a certain degree. However, new studies that emphasized the development of abilities suggest a drastically different account. According to this alternative account, the correlations between abilities reflects the influence of one ability on the acquisition of another, rather than reflecting the fact that these abilities are determined by a general factor (van der Mass et al., 2006).
1.5 Exploring Intra-individual Dynamics Using Time Series Analysis
Exploration of the such day to day dynamics is best captured using intra individual research methodology (Molenaar, 2004; Molenaar & Campbell, 2009), preferably relying on the a time series (TS) design (Wohlwill, 1973; Ford & Lerners, 1992;
Gotlieb, 1992, 2003; Molenaar, Sinclair, Rovine, Ram & Corneal, 2009; Granic &
Hollenstein, 2003). Extensively used designs, such as cross lagged Structural
Equation Modeling (e.g., Shahar & Davidson, 2003) or Latent Difference Scores
Modeling (LDS, McArdle & Hamagami, 2001), do allow for the investigation of dynamic unfolding of psychological conditions. However, these designs are limited in several important respects. First, they test hypothesized causal relationships across – rather than within individuals. As such, they make the assumption that causal relationships are identical across all, or most, of the individuals, an assumption that might be (grossly) oversimplified (Granic & Hollenstein, 2003). Second, rank order designs such as cross lagged SEM or LDS do not examine changes in absolute levels of a symptom (e.g., changes in depression symptoms) but rather estimate rank order change, namely, change in the relative positioning of participants in comparison to 11
others. Finally, although rank order designs permit intense measurement over time, in practice such intensity is difficult to employ because of the need to assess a large sample of participants. The end result is comprised of studies employing up to five or so waves of measurement, as compared to approximately 180 in this study.
TS designs circumvent these shortcomings. Such designs consist of assessments employed at short intervals (e.g., one day, in the present case). Data pertaining to each variable (e.g., depression) per each participant is then considered as a series. Each level of a variable within a series is related to the level predicted by previous fluctuations of that variable within the same individual , rather than to the sample mean or to other participants. Then, series are linked to each other intra individually, allowing to empirically examine the extent to which causal patterns are identical vs. different across individuals.
1.6 Application of TS analysis in Human Behavioral Sciences
TS analysis has been originally developed and employed in the field of economics. At its onset, this statistical application was used to construct models for the United States economy (Tinbergen, 1939). The prevailing assumption at that time was that of the classical linear model, assuming residuals were stochastically independent of each other.
Cochrane and Orcutt (1949) were the first to notice the dependency of the residuals, and to point the potential overestimation caused by positive autocorrelation. Almost at the same time, Durbin and Watson (1950/1951) developed a test for the estimation of first order autocorrelation. The techniques suggested by these authors during the following years, as they are applied today, were summarized by a textbook published in the 1970's by George E.P.Box and Gwilym M. Jenkins (1976), and received considerable attention.
Today, these techniques are widely known as Box Jenkins analysis, and are applied in
12
numerous fields of research.
Today, TS analysis is widely used in the fields of economy and physical and environmental sciences. Daily usage of TS analysis includes the evaluation of stock market quotations and unemployment analysis; in epidemiology, for the study of changes in epidemics; in functional magnetic resonance and various medical applications; for the evaluation of global warming and its relation to population; in voice and speech analysis for the development of computerized speech recognition and simulation; for the study of seismic recordings, and much more (Hamilton, 1989; Friston, Jezzard & Turner, 1994;
Gubbins, 2004).
The need for intra individual TS designs in psychological research has been noted previously, on the basis that such methods are more suited to the statistical features of psychological pro cess (Hamaker, Dolan & Molenaar, 2005; Molenaar, 2007).
Specifically, it has been argued that inter individual studies do not take under consideration the fact that not all individuals obey to the same dynamic low governing the psychological process under investigation , and that these the dynamic lows do not have time invariant statistical characteristics (i.e., stationarity). Therefore, the application of inter individual derived conclusions to the specific individuals is somewhat problematic.
The investigation of longitudinal, intra individual processes in the field of psychology in general and psychopathology in particular, is very scarce. A few reasons for this state of affairs are the complexity of data analysis, which often requires analyst judgments and expertise, and the fact that such methods, namely time series, ARIMA, impulse response (IRF) and state space modeling are usually part of training programs in engineering, economics and sciences, not psychology. These methods are also sometimes considered to be very conservative, usually demanding 13
data cleaning and pre transformations that might conceal or diminish the effects. Yet, although practical limitations do exist, these methodologies are able to provide important insights regarding anxiety and depression co occurrence, and more specifically the causal trajectory from one disorder to the other.
One of the fields which can potentially gain from the use of such methodology is psychotherapy, whereby process oriented questions are very eminent (e.g. Kazdin &
Nock, 2003; Jones, Ghannam, Nigg, & Dyer , 1993; Laurenceau, Hayes & Feldman
2007). Considering the general framework of psychotherapeutic work, it is possible to exploit the sequential regularities occurring between consecutive session in order to assess and optimize ongoing individual psychotherapeutic processes in real time.
Molenaar and his colleges (2009) have proposed an innovative and somewhat controversial computerized paradigm for such optimization, which is based on a dynamic model of the client’s state as a function of the therapeutic manipulations. Yet, insofar there have been only a very limited number of case studies employing such data collection method in psychotherapy research (Jones et al., 1993; Pole and Jones, 1998;
Pole Ablon & O'Connor ., 2008).
Theoretical models in developmental psychology, such as the Developmental
Systems Theory (DST), have also called for the adoption of intra individual variation studies, asserting that each individual can be conceived of as a high dimensional integrated dynamic system (De Groot, 1954). Additional explorations of intra individual dynamics are scattered in different and not necessarily connected fields in psychology, such as in the study of pain (Buck & Morley, 2006), drugs side effects (Soliday, Moore &
Land ., 2002), work satisfaction and mood in light of daily stress (Fuller et al., 2003) and self esteem (Ninot, Fortes, & Delignières, 2005). In psychopathology and mental illness research, intra individual studies are also very scarce. In a recent review paper, such lack
14
of sophisticated designs for the study of the course of illness and recovery processes in
Schizophrenia as been emphasized, on the basis of theoretical models exhibiting the dynamic and fluctuating nature of this illness (Peer, Kupper, Long, Brekke & Spaulding
2007; Kupper & Tschacher, 2002).
1.7 Summary of Study Objectives
Integrating the multifaceted nature of anxiety and depression, and the distinction between rank order and intraindividual changes, this study examined the direction of relationships between affective, symptomatic and cognitive components of anxiety and depression. Study participants were three patients diagnosed with comorbid
Generalized Anxiety Disorder (GAD) and Major Depressive Disorder (MDD), due to
GAD MDD high prevalence (Massion, Warshaw, & Keller, 1993 ; Wittchen, Beesdo,
Bittner & Goodwin, 2003). These patients were assessed daily over a 6 months period.
TS analyses were conducted to disentangle directionality pertaining to the three disorder components, whereby each participant serve as an entire study (e.g. Dunn,
Jacob, Hummon & Seilhamer, 1987; Brossart, Willson, Patton, Kivilighan & Multon,
1998; Pole et al., 2008). The main focus of the study was on within participant findings replicated across the three patients.
15
2. Methods
Study protocol and methods has been fully reviewed by the IRB committee at the department of Psychology of Ben Gurion University of the Negev, and was approved prior to the start of data collection.
2.1 Participants
Two hundred and twenty six female undergraduate students were evaluated for anxiety and depression using the Beck Depression Inventory (BDI) and the Beck
Anxiety Inventory (BAI). Students high in anxiety and depression, as evident by higher then cutoff score of 15 on the BDI and BAI, were invited for a structured clinical interview (SCID; First, Gibbon, Spitzer & Williams, 1996), and were assessed for the presence of current GAD and MDD. Note that each participant found to suffer from significant symptoms of a possible disorder was advised to turn to the counseling services. Of this sample of participant, 4 were invited to a clinical interview, and 2 were found to meet SCID criteria for co morbid GAD and MDD.
These participants were recruited to the follow up study and completed a 6 month follow up.
Students treated at the counseling services of Ben Gurion University were also invited to participate. An initial screening was conducted by a clinician from the counseling services based on a clinical interview and MMPI data (Butcher,
Dahlstrom, Graham, Tellegen & Kaemmer, 1989). From this pool of candidates, 8 students were evaluated using the SCID. However, only one met criteria for a diagnosis of co morbid anxiety and depression. This student participated in the next stage. Thus, a total of three participants with a SCID diagnosis of both MDD and
16
GAD completed the 6 month longitudinal daily evaluation.
2.2 Procedure
Upon signing an informed consent form, the above three participants began a
6 month follow up which included daily assessment via phone conversations with the study coordinator. Assessment was performed in fixed intervals at the participants’ preferred time during the evening. The participant was instructed to report her experiences from the last measurement. Each phone conversation was documented. In cases where participants reported elevated distress, a risk assessment and crisis intervention was conducted by Golan Shahar, who is an experienced clinical psychologist. Due to repeated administration of the experience report form, it was necessary to shorten the form as much as possible, while still including the necessary items for the evaluation of the different dimensions. Therefore, specific items were included in the experience report form.
2.3 Assessment
Participants' daily level of affect, symptoms, and cognitions were measured via a report form, developed for this study. The affective component of anxiety and depression was derived from the Positive and Negative Affect Scale – Expended Form
(PANAS X, Watson & Clark, 1994). It is a 60 item adjective check list designed to measure two higher order affects of negative and positive affect along with 11 specific affects such as guilt, self assurance, fear, sadness etc. For the purpose of the current study, 11 items addressing 2 specific affects were included: 6 items related to fear (i.e. afraid, scared, frightened) and 5 related to sadness (i.e. blue, downhearted, alone).
Symptoms of depression and anxiety were assessed using items from the Beck
17
Depression Inventory (BDI, Beck et al., 1996) and the Beck Anxiety Inventory (BAI,
Beck et al., 1988). Each consists of 21 self report items each, designed to measure symptoms of depression (BDI) or anxiety (BAI), respectively. Five items addressing depression symptoms were chosen from the BDI, and included: sadness, anhedonia, sleep disturbances, apatite and energy. Additional four items addressing anxiety symptoms were chosen from the BAI, and included: fear of the worst happening, feelings of panic, increased heartbeat and difficulty breathing.
Cognitive vulnerability to anxiety and depression was assessed by the items from the short version of the Hopelessness Helplessness Questionnaire (Lester, 2001), an 8 item likert scale, measuring helplessness, hopelessness and haplessness (the feeling of having bad luck or bad fortune). This questionnaire was adopted from the
Pessimism Scale (Back, Weissman, Lester & Trexler, 1974), and was shortened by the aid of Principal Components Analysis to include 4 items of each sub scale (Lester,
2001). In the current study, 8 items of the short version sub scales of helplessness and hopelessness were used, and included items such as “I can’t think of reasonable ways to reach my current goal” for helplessness, and “I look forward to the future with hope and enthusiasm” for hopelessness.
Cognitive vulnerability to anxiety was also assessed using items from the
Looming Maladaptive Style Questionnaire (LMSQ, Riskind et al., 2000), a measure of individual’s tendency to generate mental scenarios of potentially threatening situations that are rapidly rising in risk or intensifying in danger. The LMSQ consists of six items describing potentially stressful situations (such as hearing a strange noise from the engine of your car while driving on the highway) and participants are asked to complete 4 questions for each description using a five point Likert scale (such as: “To
18
what extent do you feel worried or anxious due to imagining this scenario?”, “Are your chances of having difficulties with your car increasing or decreasing with each moment?”). In the current study, the description was removed in order to fit the daily experience structure of the questionnaire. Therefore 4 items were re designed to address increasing feelings of worry from a general daily event (e.g., “To what degree have you felt worried or anxious?”, “Are your chances of having difficulties increasing or decreasing each moment?”).
Cognitive vulnerability to depression was derived from the Ruminative
Response Scale of the Response Style Questionnaire (RRS RSQ, Nolen Hoeksema &
Morrow, 1991). The RRS RSQ is a 22 item self report measure aimed at assessing rumination in response to depressed mood such as focusing on either the meaning of rumination or the subjective feelings related to the depressed mood (“I think about how I feel”), on symptoms and on consequences and causes (“I think I won’t be able to do my job if I won’t snap out of it”). For the current study, 3 items were chosen to represent ruminative response style, and included Items 1, 17, 26.
In summary, the questionnaire that the participants filled on a daily basis yielded the following scale scores: Fear, Sadness, Depression Symptoms, Anxiety
Symptoms, Hopelessness, Helplessness, rumination and Looming.
2.4. Data analysis
2.4.1. General overview of Statistical Methodology
Broadly speaking, TS analysis evaluates a series of observations pertaining to a specific variable (e.g., Depression Symptoms). An underlying assumption of TS is that past trends contain pertinent information with respect to subsequent trends. In other words, TS enables the examination of the influence of past values of the series
19
on its current value, referred as “auto influences”. These auto influences are represented by the three components of what is known as the Autoregressive
Integrated Moving Average (ARIMA) model (Box, Jenkins & Reinsel, 1994). The first component, the autoregressive one , represents partial accumulation from past values (e.g., today's depression is likely to spill over to tomorrow's). The second component is needed when the mean level of the variable changes over time (i.e., there is an increase or decrease, etc.). The third is the moving average component, which represents the influences of random changes in the past (also called “random shocks”) on the current level. These changes or “shocks” are said to be random because they cannot be predicted on the basis of the past behavior of the sequence.
Next stages of analysis are aimed at modeling the effect of one series (say
LMS, or “X”) on another (say, Depression symptoms, or “Y”). The underlying principle of TS is that the three auto components, or sources of influence, represented in ARIMA, should be taken into account prior to estimating the effect of X on Y. This is done as follows. First, the second ARIMA component, representing the mean change pattern, is addressed by differencing, in which the preceding value is subtracted from the current value. The other two components (i.e., autoregressive and moving average) are addressed via "prewhitening", a procedure tantamount to residualization in regression. The procedure is somewhat analogous to hierarchical regression in which the first block of predictors includes the ARIMA components
(representing Y influences upon itself) and the second block includes X.
Importantly for the study purposes, TS enables the examination of directional
(i.e., causal) relations between two series. Assessment of causal relations is conducted by evaluating an input output model consisting of a predictor (X) and outcome (Y)
20
“cleaned” from their respective auto influences.
Causal examination in TS is conducted via Granger's Causality Test (Granger,
1969), followed by fitting a “Transfer Function” (TF). The Granger Causality Test examines whether past levels of variable X determine current levels of variable Y.
Specifically, X is said to Granger cause Y if previous levels of X are significantly correlated with the current level of Y, meeting the requirement for temporal precedence in determining causality. This test includes a comparison between the residuals of two regression models, one containing only past values of the variable Y, the other containing both past values of X and past values of Y. A significant reduction in unexplained variance, as determined by the F test difference comparing the two residual series, means that residuals are significantly lower when adding past values of X into the regression model, thereby, X Granger causes Y.
Once Granger’s causality is determined, it is important to determine and quantify its directionality (e.g., whether an increase in depression causes subsequent increase or decrease in anxiety) using TF. In the TF, the current level of the variable
Y is estimated as a function of the mean level of that variable (represented by an intercept term), and the influence of current and past levels of X. Additional influences of past values of the output series, after accounting for influences of variable X, are assessed by additional ARMA procedure (also referred to as “noise function”), and are added to the model 1. Thus, the modeling process in TS involves a sequential testing of various influences. When a given influence is found not to be significant, it is dropped from the model. Model fitting is done by evaluating different combinations of parameters for the series until the residuals show no additional
21
information (such series is referred to as “white noise”) .
Table 1 summarizes the data collected and analyzed for each of the three participants. Each of the variables in Table 1 was computed as the sum of its items in any given day.
Table 1.
Summary of collected series in each data set
Anxiety Depression
Affect Fear Sadness
Symptoms Anxiety symptoms Depression symptoms
Cognitions1 Helplessness Hopelessness
Cognition2 Looming Rumination
2.4.2. Statistical Analysis and Mathematical Procedures
In Figure 1 I present a flowchart of the overall statistical procedure. Detailed guidelines regarding the Box Jenkins methodology for time series analysis and forecasting are available in tutorial books (e.g. Yaffe, 2000; Brocklebank & Dickey,
2003). In this section I will provide step by step description of the analysis, including relevant diagnostics and mathematical formulations.
1The inclusion of the noise function is needed because when each series has been cleaned from its past influence, the influences of the other series have not been taken into account. Once the other series is 22
considered, additional auto influences may be found. 23
Figure 1.
Flow chart of overall Analytic procedure in the current study.
Time seri es
A. Test Stationarity:
Review Original Series
Stationary Unit Root tests Not stationary
Transformation / B. Test For Statistical Independence: Differencing White noise Test (Lejong Box)
End Indepe ndent Dependant
C. Diagnose Form of Dependence and model fitting: AR.I.MA modeling
Review ACF, PACF, IACF
Test for tentative models
Test for Collinearity White Noise Test Test Goodness of Test Parameter (Portamanteau) Fit: Significance AIC/AICC/SBC
Forecast Yes Adequate Model No
Causality Not D. Test for causality: Causality End Detected Granger Test Detected
Diagnose Cross Correlation Function Assess Delay, Numerator and Denominator Order Perform Pre whiting Procedure
E. Test for tentative models
Test for Collinearity White Noise Test Test Goodness of Test Parameter ( ( Portamanteau) Fit: Significance AIC/AICC/SBC
24 No Adequate Model Yes End
2.4.2.1. Stationarity examination and pre-transformations
In order to apply the Box Jenkins methodology to time series data, each series
must be made stationary, i.e. it should vary randomly around a constant mean value
and have a constant variance across time (see sections A and B in Figure 1). In social
sciences, most series are non stationary. Therefore, transformation such as
differencing or log transformation is frequently needed. In order to assess stationarity,
the first stage includes examination of the time series plot and visual impression of
non stationary processes such as a trend, random walk, drift or changing variance.
Figure 2 presents plots of the evaluated series in participant RS, for illustration.
Figure 2.
Plots of the original series of participant RS, for evaluation of stationarity.
• Fear • Helplessness
• Sadness • Hopelessness
• Rumination • Anxiety Symptoms
• Depression Symptoms • Looming
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As can be seen, most series appear stationary, with the exception of Hopelessness, which shows a decreasing trend. Aside from the visual inspection, the series is examined for stationarity by inspection of the Auto Correlation Function (ACF) and
Partial Auto Correlation Function (PACF). Figure 3 presents the autocorrelation plots of series Hopelessness in participant RS for demonstration purposes.
Figure 3.
Autocorrelation and Partial autocorrelation plots for series Hopelessness in participant
RS.
The autocorrelation plot indicates that values of the series are correlated with their past values almost up to lag 14. This can be seen by the fact that the bars
(representing auto correlations) consistently cross the statistical significance line up to
Lag 14. Review of the PACF enables assessing the order of differencing needed to make the series stationary. This order is expressed as the integrated component (I) of 26
the ARIMA model, such that first differencing can be expressed as ARIMA (0,1,0).
The partial autocorrelation function is significant up to lag 1, indicating that a first
order difference transformation (namely, subtracting the preceding value (time t 1)
from the current value (time t) will be sufficient for making the series stationary.
Figure 4 presents the Hopelessness series before and after transformation. Note that
most statistical packages enable performing unit root tests for stationarity such as the
Phillips Perron, Dickey Fuller and Augmented Dickey Fuller tests (Dickey & Fuller,
1979; Phillips & Perron, 1988).
Figure 4.
Hopelessness series pre and post first order differencing and stationarity tests of the
series after differencing.
TOTNEWHOPE
TOTNEWHOPE Simple Difference
TOTNEWHOPE TOTNEWHOPE
26 8
6 24
4
22 2
20 0
-2 18
-4
16 -6 14 -8
12 -10
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Once the series has been transformed, a Chi Square statistic is used to test for additional information (see section B in Figure 1). This is done by a standard
Portamanteau test as offered by the Ljung Box formula (1978). The null hypothesis is that the current set of autocorrelations should be regarded as white noise, namely, that the pattern indicates that no additional modeling is needed. If this null hypothesis is not rejected, then the series can be said to contain no additional information and no additional analysis is done. If, however, this null hypothesis is rejected, then the pattern of dependence is further analyzed using ARIMA modeling.
2.4.2.2. ARIMA(p,d,q) modeling
After stationarity has been established, the plots of autocorrelation and partial autocorrelation of the residuals are reviewed for estimation of a tentative model to best describe the underlying process of the series (see section C in Figure 1). ARIMA modeling is based on three possible parameters: An Auto Regressive parameter (AR, p), an Integration term when the series has undergone differencing (I, d), and a
Moving Average parameter (MA, q).
An autoregressive model is generated by a weighted average of past observations going back p periods, together with a random disturbance et in the current period. An
AR possesses has an infinite memory in the sense that it is based on the correlation of each value with all preceding values, while the impact of earlier values diminishing exponentially over time. In a first order autoregressive model, the current value is a function of the immediate proceeding value, which is itself a function of the value before it, and so forth. Consequently, all proceeding vales influence current values, albeit with declining impact. For these reasons, an autocorrelation function plot of an
AR process has an exponentially decreasing appearance, reflecting the diminished 28
impact with increasing lag. Partial autocorrelations are usually used to establish the order of the autoregressive process. These partial autocorrelations remove the (linear) influence of shorter lags (so that when computing the partial autocorrelation of Lag 3, for example, the influence of Lag 1 and Lag 2 is statistically removed). However, the order of the autoregressive process is determined by the last lag for which the partial autocorrelation was significant.
In moving average models , each observation is generated by a weighted average of random disturbances going back q periods. Essentially, it is a linear regression in which the predicted value is the current value of the series and the predictor is the error term (or random shock) of one or more prior values of the series. This is the part of the variance in these past observations which is unexplained by auto regression.
Unlike the autoregressive component, which enjoys an infinite memory, the moving average process possesses a memory of limited duration, equal to the value of its order. For example, if the moving average process is of Order 1, the correlation spans to the preceding observation and no more.
Like AR, the MA process is identified by using the autocorrelation and partial autocorrelation functions. The autocorrelation plot of an MA process is usually identified by one or two spikes, while rest of the autocorrelation is essentially zero.
For illustration, the ACF of participant RS after differencing (see Figure 4) is indicative of an MA process. This can be seen in Figure 3, in which the autocorrelations do not diminish gradually. Instead, there is a blip at Lag 0. In some cases, an integrated model featuring both autoregressive and moving average components is fitted to the data. An AR and MA processes can be represented mathematically in the formulas presented in Table 2.
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Table 2.
Mathematical formulation of MA, AR, and ARMA processes.
AR(p)
MA(q)
ARMA(p,q)
Note. = the parameter estimate of the autoregressive component, = the parameter estimates of the moving average component, = an error term, assumed to be white noise in an AR model, = innovation/random shock (in a MA model).
The autocorrelation function of the changes in the Hopelessness series in
Participant RS (Figure 3) is decaying in a rate that appears exponential, a fact which indicates an AR process. Partial autocorrelation, as well as the autocorrelation itself, show a decrease in lag significance starting from lag 1, which might suggest a first order autoregressive process (going back to Lag 1). Yet, after differencing the plot shows a pattern which is more characteristic of an MA process (2 significant spikes with no significance afterwards). Although visual inspection points to an MA process, it is advised to compare a number of models before reaching a conclusion. Therefore, the first model that was tested was an AR(1) process, which predicts the change in
Hopelessness as an average change, plus some fraction of the previous change, plus a random error. Table 3 illustrates the parameter diagnostics for an AR process for
Hopelessness in participant RS.
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Table 3.
Parameter Estimates and diagnostics statistics for Hopelessness in Participant RS.
The ARIMA Procedure
Conditional Least Squares Estimation
Parameter Standard Estimate Error Approx t Value Pr> |t| Lag
MU 0.0050477 0.15003 0.03 0.9732 0
AR1,1 -0.37229 0.06919 -5.38 <.0001 1
Constant Estimate 0.006927 Correlations of Parameter Variance Estimate 7.778819 Estimates Std Error Estimate 2.789053 AIC 901.6169
SBC 908.0467 Parameter MU AR1,1 Number of Residuals 184
* AIC and SBC do not include log MU 1.000 0.004 determinant.
AR1,1 0.004 1.000
Autocorrelation Check of Residuals
To Chi-Square DF Pr>ChiSq ------Autocorrelations------Lag
6 20.90 5 0.0008 -0.107 -0.309 -0.061 -0.017 0.004
Using Conditional Least Squares Estimation, SAS statistical program allows for the evaluation of the estimated value of parameter, standard error, and t value
(these estimates are available in most statistical packages such as SAS, Eviews, R,
STATA and MATLAB). In the illustrative series presented above, pertaining to
Hopelessness in Participant RS, there are two parameters in the model: the mean term
(labeled MU) and the autoregressive parameter (labeled AR1). The t values reflect
31
statistical significance concerning the parameter, and indicate whether some terms are unnecessary. In this case, the t value for the autoregressive parameter is 5.38, and is statistically significant. The t value for MU indicates that the mean term adds little to the model.
Goodness of fit statistics include the constant and variance estimates, and the information criterions, and aid in comparing this model to other models. The Akaike information criterion (AIC) (Akaike, 1974; Harvey, 1981) and Schwarz Bayesian criterion (SBC; Schwarz, 1978) are standard tools for comparing competing models.
These information criteria are used to monitor goodness of fit by balancing number of coefficients to the residual variance. To offset the tendency to add coefficients to a model just for the sake of improving its fit, the goodness of fit (information) criteria each include a "penalty" term. Thus, the improvement in fit coming from reduction in the sum of squared residuals will eventually be offset by the penalty term pulling in the opposite direction. Once the series has been diagnosed and estimated for the suitable parameters, the fitting of the model is tested using a standard Portamanteau test. As previously stated, if the null hypothesis is not rejected, then model estimation stage is complete. As can be seen, a white noise check for the residuals indicates that the AR model does not account for all the information, therefore additional models should be fitted and compared. Table 4 presents the models estimated for the
Hopelessness series, their parameter estimates, correlations, and goodness of fit measurements.
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Table 4.
Estimated models, parameter diagnostics and correlations for the series Hopelessness in Participant RS.
Model Parameter Approxt P Information Parameter Autocorrelation of
Estimate value criteria correlation residuals *
AR(1) AR1,1( 0.34) 5.01 <.000 AIC =601.514 r=0.005 p<.001
1 SBC =607.95
ARMA(1,1) AR1,1(0.19) 18.84 <.000 AIC =554.64 r=0.59 p=.57
MA1,1(0.87) 2.08 1 SBC =564.31
<.001
MA(1) MA1,1(0.80) 18.42 <.000 AIC =557.20 r=0.02 p=.21
1 SBC =563.65
Note. Most statistical packages offer white noise tests composed of autocorrelation check of residuals up to lag 6. Herein results are presented in a similar manner, such that p < .001 indicates that the residuals are significantly auto correlated at least up to lag 6, therefore the series is not white noise.
The parameter diagnostics of the AR(1) model accounts for some information embedded in the series, yet the white noise test statistics reject the no autocorrelation hypothesis ( p < .001, for the first six lags).Therefore, the AR(1) model is not fully adequate for this series. When an ARMA(1,1) model was fitted, both the moving average and the autoregressive parameters were statistically significant, with significantly smaller AIC and SBC estimates in comparison to the AR model, indicative of an improved fit. White noise statistic shows no autocorrelations in the residual series, supporting the adequacy of the model. Yet, the correlation between the
33
parameters seems to be high ( r = .59), indicating collinearity and possible over parameterizing. In an MA model, on the other hand, the MA parameter value was statistically significant, the correlations between the parameters were low, and the white noise test indicated no autocorrelations between residuals. Therefore, the MA parameter fitted, with the differencing procedure conducted beforehand, results in a final model expressed as ARIMA (0,1,1), deemed the best model for this series. The estimated model for the series hopelessness can therefore be specified by the following equation:
Note that the notation of B denotes a Backshift operator, representing .
The notation is the error term represented as random shock.
2.4.2.3 Granger causality Test
Granger (1969) has developed a statistical concept of causality that is primarily based on prediction. The underlying principle is that while the past can cause or predict the future, the future cannot cause or predict the past. Therefore, X is said to granger cause Y if the past values of X can be used to predict Y better than the past values of Y itself. The test itself is based on estimating linear regression models of the two relevant dynamic processes by ordinary least squares (OLS). These models examine the reduction in residual variance when the lagged predictor variable is added to a baseline model containing only the autoregressive effect of the dependent variable. Then, an F test is applied to the null hypothesis that the residual variance in
Y has not diminished when previous changes in X were included in the model. If this null hypothesis is rejected, this implies that X causes Y in the Granger’s sense.
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A mathematical formulation of the restricted and unrestricted model is presented in Table 5.
Table 5.
Mathematical formulation of the Granger Causality Test.
Restricted Model
Unrestricted Model
Test Statistic
If the test statistic is greater than the specified critical value, then the null hypothesis that X does not Granger cause Y can be rejected. This model can also test the possibility that Y causes X, therefore enabling the exploration of 4 competing hypothesis: (1) X Granger causes Y (2) Y Granger causes X (3) reciprocal causality
(feedback relations) (4) independence.
Based on the fitted ARIMA models yielded by the Box and Jenkins approach, regression models for each pair of anxiety related and depression related series were
Granger examined (see section D in Figure 1). In non stationary series, differencing was performed prior to the Granger causality, and the differenced series as fitted in the
ARIMA modeling stage was entered into the regression.
2.4.2.4. Transfer Function Modeling
The transfer and noise function model has two components: the transfer model , which describes the influence of past values of X on the current value of Y, and the noise
35
function , which describes the influence of past values of Y on its current value. These are presented in greater detail below.
Identification and estimation process of the transfer noise function for an input output system includes a number of steps. The first stage consists of an identification of an
ARIMA model for the input series, as described above, and an application of this model to the input and output series. Next, the residuals are extracted in order to prepare for further modeling, a process that is referred to as “pre whitening”. The
Transfer Function part of the model is then initially assessed by a plot of the lagged signal (input) series and the residualized response (output) series, also referred to as a
“Cross Correlation Function”. Model fitting is then performed and the estimated parameters are tested using white noise diagnostics, parameter correlation matrix and information criterions such as AICC and BSC (see section E in Figure 1). When the estimation of the transfer function is completed, the residuals of the model are diagnosed for the error structure, and an ARMA model is fitted to the error terms to form the noise function component (see Table 6 for mathematical formulation).
Table 6.
Mathematical formulation of the transfer and noise function
Note . is the transfer function for the ith input series modeled as a ratio of the and polynomials: where is the numerator polynomial of the transfer function (order of lagged influence), for the ith input series and is the denominator polynomial of the transfer function for the ith input series. is the power of B, expressing the time lag from the input Xi to the output Yt . is the noise 36
series expressed as ARMA process: and represented as ratio between the MA and AR component of the noise function. Detailed expression of the formula is therefore: .
Specification of the parameters to be fitted to the model is done by examination of the
Cross Correlation Function, in much a similar manner as the autocorrelation function for fitting of an ARIMA process. A gradual, auto regressive pattern, by which the first lags show a strong correlation decreasing exponentially, warrants positioning of a denominator parameter. Such a parameter introduces an exponentially weighted, infinite distributed lags into the transfer function, and is equivalent to the AR part of the ARMA model. A relatively spiky input output lag structure suggests the need of numerator parameter estimation, introducing a linear function of the specified lagged value of the predictor series, as in an MA process of an ARMA model.
In practice, all models were estimated for numerator parameters due to a relatively local lag structure. Figure 5 illustrates a CCF for Helplessness serving as input and Depression Symptoms serving as output (in Participant HB). As can be seen, the influence of the input series does not reach statistical significance at Lags 0
4, but turns significant at Lags 5, 6, and 7 (representing a delayed process). Therefore, introduction of numerator parameters at these lags is in order.
Table 7 illustrates model testing and diagnostics for the TFM. As shown, the
CCF indicated 3 significant lags, but when including the mean parameter – the influence of Lag 7 becomes non significant. Additionally, the white noise test indicated correlation of the residuals, which warrants the evaluation of a noise model.
When applying an AR model to the residuals, the autocorrelation check of residuals 37
turned insignificant, indicating that all variance has been accounted for and the residual series ( can be described as purely white noise.
Figure 5.
Cross Correlation Function of series “helplessness” as input and series “depression symptoms” as output in participant HB.
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Table 7.
Model Testing in of “Helplessness” as input and “Depression Symptoms” as output in participant HB.
Pre whitening Model Parameters Estimate Variance AIC White Noise Filter Estimate Diagnostics ARIMA(0,1,1) 1 mean 1.95** 5.09 795 <.0001 5 0.23** 6 0.22** 7 0.10 2 mean 1.94** 5.09 798 <.0001 5 0.21** 6 0.16* 3 mean 1.88** 2.46 671 0.578 5 0.13** 6 0.09** AR1 0.72**
3 Results
3.1 Step 1: Modeling each series separately (how past levels of the series
determine its current levels)
Table 8 summarizes results of TS modeling for each of the 8 series estimated across all three participants. Detailed specification of the parameter estimates for each series is presented in Appendix I. Below I will describe patterns that are similar in at least two out of the three participants.
39
Table 8.
Summary of ARIMA models fitted to 8 collected series of each participant.
RS HB RG
Fear (1,0,0) Low variance (4,1,0)
Sadness (0,0,1) Low variance (4,1,0)
Anxiety symptoms (0,0,1) (2,0,0) (1,1,1)
Depression symptoms (0,1,1) (1,0,0) (1,1,1)
Helplessness (0,1,1) (0,1,1) (0,1,1)
Hopelessness (0,1,1) (0,1,1) (0,1,1)
Looming (0,0,1) (1,0,0) (0,0,1)
Rumination Random (1,0,0) (2,0,0)
Note. ARIMA ( p, d, q ) representation as follows: p is the order of the autoregressive component, such that ARIMA (1,0,0) represents a pure autoregressive process by which variable X is determined by accumulation of its past values going back p times. d is the order of differencing (in which time t is subtracted from t I. When I=1, for example, this would mean that the previous level of t is subtracted from its current level, i.e., t t 1), in case of series exhibiting a trend. q is the order of the moving average component, representing local influence/random shock going back q times.
Series showing low variance cannot be analyzed due to violation of normal distribution assumption.
In the affective component of Fear, there was an autoregressive component in two participants, indicating that levels of Fear accumulated. In the cognitive domain, all three participants corresponded to a moving average pattern in Helplessness and
Hopelessness, indicative of a local influence of past cognitions, rather than an accumulative one. Additionally, Rumination had a dominant autoregressive
40
component, showing that its level persisted over time. Looming was found to have a dominant moving average component in two out of three participants, indicative of local influence of past levels of Looming, rather than a persistent pattern.
3.2 Step 2: Granger’s causality tests
Causal relationships were tested using the Granger (1969) approach. All models were examined with time lag of 1(p = 1 autoregressive order), due to the fact that most ARIMA models pointed to the order of 1. In series showing high autocorrelation, indicative of a trend (non stationary series), differencing was employed prior to the Granger causality test, and the differenced series as fitted in the
ARIMA modeling stage was entered into the regression.
Table 9 presents a summary of all pairs showing statistically significant
Granger's causality (based on the F test), including the direction of causality. I will restrict the description of causal relations to those obtained for two or more participants; a schematic summary of the overall causal network across participants is presented in Figures 6 8.
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Table 9.
Significant and marginal Granger’s causality (F tests).
Predictors Fear Sadness Anxiety Depression Helplessness Hopelessness Looming Rumination Dependant symptoms symptoms Fear 4.01* (HB)
Sadness 3.74 p=.052 (RG) Anxiety 3.16 3.95* (HB) 9.81** (HB) (HB) symptoms p=.07 4.17* (RG) Depression 3.51 4.71* (HB) 4.82* (HB) 43.46** (HB) (HB) symptoms p=.06 3.20 p=.07 (RG) 3.25 p=.06 (RG) Helplessness 4.20* (HB)
Hopelessness 7.57** (RS) 6.42** (RS) 6.86** (RS) 3.93* (RG) Looming 3.66 12.99** (HB) 9.71** (HB) 8.96** (HB) (HB) p=.055 3.29 p=.06 (RG)
Rumination 13.90** (HB) 22.21** (HB) 2.93 p=.08 (RG)
Note. *p<.05, **p<.001. Blank cells indicate non significance, for results approaching
significance, p value is detailed. Case initials are reported in the parentheses.
Within depression. Hopelessness Granger caused Depression Symptoms in
two of three participants (HB, RG), while showing the reversed causal direction in the
third one (RS). As well, a non significant trend was found, whereby Sadness and
Depression Symptoms were Granger related, leading from Depression Symptoms to
Sadness in one participant (RG), and inversely in a second participant (HB, p = .06).
Within anxiety. Looming was Granger related to Anxiety Symptoms in two of
three participants, showing a unidirectional pattern in which Looming Granger caused
Anxiety Symptoms in one participant (RG), and indicating bidirectional causal
relations in the other (HB). A non significant trend was detected, whereby
Helplessness Granger caused Looming in Participants HB and RG ( p = .06).
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Figure 6-8.
Visual representation of causal network as detected by Granger Causality Test in participants RS, HB, RG, respectively.
Fear Sadness
Anxiety Depr ession Symptoms Symptoms
Helplessness Hopelessness
Looming Rumination
Fear Sadness
Anxiety Depression Symptoms Symptoms
Helplessness Hopelessness
Looming Rumination
Fear Sadness
Anxiety Depression Symptom s Symptoms
Helplessness Hopelessness
Looming Rumina tion
Note. Black arrows represent unidirectional causality, broken arrows represent marginal significance.
43
Between disorders. Looming Granger caused some aspects of depression in all three participants. Specifically, it caused Depression Symptoms in 2 out of 3 participants and caused Hopelessness in other 2 of the 3 participants. In one participant (HB) this causal relationship was bidirectional, showing a feedback loop involving Looming and Depression Symptoms. Helplessness was also found to
Granger cause Depression Symptoms in two participants and in one of them there was also a reverse causality, indicative of a feedback loop involving Helplessness and
Depression Symptoms.
3.3 Step 3: TFM: Estimating the size and positive/negative directionality of the
causal influences.
Pairs of variables showing statistically significant Granger causality results were further analyzed using TF. Each pair was first pre whitened using the filter of the input series (i.e., the ARMA process fitted to the input series).The Cross Correlation
Function (CCF) , which evaluates the similarity between each input output series as function of the time lag, was evaluated to gain an appreciation of the lag structure to be fitted, as well as for re examining directionality. Competing models were tested for the optimal information criterion (AICC, SBC; Akaike, 1979; Schwarz, 1978).
Parameter estimates were evaluated for significance and white noise diagnostics were applied to ensure that all the relevant variation in the series was modeled. Note that the models selected were those best fitting the data.
TF results are presented in Tables 10 and 11. These results are presented as regression models so to enable simple and accessible format for readers more familiar with multiple regression. Full diagnostics, information criterion, model fitting
44
procedure and pre transformations are detailed in the Appendix II and III. Note that pairs with Granger test results approaching significance and random cross correlation functions were not further analyzed (see Table 10).
Table 10.
Transfer and Noise Function Models of pairs showing Granger Causality within each disorder construct.
Case Output Intercept Transfer Function Noise Function (Input) AR MA
RS (1 B)hopeless t 0.05 1.09sad t (1 0.93B)e t
1.07sad t 1
RS (1 B)hopeless t 0.30 0.47(1 B)dep.symp t (1 0.74B)e t
HB loom t 1.81 1.80anx.symp t + (1 0.36B)le t 0.99anx.symp t1 +0.51a nx.symp t- 2+0.37anx.symp t- 3+0.38anx.symp t-4
HB Anx.symp t 0.20 0.10help t (1 0.45B) e t
HB loom t 3.60 0.27help t
HB rum t 3.74 1.11dep.symp t + (1+0.26B) e t 0.33dep.symp t 1
HB Dep.symp t 1.48 0.20hope t+0.17hope t 1
RG Anx.symp t 0.98 0.22loom t+0.07loom t 1
RG (1 B)sad t 0.05 0.12(1 B)dep.sympt t (1 0.71B) e t
RG Dep.symp t 10.55 0.44hope t+0.40hope t 1
Note. The Backshift operator is commonly used as an abbreviation in TS literature, and represents an index for lagging the expression in parenthesis, e.g., (1 B) Output t represents a series that has undergone differencing procedure of Order 1, and is factored into: (1 B) Output t = Output t – Output t 1. et represents the residuals (noise 45
series) of the output series after accounting for the input variance.
Table 11.
Transfer and Noise Function Models of pairs showing Granger Causality between anxiety components and depression components.
Case Output Intercept Transfer Function (Input) Noise Function AR MA
RS hopeless t = 16.77 + 0.27 loom t +
0.10 loom t 1 +
RG (1 B)hopeless t= 0.05(1 B )loom t+
RG (1 B)dep.symp t= 0.12(1 B)loom t+
HB dep.symp t = 1.88 + 0.10helpless t + 0.13helpless t 5 + 0.09helpless t 6
HB dep.symps t = 1.10 + 0.28loom t + 0.13loom t 1
The following sections are subdivided into between disorders, within depression and within anxiety. Each sub section consist of two parts: the causality pattern and the influences of a series on itself (indicating accumulation over time vs. local influences) once causality was considered (Noise Functions).
3.3.1 Within Disorders.
Table 9 represents the TFM and Noise Functions for all pairs showing significant causality within each disorder.
3.3.1.1 Within depression.
Causal relations between series. In Participants HB and RG, Hopelessness positively caused Depression Symptoms at Times t and t 1 (ω( hopeless t) = .20, p <
46
.001 , ω(hopeless t 1) = .17, p < .05;ω( hopeless t) = .44, p < .001 , ω(hopeless t 1) = .40, p < .01, respectively). For participant RS, the inverse temporal causal direction prevailed, showing that changes in Depression Symptoms from day before yesterday to yesterday positively caused changes in Hopelessness (ω( hopeless t hopeless t 1) =
.47, p < .01).
Noise Function. The inclusion of Hopelessness in the models (reported in the above section) revealed additional influences of series on themselves. In Participant
RS, a MA component showing that Depression Symptoms were influenced by local past influences ( θ (dep.symp t 1) = .93, p < .001). In Participant RG, Depression symptoms accumulated as indicated by an AR component (φ( dep.symp t 1) = .38).
3.3.1.2 Within anxiety.
Causal relations between series. Looming positively caused Anxiety
Symptoms at Times t and t 1 in Participant RG (ω( loom t)= .22, p < .01, ω( loom t 1) =
.07, p < .05). In Participant HB Anxiety Symptoms positively caused Looming going back t 4 days (ω( loom t)= 1.80, p < .01, ω( loom t 1) = .99, p < .01), ω( loom t 2) = .51, p
< .01, ω( loom t 3) = .37, p < .05, ω( loom t 4) = .38, p < .05).
Noise Function. When the inter series causal relations (reported in the preceding section) were included in the model, I identified additional influences of series on themselves. In Participant HB, LMS both accumulated and was influenced by local past influences as indicated by an ARMA (1,1) model (φ( loom t 1) = .70, ( θ
(loom t 1) = .38, p < .001). In Participant RG, Anxiety Symptoms accumulated (AR component) (φ( anx.symp t 1) = .50, p < .001).
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3.3.2 Between disorders.
Causal relations between series . Results presented in Table 5 confirm those yielded by the Granger causality test. In two participants (RG, HB), Looming positively Granger caused Depression Symptoms, with the most apparent effect seen for t 1 and t. These results mean that yesterday’s and today’s looming predicts today’s depression symptoms in two participants. In participant RG, the output series represents differenced values (i.e. level of change from yesterday to today) rather than absolute values, making the interpretation slightly more complex. Nonetheless, the essentially positive causal direction remained. Specifically, changes in Looming from yesterday to today positively caused changes in Depression Symptoms from today to tomorrow (ω (loom t loom t 1) = .12, p < .001). In Participant HB, the same trajectory prevails, in which changes in Looming from day before yesterday to yesterday positively caused changes in Depression Symptoms from yesterday to today (ω( loom t)
= .28, ω (loom t 1) = .14, p < .001). In Participant RS, elevated Looming today and yesterday predicted high current level of Hopelessness (ω( loom t) = .26, p < .001 ,
ω(loom t 1) = .012, p < .005). In Participant RG, changes in Looming from day before yesterday to yesterday positively caused changes in Hopelessness (ω (loom t loom t 1) = .05, p < .001). In addition, changes in Helplessness 5 and 6 days ago positively caused changes in today’s Depression Symptoms in Participant HB
(ω( Helpless t 5) = .13, ω( Helpless t 6) = .09, p < .001).
Noise function. The Noise Functions reveal influences of a series on itself that are seen only after causal relations from other variables are entered into the model in the TFM). In Participant RS, there was an AR component indicating accumulating effects of Hopelessness (after the influence of Looming was included in the model,
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φ( hopeless t 1) = .41, p < .001). A similar accumulating effect (AR component) for
Depression Symptoms was apparent in Participants RG and HB (after Looming was entered into the model, φ( hopeless t 1) = .31, .72 correspondently, p < .001). In
Participant RG, local leaps in either Depression Symptoms (θ (dep.symp t 1) = .90, p <
.001) or Hopelessness ( θ(hopeless t 1) = .79, p < .001), caused the reverse effect the following day (an MA component).
4 Discussion
Espousing a multidimensional, within individual, TS study of the associations between aspects of anxiety and depression in three participants with comorbid MDD and GAD, I found evidence consistent with causal relations in each of the three participants. While some causal pairs seemed to be unique to the studied individual, others were replicated across at least two participants, suggesting a general causal pattern.
Thus, I found that LMS was predictive of Depression Symptoms in two participants. I also found that LMS predicted Hopelessness, a cognitive vulnerability marker of depression, in other two participants. This pattern of results provides a very strong test for the vulnerability status of the LMS, not only in the context of anxiety, but also – consistent with Rector et al.'s (2008) clinical case illustration in the context of depressive symptoms and cognitive vulnerability to depression.
Within each disorder components, I identified directional (i.e., Granger causal) relationships involving Hopelessness and Depression Symptoms across all three participants. In two participants, these relationships were unidirectional, leading from
49
Hopelessness to Depression Symptoms. In the third participant, an opposite pattern, leading from Depression Symptoms to Hopelessness, was found.
The importance of these findings is twofold. First, they provide, to the best of my knowledge for the first time, support for the Hopelessness Theory for Depression using an intra individual, TS design. Second, my findings show that hopelessness, as a cognitive vulnerability factor, may also be influenced by depression symptoms, an effect that is consistent with the highly debated scarring hypothesis (Lewinsohn,
Steinmetz, Larson & Franklin, 1981; Shahar & Davidson, 2003; Shahar & Henrich,
2010). According to the scarring hypothesis, a depressive episode might cause an enduring psychological effect – a scar – which may in turn resolve in an elevated risk for developing future depression. The fact that one of the participants showed a reversed pattern, by which depressive symptoms caused subsequent hopelessness, might suggest that symptoms of depression have a lingering effect on depression related cognitions.
Within anxiety related constructs, I found evidence for causal relations involving Looming and Anxiety Symptoms, with a pattern leading from Anxiety
Symptoms to Looming in one participant, and a reversed pattern in another.
Considering the intra individual nature of my analysis, it is possible that such pattern is unique to the studied participant. Another option is that in the day to day run, the looming anxiety relations progress in a feedback loop without a specific trajectory in patients with comorbid anxiety and depression. Riskind and Williams (2006) offered such reciprocal feedback loop in which distorted mental representations limit coping actions and creating anxiety, and by doing so create a “confirmation bias” which strengthens dysfunctional attitude and catalyzing a slip into a vicious spiral. Such
50
reciprocal mechanism between vulnerability markers and symptoms has been reported previously with regards to depression (Shahar, Blatt, Zuroff, Krupnick & Sotsky
2004), and raises an important question regarding the causal interaction between vulnerabilities and symptoms. Future studies with a larger number of participants are needed in order to establish the general trajectory of these two components.
The present results bear important methodological implications. First, the fact that each individual had her own specific causal network, with specific trajectories not always congruent with known literature – highlights the limitations inherent in cross sectional and “snap shot” longitudinal designs in terms of capturing clinical dynamics.
As such, the present findings are in line with theoretical models suggesting the need for more complex, novel tools of analysis (Essex & Smythe 1999; Grace 2001;
Molenaar, 2004; Molenaar & Valsiner 2005; Sohn 1999; Toomela, 2007; Molennar,
2007).
One of the advantages of intra individual time series analysis lies in the ability to model multiple etiological processes based on bivariate associations. Such an approach seems to bear closer resemblance to the reality of mental disorders in general, and psychiatric comorbidity, along all DSM axis, in particular. Future studies can extend the scope of causal modeling to include behavioral, physiological and perhaps even neuro physiological components and offer a broader conceptual framework to the understanding of mental disorders.
The application of TS design and analysis also bares important implications for treatment and assessment purposes. The necessity of individualized treatment programs has been emphasized previously with regards to behavioral therapy, whereby causal variables guide subsequent treatment by constructing a unique causal
51
model per each patient (Haynes & O’Brien, 2000; Haynes, 1997; Haynes & Williams,
2003). My findings support such an approach while illustrating the complexity of utilizing a standard treatment protocol based solely on diagnosis. For illustration, focusing treatment on cognitive reconstruction of hopelessness might have brought improvement in depression symptoms in two of my patients, but not have done so in the third one, which showed the opposite causal relation. Therefore, knowledge regarding the specific trajectory might change treatment plan drastically, and allow a more effective and focused program for intervention.
Using bivariate modeling between each two variables for detecting their causal direction and duration, I was able to form a fairly accessible visual representation of the dynamic relations between essential components of anxiety and depression. Such representation can be adopted for treatment purposes, by presenting such representation to the patient. Some theoretical conceptualizations such as The Action
Formulation (TAF, Shahar & Porcerelli, 2006) and Finn’s model of therapeutic assessment (Finn, 1996a, 1996b, 2003; Finn & Tonsager, 1997) encourage client’s engagement in the assessment stages as part of an intervention process, and highlight the patients’ role in shaping her or his surroundings. The use of TS design for such representation extend such intervention even further, by allowing to portray changes in the dynamic structure ad hoc, as the patient progresses along the therapeutic process.
5 Limitations
The most salient limitation of this study should be acknowledged. Because I focused on intra individual network of causal relations, each participant was treated as a separate study, leading to a sample of N = 3. While this is common in Time Series
52
studies (Dunn et al, 1987; Brossart et al., 1998; Pole et al, 2008), replications with additional participants are needed. Such replications can be regarded as meta analysis of a number of studies, in which intra individual causal maps are compared in order to detect common and unique patterns. Within the scope of the current study, it is not unlikely that psychopathology includes both unique causal patterns as well as common trajectories, as was evident in the causal maps of the study participants.
Future studies are encouraged to broaden the scope of research to include even more specific components such as life events, psychotherapy, physiology and social and familial relations.
Intra individually, the sample of N=3 used in this study produced meaningful insights regarding the nature of daily causal dynamics for each of the participants, and pointed to the possibility that each individual carries a unique pattern of causal network. Within such individuality, the common pathways evident in all three participants are prominent. Although causal relations were evident across all three participants, studies with larger samples are needed in order to make inter individual inferences. For example, it is important to determine whether there is a direct association between Looming and symptoms of depression, as was evident in two participants, or whether the associations are between anxiety and depression vulnerabilities, as suggested by the third. Although specific causal relations were also evident within each disorder components, future studies are needed in order to make inferences regarding the exact directionality.
Additional limitations should be noted. My exclusive reliance on self report measures might have inflated shared method variance, inadvertently boosting the associations between the study variables. Replications with observant based measures
53
would be very important. Third, whereas the time scale employed in the present study was based on days, important changes in depression, anxiety, and their interrelations might occurred on other time scales (hours, weeks, months), and these findings could not be generalized to these time scales.
Although study design was accommodated to the use of time series analysis, specific features of the measurement tools were not completely suited to time series basic statistical assumptions. The fact that participants reported their experiences using whole numbers ranging on relatively low scale demanded relatively high variance in order to perform the analysis. As such, time series violating the assumption of normal distribution could not be analyzed using standard parametric estimation methods. Indeed the use of phone sampling enabled control over time interval and reliability of reports, but limited the use of more suitable scales such as the Visual Analogue Scale (VAS). Future studies can overcome these barriers by using handhelds with online synchronization in order to assure reliability of reports and the absence of missing values.
6 Conclusions
Within the context of these limitations, the present study stands out in two respects. First, it provides a detailed examination of the anxiety depression comorbidity by differentiating between symptoms, affective, and cognitive vulnerability dimensions that characterize each of the disorders. Second, and equally important, this study employs a TS analysis to examine intra individual causal relationships between these dimensions, both within and across the two disorders.
These noteworthy strengths, coupled with the fact that the study sample is comprised of SCID diagnosed young adults with comorbid GAD/MDD, bolster my confidence in
54
the obtained findings, and – hopefully – inspire additional TSA research on comorbid psychopathological conditions.
55
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Appendix I.
Summary of ARIMA models fitted to 8 collected series of each participant.
RS HB RG Fear AR(1) Not normally distributed ARIMA(4,1,0)
Sadness MA(1) Not normally Distributed ARIMA(4,1,0)
Anxiety MA(1) AR(2) ARIMA(1,1,1) symptoms
Depression MA(1) AR(1) ARIMA(1,1,1) symptoms
Helplessness MA(1) ARIMA(0,1,1) ARIMA(0,1,1)
Hopelessness ARIMA(0,1,1) ARIMA(0,1,1) ARIMA(0,1,1)
Looming MA(1) AR(1) MA(1)
Rumination Random AR(1) AR(2) 69
Note. Variables names has been shortened for formula simplification: Sadness=Sad, Anxiety Symptoms=SymAnx, Depression Symptoms=SymDep,
Helplessness=Help, Hopelessness=Hope, Looming=Loom, Rumination= rum. Notations: ARIMA=Auto Regressive Integrated Moving Average;
B=Backshift operator, representing ; = error term represented as random shock; represents a white noise process;
70
Appendix II.
Final transfer and noise function for between anxiety and depression components.
Case Input Output Pre transformations Parameters Estimate Variance AIC White Noise Final Mathematical model Pre whitening Detrending Estimate Diagnostics RS Loom mean 16.77** 5.02 823 0.0584 Hopeless 0 0.27** 1 0.10* AR1 0.41**
RG Loom MA(1) d=1 0 0.05** 1.15 554 0.211 Hopeless 1 0.05** MA1 0.79** RG Loom MA(1) d=1 0 0.12** 1.65 622 0.456 Dep.Symp 1 0.12** AR1 0.31** MA1 0.90** HB Helpless ARIMA(0,1,1) mean 1.88** 2.46 671 0.57 Dep.Symp 0 0.10** 5 0.13** 6 0.09* AR1 0.72**
HB Loom AR(1) mean 1.10** 574 574 0.33 Dep.Symp 0 0.28** 1 0.13** 71
Appendix III.
Final transfer and noise function within anxiety and depression components.
Case Input Output Pre whitening Parameters Estimate Variance AIC White Noise Final Mathematical model Estimate Diagnostics RS Sad mean 16.66** 4.41 804 0.09 0 1.09** AR1 0.98** MA1 0.87** RS mean 17.24** 4.48 807 0.29 1 0.55** AR1 0.98** MA1 0.87 HB AR(1) mean 1.81** 6.98 873 0.90 1 0.99** 0.51** 3 0.37* 4 0.18* AR1 0.70** MA1 0.35* HB ARIMA(0,1,1) mean 0.20 1.12 550 0.42 1 0.10** AR1 0.83** MA1 0.45** HB ARIMA(0,1,1) mean 3.60* 12.09 574 0.33 1 0.27* 72 0.72** AR1 Case Input Pre whitening Parameters Estimate Variance AIC White Noise Final Mathematical model Output Estimate Diagnostics
HB AR(1) Mean 3.74** 7.29 891 0.41 1 1.11** 2 0.33** MA 0.26**
HB ARIMA(0,1,1) Mean 1.48 4.77 812 0.34 0 0.20* 1 0.17* RG Loom ARIMA(0,1,1) Mean 0.98 2.45 695 0.06 Loom0 0.22** Loom1 0.07* AR1 0.50** RG ARIMA(1,1,1) Mean 2.59 0.21 240 0.54 0 0.12** 1 0.05* AR1 0.99** MA1 0.66** RG ARIMA(0,1,1) Mean 1.80 638 0.90 Hope0 10.55** Hope1 0.44** AR1 0.40** 0.38**
73
נמצא כיוון הפוך , המוביל מתסימיני דיכאון לחוסר תקווה . בתוך רכיבי החרדה , מצאתי עדות לקשר סיבתי
בין משתנה ה - LMS לבין תסמיני חרדה , בכיוון המוביל מתסמיני חרדה ל - LMS בנבדקת אחת , ואילו הכיוון
ההפכי בנבדקת השנייה. ממצאי המחקר הנוכחי הינם בעלי השלכות קונספטואליות ומתודולוגיות , והם רלוונטיים לנושאים
הקשורים גם להערכה וטיפול . תחילה , ממצאים אלו מספקים עדות תוך נבדקית לתיאורית חוסר התקווה
בדיכאון , כמו גם לתפקיד של ה - LMS כגורם פגיעות לחרדה . בנוסף לכך , ממצאי המחקר מציעים את קיומו
של מנגנון סיבתי המקשר בין חרדה ודיכאון דר ך מנגנון קוגניטיבי של ה - LMS . העובדה כי כל נבדקת הראתה
רשת סיבתית ייחודית הינה בעלת משמעויות מתודולוגיות נרחבות , הנוגעות ליכולת להקיש וליישם ממצאים
קרוס- סקציונאליים על האינדיבידואל , כמו גם אימפליקציות קליניות משמעותיות בנוגע לפרוטוקולים
טיפוליים מבוססי- אבחנה . ממצאי המחקר נוטים לתמוך ברעיון של פיתוח תוכניות טיפול אינדיבידואליות על
סמך ביצוע הערכה מקיפה המבוססת על הרשת הסיבתית המניעה את המטופל ( ;Haynes & O’Brien, 2001
Haynes et al., 1997; Haynes & Williams, 2003 ). ככלל , ממצאי המחקר מדגישים את הצורך בניתוח
תוך נבדקי על מנת לבאר את טבע הקו מורבידיות , כמו גם לצורך הטמעה של הערכה לונגיטודינאלית לצרכי טיפול . .
ה כתסמיני חרדה . רכיבים קוגניטיביים לחרדה ודיכאון הוערכו על פני שני מימדים עיקריים : הראשון , מימד של
חוסר אונים מול חוסר תקווה , נאמד באמצעות גירסא מקוצרת של שאלון חוסר אונים וחוסר תקווה
( Hopelessness Helplessness Questionnaire, Lester, 2001 ). השני , על ציר של סגנון חשיבה לא אדפטיבי
הנע על ציר החרדה ועל ציר הדיכאון . על ציר החרדה , נמדדה עוצמת ה" לומינג " ( Looming או LMS ) , )
המתייחסת לנטייה ליצור תרחיש ים מנטליים לאירועים מאיימים ככאלו הגדלים ברמת הסיכון שלהם
באמצעות שאלון ה - the Looming Maladaptive Style Questionnaire, Riskind et al., 2000 ) LMSQ ). על
ציר הדיכאון , נמדדה הנטייה ל" רומינציה " ( Rumination ) , המתייחסת לנטייה להתמקדות המשמעות
הסובייקטיבית של המצ ב רוח השלילי ומאפייניו , באמצעות שאלון ה- Response Style ) RSQ
Questionnaire, Nolen-Hoeksema & Morrow, 1991 ). סך הכל , נמדדו כשמונה רכיבים של חרדה ודיכאון
לכל אחת מהמשתתפות , הכוללים עצב , פחד , סימפטומים של חרדה , סימפטומים של דיכאון , חוסר אונים ,
חוסר תקווה , לומי נג , ורומינציות . הערכים שנאמדו מידי יום לצורך ניתוח הנתונים נאספו עבור כל אחת מהנבדקות , כאשר כל נבדקת
היוותה סט נתונים נפרד שנותח כמחקר בפני עצמו . כל אחד ממחקרים אלו כלל 8 משתנים הבנויים מ- 180
מדידות יומיומיות . ניתוחי סדרות זמן כללו שלושה שלבים מרכזיים : בש לב הראשון , כל סדרה נותחה בנפרש על מנת להעריך את השפעתם של ערכי העבר על הנתונים העדכניים , כמו גם העתידיים . מבחני סיבתיות
מבוססי- רגרסיה ( Granger, 1969 ) הוערכו עבור כל סט של שני משתנים , על מנת לבדוק את קיומם או
היעדרם של יחסים סיבתיים , וכיוונם . ניתוח זה איפשר הערכה של קשרים סיבתיים בתוך כל הפרעה ( כגון קשר סיבתי בין עצב וסימפטומים של דיכאון ) ובין שתי ההפרעות ( כגון בין תסמינים של חרדה וחוסר תקווה ).
בשלב השלישי , כל זוג משתנים שהראה יחסים סיבתיים הוערך באמצעות מודל התמרה ( Transfer-Function
Model ) , על מנת להעריך את מידת העוצמה , ומשך וכיוון ההשפעה ( Box, Jenkins & Reinsel, 1994 ). ).
תוצאותיהם של ניתוחי סדרות הזמן הראו שמשתנה ה - LMS ניבא תסמינים של דיכאון בקרב שתי
משתתפות , וכן ניבא חוסר תקווה , המהווה גורם פגיעות לדיכאון , בקרב שתי נבדקות אחרות . בתוך כל אחת
מההפרעות , נמצאו יחסים סיבתיים בין חוסר תקווה לתסמינים של דיכאון אצל כל שלושת הנבדקות . בשתיים מתוכן כיוון היחסים היה חד כיווני והוביל מחוסר תקווה לתסמיני דיכאון , ואילו אצל הנבדקת השלישית
ד תקציר
במהלך שני העשורים האחרונים , נערך מחקר רב בנוגע להופעה המשותפת של חרדה ודיכאון . זאת
לאור שכיחותה הרבה באוכלוסייה ובמרפאות ראשוניות , הגבוהה באופן משמעותי מהופעה נפרדת של אחת
מהפרעות אלו . הפרוגנוזה השלילית , דרגת הנכות הגבוהה , והעומס המשפחתי והכלכלי הנגרם מקומורבידיות של חרדה ודיכאון , כולם גורמים לשאלת האתיולוגיה העומדת בבסיס הו פעה משותפת זו להיות נושא למחקר
מתמשך . עם זאת , למרות מחקר אמפירי וקליני מעמיק , נראה כי המכניזם העומד בבסיס הקו מורבידיות של
חרדה ודיכאון אינו מובן דיו . . בניסיון לבצע אינטגרציה בין מספר רב של ממצאים בנוגע לקומורבידיות של חרדה ודיכאון , מודלים מסבירים
מתמקדים ע ל חקר המכניזם העומד בבסיס הופעה משותפת זו . הגישה המסורתית הינה זו המבוססת על
היפותזת הגורם המשותף , והנחתה היא כי גורם פסיכופתולוגי מסדר גבוה יותר הוא העומד בבסיס הופעה משותפת זו . גישות עדכניות יותר , לעומת זאת , מבוססות על השערה של סיבתיות , וגורסות כי הפרעה אחת , או
אחד ממרכיבי ההפרעה , יכולים להוות גורם סיבתי בהופעתה של ההפרעה השנייה. סוג כזה של יחסים
סיבתיים לרוב נקבע על פי קדימותה של הפרעה אחת על פני האחרת , עם זאת מחקרים אמפיריים בתחום זה נוטים להראות ממצאים סותרים , כך שטרם נמצא מסלול סיבתי ברור בין שתי הפרעו ת אלו . .
על מנת לחקור אפשרות זו של קשרים סיבתיים , מחקר הדוקטורט שלי בודק את היחסים הדינאמיים
בין מרכיבים של חרדה ודיכאון לאורך זמן , תוך הדגשת המאפיינים הרב מימדיים של ההפרעות במבנה תוך נבדקי . לצורך כך , ביצעתי מחקר אינטנסיבי במערך של סדרות זמן , בו שלוש מטופלות הסובלות מהופעה
משותפת של הפרעת חרדה מוכללת ((Generalized Anxiety Disorder (GAD ) והפרעת דיכאון מג' ורי
((Major Depression Disorder (MDD ) הוערכו מידי יום באמצעות דגימה טלפונית , למשך תקופה של
כשישה חודשים . על מנת להתאים למבנה הייחודי של המחקר , נבנה שאל ון אחיד המכיל פריטים משאלונים הבודקים רכיבים אפקטיביים , קוגניטיביים וסימפטומטיים של חרדה ודיכאון . רכיבים אפקטיביים של חרדה
ודיכאון הוערכו באמצעות שאלון ה- Watson & Clark, 1994 ) PANAS-X ) וכללו בעיקר פריטים
המתייחסים לעצב ולפחד . רכיבים סימפטומטיים של חרדה וד יכאון הוערכו באמצעות שאלוני ה- BDI -וה BAI
( Beck, Steer & Brown, 1996; Beck, Epstein, Brown et al., 1988 ) וכללו פריטים הנוגעים לחוסר
הנאה , קשיי שינה ואובדן תיאבון כתסמיני דיכאון , ותחושת פאניקה , פחד שהגרוע מכל יקרה וקצב לב מוגבר
ג
העבודה נעשתה בהדרכת
פרופסור נחשון מירן ופרופסור גולן שחר
במחלקה לפסיכולוגיה בפקולטה למדעי החברה
ב
האם סגנון קוגניטיבי של לומינג מהווה מנגנון מרכזי בקו מורבידיות של הפרעת חרדה מוכללת והפרעת דיכאון מג'ורי: מחקר סדרות זמן
מחקר לשם מילוי חלקי של הדרישות לקבלת תואר " דוקטור לפילוסופיה"
מאת
דנה צור - ביתן
הוגש לסינאט אוניברסיטת בן גוריון בנגב
אישור המנח ים ______
אישור דיקן בית הספר ללימודי מחקר מתקדמים ע" ש קרייטמן ______
ניסן תשע" א מאי 2011
באר שבע
א
האם סגנון קוגניטיבי של לומינג מהווה מנגנון מרכזי בקו מורבידיות של הפרעת חרדה מוכללת והפרעת דיכאון מג'ורי: מחקר סדרות זמן
מחקר לשם מילוי חלקי של הדרישות לקבלת תואר " דוקטור לפילוסופיה"
מאת
דנה צור - ביתן
הוגש לסינאט אוניברסיטת בן גוריון בנגב
ניסן תשע" א מאי 2011
באר שבע