1. University of Texas Health Science Center at San Antonio
DYNAMIC CO-VARIATION OF SYMPTOMS OF ANXIETY AND DEPRESSION AMONG NEWLY-DIAGNOSED PATIENTS WITH MAJOR DEPRESSIVE EPISODE, PANIC DISORDER, AND CONTROLS
David Katerndahl
Chen-Pin Wang
University of Texas Health Science Center at San Antonio
San Antonio, Texas

2. ANXIETY-DEPRESSION CORRELATIONS
Symptom Levels Correlate
Community-Dwelling Adults
Adults Seeking Psychiatric Treatment
Patients With:
Hypertension
Depression
Symptom Variabilities Similar
Posttraumatic Stress Disorder
Controls Most Similar

3. DETERMINANTS OF DYNAMICS Attractors

4. Attractors
An attractor is a point or a collection of points on which the system can limit. These often take the form of
-Fixed Points
-Periodic Orbits
-Strange Attractors

5. Basins of Attraction
The Basin of Attraction for an attractor is the set of points which limit on the attractor.

6. Basins of Attraction
The set of all points in phase space that are under the influence of an attractor, or, more generally, the initial conditions of a system that evolve into the range of behavior allowed by the attractor. If one imagines a complex system as a sink, then the attractor can be considered the drain at the bottom, and the basin of attraction is the sink’s basin.

7. PURPOSE
Explore The Relationship Between Dynamics Of Symptoms Of Anxiety And Depression
Do Anxiety And Depression Co-Vary?
Are There Diagnostic Differences In:
Symptom Dynamics
Bivariate Attractors

8. SAMPLE Setting Family Health Center Acute Care Clinic
5 Patients Per Diagnostic Group – Referred By PCP
Panic Disorder
Major Depression
Neither
Verification – SCID-IV
Major Depressive Episode

9. PROCEDURE Baseline Information Demographic Information Chart Audit
Active Diagnoses
Prior Mental Health Treatments
Treatment For Newly-Diagnosed Illnesses

10. PROCEDURE Mood Diary Procedure
Hourly (While Awake) Assessments Of Levels
Anxiety - “very relaxed” to “very nervous”
Depression - “very happy” to “very sad”
100-mm Visual Analog Scales
Symptoms Recoded 1-10
Procedure
Enrollment In Clinic
Wrist Watch With Hourly Chime As Reminder
Weekly Telephone Encouragement
Termination After 30 Days

11. COVARIATION ANALYSES Intrapatient Symptom Correlation
dSEM Comparing Fit Statistics Predicting Acceleration
Intergroup Comparison
Z-Transformed Correlations – Kruskal-Wallis ANOVA (p ≤ .15)
dSEM – Significance Of Diagnostic Terms (p ≤ .05)

12. Differential Structural Equation Modeling (DSEM)
Extension Of SEM
Models Derivatives Of Scores
Velocity
Acceleration
Forces
Equilibrium (Linearity) – Acceleration And Score
Friction – Acceleration And Velocity
Can Study Correlation Between Multiple Dynamic Systems

13. DIFFERENTIAL STRUCTURAL EQUATION MODELING
Anxiety
d Anxiety
d2 Anxiety
Depression
d Depression
d2 Depression

14. ATTRACTOR ANALYSES State Space Grid Identify Attractors Attractiveness
Plot Anxiety State (1-10) versus Depression State (1-10)
Identify Attractors
Compute Heterogeneities (Cell Deviation From Randomness)
Winnowing Using Scree
Attractiveness
Influence = Probability Outside Event Moves To Attractor
Stability = Once Exited From Attractor, Time Until Returned
Consistency = Recurrence Of Attractor Over Time
Intergroup Comparisons – Kruskal-Wallis ANOVA
Subjects (p ≤ .15)
Attractors (p ≤ .05)

15. STATE SPACE GRID (example)
Level Of Depression 1 2 3 4 5 6 7 8 9 10
2 4
Level Of Anxiety

16. CALCULATING HETEROGENEITY (Cell-Based Analysis)
Identify
Total Duration Of Time
Total Number Of Unique Cells Visited
Expected Duration Per Cell = Total Duration / Number Of Cells
Order
Cell Duration Times (From Least-To-Most)
Record Number Of Cells With Each Duration
Calculate
Heterogeneity For Each Cell Duration Time
Total Heterogeneity = Sum Of Cell Heterogeneities
Mean Heterogeneity = Total Heterogeneity / Number Of Cells
- If Initial Mean Heterogeneity < 1, No Attractor Present
Eliminate Cells With Smallest Duration
Re-Do Steps 1-4 Until Only Largest Duration Cell(s) Left
Assessment
For Each Step, Calculate The Proportional Mean Heterogeneity Against The Original Mean Heterogeneity
Construct Scree Plot
Identify Attractor
Drop Of 50% Heterogeneity
Greatest Drop In Heterogeneity
Final Drop
Eliminate Primary Attractor(s) And Recalculate Total Mean Heterogeneity
- If > 1, Secondary Attractor Can Be Identified

17. IDENTIFYING ATTRACTORS

18. PRIMARY INITIAL ATTRACTORS
Level Of Depression 1 2 3 4 5 6 7 8 9 10 1 4 3 1
Level Of Anxiety
Control
Depression
Panic

19. ATTRACTOR CONSISTENCY (P04)
Level Of Depression 1 2 3 4 5 6 7 8 9 10
Level Of Anxiety
Week 1
Week 2
Week 3
Week 4

20. ATTRACTOR EVOLUTION (D03)
Level Of Depression 1 2 3 4 5 6 7 8 9 10
Level Of Anxiety
Week 1
Week 2
Week 3
Week 4

21. DEMOGRAPHICS OF SAMPLE
Characteristic
Controls
(n=5)
Subjects With MDE
Subjects With PD
Gender (#female)
Ethnicity (Hispanic)
Age (years)
#<40
#≥40
Education
# 0-11 Years
# High School Grad
#>12 Years
Income
#<$10,000
#$10,000-$30,000
Antidepressants Started
Missing Data (Anx / Dep)
Subject #1
Subject #2
Subject #3
Subject #4 3 5 4 1 2
0.0% 1.2%
0.4% 0.2%
0.0% 0.0%
2.4% 0.7%
0.0% 0.2%
40.1% %
0.8% 1.9%
0.6% 0.4%

22. INTERGROUP COMPARISON OF SYMPTOM EXTREMES AND CORRELATION
Mean Daily Maximum
Anxiety* Depression**
Mean Daily Minimum
Anxiety Depression
Correlation
r***
Controls
Depression
Panic
.70
.40
.44
* p ≤ Controls < Depression, Panic
** p ≤ Controls < Depression, Panic
*** p ≤ Controls > Depression, Panic

23. Depression Acceleration
DSEM RESULTS
Dependent Variable
Depression Acceleration
MODEL 1
MODEL 2
Anxiety Acceleration
Fit Statistics
-LogL
AIC
BIC
Adjusted BIC
583
1179
1218
1199
253
524
582
554
898
1807
1846
1827
660
1338
1396
1367

24. DSEM RESULTS Characteristics Depression Acceleration Anxiety
Estimate p-Value
Anxiety
Within Subjects
Anxiety Level
Anxiety Velocity
Anxiety Acceleration
Depression Level
Depression Velocity
Depression Acceleration
Between Subjects
Depression Dx
Panic Dx
<.001
<.001
<.001
<.001
TOTAL

25. INTERGROUP ATTRACTOR COMPARISONS (Subjects)
Initial Cells Used **C
(#)
Initial Attractors
Total Attractors*A
Initial Attractor Consistency*B
(# weeks)
Duration On Attractors*D
(% hours)
Controls
14.0
1.3
1.8
2.0
64%
Depression
26.3
5.0
0.0
41%
Panic
3.0
34%
* p ≤ .15
** p ≤ .05
A = Depression > Panic, Control C = Control < Panic, Depression
B = Depression < Panic, Control D = Control > Panic, Depression

26. INTERGROUP ATTRACTOR COMPARISONS (Attractors)
Size**A
(# cells)
Proportional
Duration**A
(% time)
Stability*B
(return hours)
Influence
(% to attractor)
Consistency*C
(# weeks)
Controls
2.6
50%
1.04
18%
1.8
Depression
2.0
36%
2.45 9%
0.4
Panic
23%
2.03
0.9
* p ≤ .05
** p ≤ .01
A = Control > MDE, Panic
B = Control < MDE, Panic
C = Depression < Panic, Control

27. DISCUSSION Co-Variation Of Anxiety And Depression
Significant Anxiety-Depression Correlation
dSEM Fit Better With Both Symptoms In Model
Presence Of Attractors

28. DISCUSSION Diagnostic Differences (Controls vs Illness)
SymptomMAX & Correlations Differ
dSEM – Both Disorders Contribute To d2 Depression
Attractors
Subjects (Controls)
Fewer Initial Cells Used
More Time On Attractors
Attractors (Controls)
Larger Attractors
More Time On Attractor
Quicker Return Time

29. DISCUSSION Diagnostic Differences (Depression vs Panic)
No SymptomMAX & Correlation Differences
dSEM – No Diagnostic Differences
Attractors (Depression vs Panic)
Subjects
More Total Attractors
Less Consistent Initial Attractors
Attractors – Less Consistency

30. IMPLICATIONS Understanding Normalcy
Emotional Variability
Anxiety-Depression Interrelationship
Psychopathology May Represent Weakening Of Attractors
Perceived Instability
Perceived Lack Of Control
Diagnostic Differences Due To Dynamics Rather Than Levels?
New Interventions To Strengthen Attractors

31. LIMITATIONS Small Sample Size Referral Of Subjects – Selection Bias?
Missing Data
Visual Analog Scales – Single Measurement
Measures Taken Only While Awake
Attractor-Level Comparisons Not Independent

32. CONCLUSIONS High Co-Variability Between Symptoms
Dynamic Differences Seen
Controls versus Patients
Depression versus Panic
Methodological Potential
dSEM
State Space Grid