Running head: FLUCTUATIONS IN DEPRESSION AND RISK
1
Appendix: Supplemental Digital Content
Appendix A: Additional Sample Description
Table A.1
Participant Characteristics
Measure
Age
Race
African-American
Latino/Hispanic
White/Caucasian
Other
Education
High school or Less
Some College
College/Graduate Degree
Yearly Income
$0-$10,000
$11-$20,000
$21,000+
Employment Status
Working
Disability
Unemployed
Student/Other
Relationship Status
Having sex with one partner
Having sex with more than one partner
Any UAI in the last 2 months
Yes
No
Sexual identity
Gay/homosexual
Bisexual
Other
Any drug use in the last 2 months
Yes
No
Any alcohol use in the last 7 days
Yes
No
HIV disease status
Undetectable viral load (≤ 50 copies/mL)
AIDS diagnosis (CD4 ≤ 200)
N
106
105
M (SD)
%
38.3 (9.7)
51.9
25.5
20.8
1.9
105
25.7
42.9
31.4
105
37.1
32.4
30.5
105
17.1
39.1
28.6
15.2
105
19.1
81.0
106
66.0
34.0
105
81.9
14.3
3.8
106
82.1
17.9
106
67.0
33.0
89
101
43.8
11.9
Running head: FLUCTUATIONS IN DEPRESSION AND RISK
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Appendix B: Reliability and Correlation of the Well-Being and Depression Measures
Reliability. To describe sources of variance and reliability of the time-varying predictors,
we differentiate the available variance in the predictor variables depression and wellbeing, following Cronbach’s generalizability theory approach, as described by Shrout
and colleagues (Shrout & Lane, 2011; Cranford, Shrout, Iida, Rafaeli, Yip, & Bolger,
2006).
Table B.1 shows the variance components of the item ratings for depressed mood and
well-being. Variability between persons is substantial for well-being and depressed
mood, explaining 12% and 24% of the variance. Variability across time was 0, indicating
that neither depressed mood nor well-being showed systematic change over time.
Variability across items was 19% and 16%, indicating that some items were rated
systematically higher or lower than other items in both scales. Person-by-time variability
was 9% and 10%, indicating that some participants rated their depressed affect and
well-being as higher or lower across all items at certain time points. Person-by-item
variability was the second largest variance components for both scales with 30% and
32%, indicating that some participants rated some items higher or lower across all time
points. Time-by-item variability was 0 for both scales, indicating that none of the items
showed systematic time trends. For depression and well-being, residual variability was
the largest variance component, indicating that some persons rated some of the items
within the scales in some weeks unusually high or low. Based on these variance
components, we calculated between-person reliability RBetw and within-person reliability
RChange; reliabilities were high for both depressed affect and well-being.
Table C.1
Variance Decomposition and Between- and Within-Person Reliability Estimates for
Depression and Well-Being
Source of Variance
Depressed
Mood
(CES-D)
0.10
%
12
WellBeing
(FAHI)
0.35
%
24
Variability across persons
σ2PERSON
Variability across time
σ2TIME
0.00
0
0.00
0
Variability across items
σ2ITEM
0.20
19
0.27
16
Person-by-time variability
σ2PERSON*TIME
0.07
9
0.14
10
Person-by-item variability
σ2PERSON*ITEM
0.25
30
0.45
32
Time-by-item variability
σ2TIME*ITEM
0.00
0
0.00
0
Residual variability
σ2ERROR
0.40
49
0.47
33
100
1.41
100
Total
Between-person reliability
RBetw
0.94
0.98
Within-person reliability
RChange
0.93
0.96
Correlation of Depression and Well-Being. We also examined the correlations between
depression and well-being. The between-person correlation was high (r = -.75, p <.01).
Running head: FLUCTUATIONS IN DEPRESSION AND RISK
The average within-person correlation was moderate in size (r = -.30, p =.01). To
calculate the average within-person correlation, we followed the procedure in Green,
Rafaeli, Bolger, Shrout, and Reis (2006). We standardized the deviations in depression
and well-being so that they had a mean of 0 and within-person standard deviation of 1.
Then we used a mixed model to regress standardized depression on standardized wellbeing. As both depression and well-being were standardized within person, we got the
average within-person correlation from the slope of this model.
3
Running head: FLUCTUATIONS IN DEPRESSION AND RISK
4
Appendix C: Detailed Description of the Data Analysis and Results
Study Design. We designed a study that included bi-weekly repeated assessments of
well-being and risk behavior. Specifically, participants were asked to report on
depression, well-being, and sexual risk episodes in the prior week in Weeks 1, 3, and 5
of the study.
Rationale for Choice of Data Analysis Strategy. The current analysis is our attempt at the
“integration of theoretical model, temporal design, and statistical model” important when
analyzing repeated assessments (Collins, 2006, p. 509). We assume that
depression/well-being and sexual risk episodes fluctuate in relatively brief time periods
of hours or days. Therefore, we measured depression/well-being and sexual risk
episodes within the same week, and analyzed the data that way. We chose a
contemporaneous analysis approach over a time-lagged approach because we believe
that the 2-week lags between assessment waves were too long to capture processes
that would be expected to play out in hours or days. It also seemed unlikely that
depression and well-being in a given week would influence risk behavior 2 weeks later.
Thus, we assume that depression and well-being in a certain week are related to risk
episodes in that same week.
Data Analysis Strategy. We conducted within-person analyses where we asked the
question: On weeks when depression and well-being is higher than the person’s
average, is the person’s likelihood of a risk episode higher than average? To address
this question, we separated each predictor variable into a within- and a between-person
component and then entered both of them in the regression model, following
recommendations by Allison (2009), Bolger and Laurenceau (2013), Raudenbush and
Bryk (2002), Curran and Bauer (2011), and West, Ryu, Kwok, and Cham (2011).
Analyses were carried out using the GENMOD procedure in SAS 9.3 with a significance
level of p≤.05.
We will first focus on the analysis of depression and any UAI episodes. Equation C.1
shows that the raw depression score for individiual i at time t, Depressionit, can be split
up into the weekly within-person deviation in depression, Depression_Wit, from each
individual i's average depression level across Week 1, 3, and 5, Depression_Bi.
Depressionit = Depression_Wit + Depression_Bi
(C.1)
Therefore, we first calculated average depression for each individual i across Week 1, 3,
and 5, Depression_Bi. Then we subtracted each person’s average from the raw
depression score, Depressionit, to arrive at the deviation in depression, Depression_Wit.
Depression deviations and person means were divided by the between-person standard
deviation to standardize them and facilitate interpretation of effects. Then we entered
depression deviations and person averages, the latter centered at the grand mean, into
a logistic regression (Equation C.2).
ln
Pr(UAIit = 1)
Pr(UAIit = 0)
= 1
+ 2 Depression_Wit
+ 3 Depression_Bi
(C.2)
We modeled the probability of any UAI episode as a logistic function with two predictors:
(a) deviations for person i at time t (Depression_Wit) from the person mean level of
depression, and (b) between-person mean levels of depression, centered at the grand
Running head: FLUCTUATIONS IN DEPRESSION AND RISK
5
mean (Depression_Bi). This approach of centering time-varying predictors within person
separates the effect of depression into an average within-person effect (indicating how
deviations from the person’s average level of depression are related to the probability of
any UAI episode) and a between-person individual differences effect (indicating how
each person’s average level of depression is related to the probability of any UAI
episode). These two components can have different effect sizes and be in opposite
directions.
Equation C.2 shows the logistic regression model as logit expressions so that the
predictors appear in the linear form familiar from ordinary least squares regression. The
model predicts the odds that the most recent sexual encounter for individual i at time t
was a UAI episode. These odds are defined as the probability of reporting any UAI
episode, Pr(Yit = 1), divided by the probability of not reporting any UAI episode, Pr(Yit =
0). To obtain meaningful values for the intercept 1, we centered the between-person
predictor Depression_Bi at the grand mean in the sample. The intercept 1 indicates the
odds of any UAI episode when all other predictors are 0, i.e., when there is no deviation
from person average depression, Depression_Wit, and Depression_Bi, is at the grand
mean in the sample across the weeks of the study. The coefficient 2 tests whether on
weeks when a person was more depressed than usual he showed a greater probability
of a UAI episode (within-person association). The coefficient 3 tests whether persons
who were higher in average depression were also higher in average risk (betweenperson association).
Both outcomes, the probability of any UAI episode (UAIit) and probability of a discordant
UAI episode (dUAIit), were examined for depression and well-being, resulting in four
regression models (Equations C.2 to C.5).
ln
Pr(UAIit = 1)
Pr(UAIit = 0)
= 4
+ 5 Well-being_Wit
+ 6 Well-being_Bi
(C.3)
ln
Pr(dUAIit = 1)
Pr(dUAIit = 0)
= 7
+ 8 Depression_Wit
+ 9 Depression_Bi
(C.4)
Pr(dUAIit = 1)
Pr(dUAIit = 0)
= 10
+ 11 Well-being_Wit
+ 12 Well-being_Bi
(C.5)
ln
We tested quadratic relationships between depression/well-being and sexual risk
episodes in all models by adding quadratic terms for each within- and between-effect in
Equations C.2 to C.5. Across the eight effects we examined, there was little support for
a consistent quadratic relationship between depression/well-being and risk. Using QIC
and QICu as fit criteria, the models including quadratic terms did not show improvements
in model fit. Therefore, the models reported in the article focus on the linear within- and
between-person associations of well-being and depression with risk without including
quadratic terms.
A time trend that is not accounted for could induce a spurious association between a
within-person predictor and the outcome (i.e., time could act as a third variable
explaining the association between the within-person predictor and the outcome; Bolger
& Laurenceau, 2013; Curran & Bauer, 2011). Therefore, in exploratory analyses we
tested if participants reported on average more or less risk episodes over time. These
Running head: FLUCTUATIONS IN DEPRESSION AND RISK
6
analyses did not show a significant time trend across the three time points of the study.
The percentage of participants reporting any UAI episode or a discordant UAI episode
was relatively stable across the three time points of the study. Therefore, the models
reported in the article focus on within- and between-person associations of depression
and well-being with sexual risk episodes (see Equations C.2 to C.5).
Table C.2
Within-Person Differences in Depression and Well-being Are Associated with the
Probability of a Sexual Risk Episode
Probability of any UAI episode
Predictor
Intercept
Depression_Wit
Depression_Bi
Intercept
Well-being_Wit
Well-being_Bi
Estimate
0.26
0.53
0.22
0.27
-0.91
-0.29
SE
0.18
0.27
0.19
0.18
0.31
0.20
z
1.45
1.97
1.17
1.48
-2.95
-1.44
p
0.148
0.048
0.241
0.139
0.003
0.150
OR
1.29
1.71
1.25
1.31
0.40
0.75
95% CI
Low
High
0.91
1.83
1.00
2.90
0.86
1.80
0.92
1.86
0.22
0.74
0.50
1.11
Probability of a serodiscordant UAI episode
95% CI
Predictor
Estimate
SE
z
p
OR
Low
High
Intercept
-1.62
0.23
-6.96
<.001
0.20
0.13
0.31
Depression_Wit
0.91
0.33
2.77
0.006
2.49
1.31
4.73
Depression_Bi
0.01
0.22
0.06
0.950
1.01
0.66
1.57
Intercept
-1.64
0.23
-7.00
<.001
0.19
0.12
0.31
Well-being_Wit
-0.87
0.34
-2.58
0.010
0.42
0.22
0.81
Well-being_Bi
-0.06
0.21
-0.27
0.788
0.95
0.63
1.42
Note. Depression was measured with the Centers for Epidemiological Studies–
Depression scale and well-being was measured with the Functional Assessment of HIV
Infection scale.
The Contemporaneous Analysis Approach. We intentionally characterize our approach
to the analysis as contemporaneous, to distinguish it from a classic correlational
analysis. The study is designed with repeated contemporaneous assessments that
could be called multiple cross-sections. These repeated cross-sections allow for a
contemporaneous analysis that enables us to distinguish between- and within-person
variability (i.e., stable person means and deviations).
No matter if we are looking at a single cross-section or repeated time points, we can
represent the assessment of a certain person i taken at time t as the sum of two
components (e.g., Allison, 2009; Bolger & Laurenceau, 2013, Raudenbush & Bryk, 2002;
Curran & Bauer, 2011; Hamaker, 2012). The first component is the person’s average
level, often called a trait score, and the second component is the person’s temporal
deviation from this person’s average level, the person’s state score at this time point
(see Equation C.1 for the example of depression). As Hamaker (2012, p. 49) has
pointed out about single cross-sections, “when we take a cross section and analyze
these data, both within-person (or state-like) aspects and between-person (or trait-like
aspects) influence our results.” But a single cross-section does not allow for
Running head: FLUCTUATIONS IN DEPRESSION AND RISK
distinguishing state- and trait-like aspects. Only with repeated assessments can we
separate how much of the variability is due to trait aspects and state aspects of a
construct of interest.
A study that includes repeated assessments and time-sensitive measurement
instruments (often called state measures) allows for the examination of both state and
trait variability in constructs of interest, as Hamaker (2012) has pointed out. It is a
common misconception that using a “state measure” ensures that all the variability
captured is due to states. But stable between-person differences still influence reports
on state measures. Thus, our analyses aimed to examine both within- and the betweenperson associations. We separate the within- and between-person variability in the
predictor and enter them separately to get at the within- and between-person association
of depression/well-being and risk.
The contemporaneous analysis approach with differentiation of within- and betweenperson associations does not allow causal conclusions. This study shows that the
depression-to-sexual risk link seems to be not a stable characteristic of HIV-positive
MSM, but rather a dynamic one. The depression-risk link seems to be more dynamic
than prior studies had assumed. When depression was higher than usual, sexual risk
episodes were more likely to occur. Future studies that employ at least weekly repeated
assessments of depression and sexual risk episodes are needed to examine temporal
ordering and causality. These studies will be able to test if increases in normal
depression precede sexual risk episodes, if sexual risk episodes precede depression
increases, or if there are time-varying circumstances (e.g., stressors) that precede
increases both in depression and sexual risk episodes.
7
Running head: FLUCTUATIONS IN DEPRESSION AND RISK
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