Parsing Within & Between-Person Dynamics of Therapy Homework Completion and Clinical Symptoms in Two Cognitive Behavioral Treatments for Adults with Anhedonia

Abstract

Objective:

Homework is a key theoretical component of cognitive-behavioral therapies, however, the effects of homework on clinical outcomes have largely been evaluated between-persons rather than within-persons.

Methods:

The effects of homework completion on treatment response were examined in a randomized trial comparing Behavioral Activation Treatment for Anhedonia (BATA, n=38), a novel psychotherapy, to Mindfulness-Based Cognitive Therapy (MBCT, n=35). The primary endpoint was consummatory reward sensitivity, measured weekly by the Snaith Hamilton Pleasure Scale (SHAPS), up to 15 weeks. Multilevel models evaluated change in SHAPS scores over time and the effects of clinician-reported and participant-reported homework.

Results:

BATA and MBCT resulted in significant, equivalent reductions in SHAPS scores. Unexpectedly, participants who completed greater mean total amounts of homework did not improve at a faster rate (i.e., no between-person effect). However, sessions with greater than average participant-reported homework completion were associated with greater than average reductions in SHAPS scores (i.e., a within-person effect). For clinician-reported homework, this effect was only evident within the BATA condition.

Conclusion:

This study shows psychotherapy homework completion relates to symptomatic improvement in cognitive-behavioral treatments for anhedonia when session-to-session changes are examined within-person. On the contrary, we found no evidence that total homework completion predicted greater improvements between-person. When possible, psychotherapy researchers should evaluate their constructs of interest across multiple sessions (not just pre/post) to allow more direct tests of hypotheses predicted by theoretical models of individual change processes.

Introduction

Work between therapy sessions is a key theoretical component of cognitive behavioral therapies, including behavioral activation and mindfulness-based cognitive therapy (MBCT). Cognitive and behavioral therapies typically refer to between-session work as “homework,” (Beck, 2020) while mindfulness-based interventions often use the term “home practice” (Segal & Teasdale, 2018). In behavioral activation, between-session engagement in typically valued and/or enjoyable behaviors is thought to result in positive reinforcement, thus increasing positive affect and motivation to engage in further reinforced behaviors (Nagy et al., 2020). In MBCT, regular mindfulness practice is thought to be a critical means to facilitate experiential learning of mindfulness. Formal practice (e.g., structured, longer meditations such as body scan or sitting practice) as well as informal practice (e.g., bringing mindful attention to everyday tasks such as showering/eating) extend that learning into the everyday lives of patients (Segal & Teasdale, 2018). Across both interventions, therapy homework is assumed to influence the effectiveness of treatment by teaching and reinforcing important skills needed to manage depressive symptoms (Beck, 2020; Segal & Teasdale, 2018).

Despite its theoretical importance, empirical studies of the impact of therapy homework on clinical outcomes have not shown effects as large as theory might predict. In a meta-analysis of 46 studies of cognitive behavioral therapy (CBT) representing 1,072 participants, therapies that included a homework component showed a small-to-medium effect (d = .48) when compared to therapies that did not include homework, though frequency or duration of completed homework by individual participants was not assessed (Kazantzis et al., 2010). A meta-analysis of 23 CBT studies that did include measures of individual homework completion likewise found a small-to-medium effect (r = .26) of homework adherence on clinical outcomes (Mausbach et al., 2010). Few studies have examined the impact of homework completion in behavioral activation interventions specifically, though there is some evidence that engagement with socially oriented homework assignments is especially impactful in depressed older adults (Solomonov et al., 2019).

A recent review of home practice in MBCT highlighted that relationships between the duration and frequency of formal home practice with depression severity is not as strong as would be expected, and that support for the impact of informal practice is especially limited (Segal, Dimidjian, et al., 2019). However, there is more robust support for an impact of home practice on more proximal mediating variables of treatment response. For example, a recent study found that more frequent home practice had an indirect effect on depressive relapse through its influence on the ability to decenter from thoughts and emotions (Segal, Anderson, et al., 2019). Likewise in data from combined trials of MBCT and mindfulness-based stress reduction, formal practice in particular was associated with reductions in rumination, which in turn predicted greater depressive symptom change (Hawley et al., 2014).

Within the therapy homework literature, limited attention has been paid to the time-varying effects of homework completion within individuals. Whereas studies typically monitor adherence with homework assignments at each session, primary clinical outcomes are rarely measured this frequently, impeding the ability to model session-to-session changes in homework completion and progress. In a recent meta-analysis of CBT homework quantity and quality effects on wide-ranging clinical outcomes, all the constituent studies evaluated homework completion using composite scores (e.g., means or sums) to predict post-treatment outcomes, usually controlling for pre-treatment severity and demographics (Kazantzis et al., 2016). Results indicate that individuals who completed relatively more (or better quality) homework than others within the trial also showed relatively greater improvements. However, this meta-analysis did not address whether the specific occasions in which individuals complete relatively more homework were associated with greater improvements within those same individuals (i.e., a within-person effect of homework). Examining effects solely between-persons allows for the possibility that individual differences in traits (e.g., conscientiousness, high executive functioning, etc.) may directly relate to the propensity to complete homework and improve from therapy.

At least two studies are notable exceptions in the literature because their methodologies account for potential between-person characteristics by explicitly examining within-person processes. Conklin and Strunk (2015) explored session-to-session relations between homework completion and depressive symptoms among 53 adults undergoing cognitive therapy. They found that intervals in which participants engaged in more homework (measured in absolute quantities rather than percentages) were associated with relatively greater improvements in depression. Interestingly, the between-person effect of homework completion, albeit nonsignificant, was in the opposite direction (i.e., those who improved more completed less homework). The authors speculated that therapists may have ultimately assigned larger quantities of self-monitoring homework to individuals who showed less marked improvements in early treatment. Using a similar analytic approach, Haller and Watzke (2021) examined relations between homework completion and depressive symptoms among 22 adults undergoing telephone-based CBT. They found that occasions of greater homework completion were associated with greater improvements in depression.

In the current study we examined how therapy homework completion impacted self-reported consummatory reward sensitivity in an ongoing transdiagnostic adult sample undergoing psychotherapy for anhedonia (ClinicalTrials.gov Identifiers NCT02874534 and NCT04036136). The trial compares Behavioral Activation Therapy for Anhedonia (BATA), a novel adaptation of Behavioral Activation Therapy for Depression (Lejuez et al., 2011), to individually administered MBCT. We previously reported results of an interim analysis of this trial that showed that both treatments significantly and equivalently improved self-reported reward sensitivity (Cernasov et al., 2021). The purpose of this study was to investigate the impact of homework completion on anhedonia symptoms using multilevel models to disaggregate between-person and within-person effects. For the between-person effects of homework we tested whether participants who completed greater mean total homework showed faster rates of improvement over time. For the within-person analysis we tested the covariance between homework completed at each session and improvement in symptoms at each session. We predicted that participants who completed greater mean total homework would demonstrate a faster rate of improvement, and that occasions in which individuals completed relatively more homework would also be associated with relatively greater improvement.

Methods

Participants

The present analyses include 73 participants from an ongoing clinical trial targeting anhedonia in a transdiagnostic sample. Fifty-one participants completed treatment and 22 withdrew or were lost-to-follow-up. Data from all 73 participants were included in analyses using multilevel models. Participants were randomized to one of two psychotherapy interventions (BATA n=38, MBCT n=35) and attended at least one therapy session prior to March 2020 (i.e., before temporary suspension of research activities and subsequent transition to teletherapy due the SARS-CoV-2 pandemic). Inclusion criteria were age 18-50 years old, clinically significant anhedonia defined by Snaith Hamilton Pleasure Scale (SHAPS) scores > 20 (Franken et al., 2007; Snaith et al., 1995) and Clinical Global Impressions-Severity scores ≥ 3 (at least mildly ill). Exclusion criteria were psychotropic medication use in the past 30 days, MRI contradictions (a key goal of the study was to evaluate neural mechanisms), concurrent psychotherapy, prior behavioral activation or mindfulness-based psychotherapy, or history of moderate or severe substance use disorder, eating disorder, bipolar disorder, or psychotic disorder assessed via the Structured Clinical Interview for DSM-5, Research Version (SCID-5) (First MB, 2015). Sample characteristics are reported in Table 1, and the treatments did not cause any adverse events.

Table 1.

Demographics and Sample Characteristics.

	Total Sample (n=73)	BATA (n=38)	MBCT (n=35)	Test Statistic	Estimate	p-value
Age (years), mean (SD)	29.7 (9.1)	27.9 (8.8)	31.8 (9.2)	t	1.85	.07
Sex (female), n (%)	51 (70)	27 (71)	24 (69)	χ2	0	1
Annual Income, mean (SD)	$71,170 (67K)	$85,945 (77K)	$59,280 (51K)	t	1.7	.09
Attrition, n (%)	22 (30)	8 (21)	14 (40)	χ2	2.27	.13
Race, n (%)				χ2	5.2	.27
Asian	14 (19)	9 (24)	5 (14)
Black	15 (21)	8 (21)	7 (20)
Native American	1 (1)	0 (0)	1 (3)
Other	0 (0)	0 (0)	3 (9)
White	40 (55)	21 (55)	19 (54)
Ethnicity, n (%)				χ2	5.7	.06
Hispanic or Latino	67 (89)	1 (3)	6 (17)
Not Hispanic or Latino	7 (10)	37 (97)	28 (80)
Prefer Not to Answer	1 (1)	0 (0)	1 (3)
Baseline Clinical Symptoms, mean (SD)
SHAPS	36.2 (4.6)	35.7 (3.8)	36.9 (5.3)	t	1.12	.27
BDI-II	22 (9.4)	20.2 (8.2)	24 (10.3)	t	1.71	.09
BAI	11.5 (8.3)	11.3 (8.3)	11.8 (8.3)	t	.24	.81
PCL5	24.1 (13.7)	21.9 (10.9)	26.4 (16)	t	1.4	.16
Post-Tx Clinical Symptoms, mean (SD)
SHAPS	29 (6.4)	29.3 (5.4)	28.6 (7.5)	F	.22	.64
BDI-II	10.8 (11.5)	9.1 (9.4)	12.6 (13.2)	F	2.27	.14
BAI	6.8 (7.1)	5.2 (5.3)	8.5 (8.4)	F	5.69	.02
PCL5	14.4 (14.3)	11.9 (13.3)	17 (14.9)	F	4.14	.05
Primary DSM-5 Diagnosis, n (%)
Major Depressive Disorder	24 (33)	13 (8)	11 (31)
No Diagnosis	17 (23)	11 (29)	6 (17)
Generalized Anxiety Disorder	11 (15)	7 (18)	4 (11)
Post-Traumatic Stress Disorder	7 (10)	1 (3)	6 (17)
Persistent Depressive Disorder	5 (7)	3 (8)	2 (6)
Social Anxiety Disorder	2 (3)	1 (3)	1 (3)
OS Anxiety Disorder	2 (3)	0 (0)	2 (6)
OS Traumatic Stress Disorder	1 (1)	1 (3)	0 (0)
ADHD	1 (1)	1 (3)	0 (0)
Adjustment Disorder	1 (1)	1 (3)	0 (0)
Treatment Engagement, mean (SD)
Total Sessions Attended	9.4 (3.6)	9.8 (3.4)	9 (3.9)	t	.93	.35
% Clinician-Reported HW	75 (21)	76 (21)	75 (21)	t	.1	.92
% Participant-Reported HW	78 (20)	79 (21)	78 (2)	t	.15	.88
TAQ	8.7 (5.1)	8.9 (4.5)	8.5 (5.8)	t	.28	.78

Note. Post-treatment outcomes were compared between treatment conditions using an analysis of covariance with baseline scores as a covariate. ADHD – Attention-Deficit/Hyperactivity Disorder, BATA – Behavioral Activation Therapy for Anhedonia, BAI – Beck Anxiety Inventory, BDI-II – Beck Depression Inventory II, HW – Homework Completion, MBCT – Mindfulness Based Cognitive Therapy, OS – Other Specified, PCL5 – Post-Traumatic Stress Disorder Checklist for the Diagnostic and Statistical Manual 5, SHAPS – Snaith Hamilton Pleasure Scale, TAQ – Treatment Acceptability Questionnaire, Tx – Treatment

Procedures

This protocol was approved by the Institutional Review Boards at the University of North Carolina, Chapel Hill and the Duke University Health System. Participants were randomized to weekly individual 45–60-minute sessions of BATA or MBCT for up to 15 sessions. Treatment descriptions from Cernasov et al. (2021) are included below. Treatments were delivered using a crossed-therapist design. Participants were eligible to complete treatment after attending a minimum of eight sessions if the clinician and patient concurred that maximal benefit was achieved. The primary clinical outcome measure was the SHAPS, an anhedonia self-report questionnaire, administered at screening, weekly therapy sessions, neuroimaging appointments (pre-treatment, session 8, session 12, and post-treatment), and study completion visits. The CONSORT Flow Diagram is provided in Figure 1.

Figure 1.

CONSORT flow diagram of participants assessed for eligibility and enrolled in the trial.

Behavioral Activation Therapy for Anhedonia (BATA)

BATA is a modification of Behavioral Activation Treatment for Depression (Lejuez et al., 2011) developed to treat anhedonia transdiagnostically. BATA entails psychoeducation of reward and learning processes to frame experiences with anhedonia in a neuroscientific perspective. Patients are encouraged to engage in activities that increase contact with personally relevant, values-congruent reinforcers. While achievable goal setting is often impaired in anhedonia, therapists use motivational techniques to elicit goal-directed behaviors. Differences from traditional behavioral activation treatment include a focus on initiating new behaviors outside the established behavioral set (i.e., “dabbling”) and moment-savoring exercises to enhance consummatory reward experiences. Increased positive affect and decreased negative affect are theorized to result from reduced behavioral avoidance and consequently increased contact with potential reinforcers. Homework tasks in BATA included completion of daily and weekly monitoring forms, completion of values assessment worksheets, and beginning with the third session, 2-4 weekly behavioral goals based on the participant’s identified values (e.g., go for a walk three times in the next week to support health values; call sister on Saturday to support a value of family connectedness.)

Mindfulness-Based Cognitive Therapy (MBCT)

MBCT was administered in an individual format (Segal & Teasdale, 2018; Wahbeh et al., 2014). This format retains the primary components of traditional group MBCT including didactic instruction, guided in-session meditations, between-session home practice, and inquiry of subjective experience. Mindfulness is presented as a skill to facilitate flexible cognitive-emotional responses to events and reduce habitual reactions. Practices emphasize core mindfulness skills of attention, decentering, and nonjudgmental acceptance through exercises such as body scans, mindful movement, and focused awareness of breath. Guided inquiry is geared toward awareness of the interrelations among thoughts, emotions, and sensations, as well as the recognition of habitual patterns that can interfere with the experience of pleasure. Home practice tasks in the MBCT condition included daily informal mindfulness of an everyday activity (e.g., mindfully attend while drinking coffee in the morning), formal mindful practice (e.g., audio-guided body scan or mindfulness of breath practice), and occasional additional tasks (e.g., for one week, log unpleasant events to note the thoughts, emotions, and body sensations that accompanied the events).

Snaith Hamilton Pleasure Scale (SHAPS)

The SHAPS was the primary anhedonia outcome measure for this trial. It is a 14-item self-report questionnaire assessing hedonic functioning, particularly with respect to consummatory reward processing (Snaith et al., 1995). Each item on the SHAPS pertains to a typically pleasurable activity (e.g., watching a favorite television program). Individuals indicate whether they were likely to enjoy each activity “in the last few days” using one of four responses – strongly disagree, disagree, agree, or strongly agree. Total scores range between 14 – 56, with higher values indicating worse consummatory reward responsivity and thus greater anhedonia severity (Franken et al., 2007).

Therapy Homework Completion

Therapy homework completion was assessed at each session independently by the participant and the clinician using a subjective 0 – 100% scale. Participants were asked, “What percentage of homework from the past week did you complete?” Clinicians were instructed to attend to the participant’s homework log, if completed, as well as how the participant described their homework completion in the therapy session (e.g., attending to a participant’s tendency to over- or under-estimate their goal completion or task engagement.) We use “Pt-Hw” to denote participant-reported homework and “Cl-Hw” to denote clinician-reported homework. In BATA, homework consisted of values-congruent goals mutually agreed upon by the patient and therapist (e.g., have three phone conversations with friends/family over the next week). In MBCT, homework involved formal mindfulness practices (e.g., 10-minute breath awareness meditation for six days a week) and informal mindful awareness exercises (e.g., bringing awareness to a routine activity such as showering).

Treatment Acceptability Questionnaire (TAQ)

A modified self-report TAQ (Hunsley, 1992) was analyzed to examine differences between treatment modalities in terms of treatment engagement. Seven questions were rated on a five-point Likert scale assessing overall satisfaction with the treatment, therapist, therapy sessions, handouts, homework assignments, the likelihood of enduring benefits from therapy, and the likelihood to recommend the treatment to others. TAQ scores ranged between -14 – 14, with higher values indicating greater overall satisfaction.

Analytic Plan

Overview of Analyses

Prior to our substantive analyses, we imputed missing values for a small number of homework completion ratings using participant-specific regression equations derived from mixed effects models. We also compared metrics of treatment engagement (e.g., mean total homework completion, TAQ scores, sessions attended) between BATA and MBCT. Next, we evaluated the functional form of SHAPS scores over time using a series of multilevel models with time as the sole predictor variable. These unconditional growth curve models provided information about overall rate of change, variation in baseline severity, variation in improvement, and relations between baseline severity and improvement (Curran et al., 2010). The growth curve model was then expanded to evaluate potential predictors of change over time: age, sex, income, total number of sessions attended, and treatment condition.

For our primary aims, we evaluated between-person and within-person effects of homework on SHAPS scores using separate multilevel models. For the between-person effect of homework, we estimated growth curve models with cross-level interactions between mean total homework completion and time, followed by three-way interactions between homework, time, and treatment condition. These analyses indicated whether participants who did more homework on average also improved at a faster rate, and whether this effect differed between BATA and MBCT. For the within-person effect of homework, we used multilevel models with session-to-session change in SHAPS scores (i.e., ΔSHAPS) as the dependent variable and time-varying homework completion as the predictor, followed by an interaction between time-varying homework completion and treatment condition. These analyses indicated whether occasions in which relatively more homework was completed were associated with relatively greater improvements within individuals, and whether this effect differed between BATA and MBCT.

All multilevel models were estimated using R’s nlme package (Pinheiro J, 2021). Total variance explained (R²) was calculated using the multivariate variance partitioning method described by LaHuis (2014). Model diagnostics included plotting level 1 residuals and level 2 random effects as histograms and QQ plots, plotting residuals by predicted values from fixed effects, and residuals by predictor variables (Hodges, 1998).

Missing Homework Completion Ratings

Data were missing for 10 instances of Cl-Hw completion ratings and 16 instances of Pt-Hw completion ratings (out of 586 total instances). There were never instances in which both ratings were missing from the same therapy session. We ran a Pearson correlation between all observed values of Cl-Hw and Pt-Hw completion to determine the appropriateness of imputing missing values. We used single predictor, mixed effects models (i.e., Cl-Hw completion regressed on Pt-Hw completion and vice versa) to derive participant-specific regression equations (i.e., from the combination of fixed and random effects) and impute missing homework completion ratings.

Treatment Engagement Metrics

A chi-square test of independence compared therapy completion rates between BATA and MBCT. The total number of sessions attended, mean total homework completion (Cl-Hw & Pt-Hw), and TAQ scores were compared between BATA and MBCT using independent sample t-tests.

Functional Form of SHAPS Over Time

A histogram of SHAPS scores across observations was plotted to assess the distribution of the outcome variable. Time was coded using a variable representing the number of therapy sessions attended prior to that observation. For example, SHAPS values recorded at screening and the first therapy session were both coded time = 0, and values recorded at the second therapy session were coded time = 1, regardless of days elapsed between sessions. Using this metric, we created spaghetti plots of raw change in SHAPS over time across the entire sample, and separately by treatment condition, to discern potential trends in the trajectories.

A random effects analysis of variance model was fit to compute the intraclass correlation coefficient (ICC) of SHAPS, which characterizes the degree of clustering in the data. The ICC was calculated dividing between-participant variance τ₀₀ by total variance (τ₀₀ + σ²).

The functional form of change in SHAPS over time was evaluated through a series of nested models. Comparisons between models were made using likelihood ratio tests (LRT) and changes in Akaike Information Criterion (AIC) to determine whether adding parameters improved or worsened fit (Portet, 2020). Nested models differing in random effects were estimated using restricted maximum likelihood, while those differing in fixed effects (e.g., adding a quadratic effect of time) were estimated using full information maximum likelihood (Faraway, 2006). Parameters were evaluated in the order listed below. If a parameter did not significantly improve fit, it was removed from subsequent model comparisons.

1. Random intercept variance (τ₀₀) – The base unconditional model implies variation in initial SHAPS scores but fixed trajectories over time between participants.

2. Random slope variance (τ₁₁) – Incorporating random slope variance allows for interindividual differences in SHAPS change over time, but the slope-intercept covariance is fixed to zero. Comparison to the previous model tests whether the variability in rate of change over time across participants is significant.

3. Random slope-intercept covariance (τ₁₀/τ₀₁) – The slope-intercept covariance represents the relation between baseline SHAPS scores and rate of change over time. Comparison to the previous model tests whether participants with greater/lesser anhedonia at onset show more/less rapid improvement over time.

4. Autoregressive-1 (AR-1) residual correlation (ϕ) – The AR-1 model indicates a linear dependency between the residuals. The correlation between adjacent observations is denoted by ϕ, between observations two units apart denoted by ϕ², and so on. Comparison to the previous model tests whether SHAPS values at time t are related to values at time t − 1.

Non-linear change over time was evaluated by testing a quadratic fixed effect of time. Lastly, a series of piecewise linear models with two periods of linear growth were evaluated to test an alternative trajectory of non-constant change over time. The knot (i.e., where the line segments join) in the model was tested at a range of values from time = 3 – 8 (the median number of therapy sessions attended was 10). Piecewise models were defined using an added rate parameterization method where β_1j represented the slope of SHAPS scores in the first segment and β_2j represented the difference in slope between the two segments (see equations below).

$${\mathit{\text{SHAPS}}}_{ij}={\beta }_{0j}+{\beta }_{1j}{\mathit{\text{Time}}}_{1ij}+{\beta }_{2j}{\mathit{\text{Time}}}_{2ij}+r_{ij}$$ Level-1 Equation

$$\begin{gathered} {\beta }_{0j}={\gamma }_{00}+u_{0j} \\ {\beta }_{1j}={\gamma }_{10}+u_{1j} \\ {\beta }_{2j}={\gamma }_{20}+u_{2j} \end{gathered}$$ Level-2 Equation

Age, Sex, Income, Total Session, and Treatment Effects on SHAPS

Once the optimal unconditional model was determined, we explored the fixed effects of sex, age, and income on SHAPS intercept and slope variation to determine whether they should be included as covariates in subsequent analyses. We also explored the effects of total number of therapy sessions and of treatment condition, though these variables were retained in subsequent analyses regardless of their statistical significance in the initial models.

$$SHAP{S}_{ij}={\beta }_{0j}+{\beta }_{1j}{Time}_{ij}+{\epsilon }_{ij}$$ Level-1 Equation

$$\begin{gathered} {\beta }_{0j}={\gamma }_{00}+{\gamma }_{01}{\mathit{\text{Age}}}_j+{\gamma }_{02}{\mathit{\text{Sex}}}_j+{\gamma }_{03}{\mathit{\text{Income}}}_j+{\gamma }_{04}{\mathit{\text{Total Sessions}}}_j+{\gamma }_{05}{\mathit{\text{Treatment}}}_j+u_{0j} \\ {\beta }_{1j}={\gamma }_{10}+{\gamma }_{11}{\mathit{\text{Age}}}_j+{\gamma }_{12}{\mathit{\text{Sex}}}_j+{\gamma }_{13}{\mathit{\text{Income}}}_j+{\gamma }_{14}{\mathit{\text{Total Sessions}}}_j+{\gamma }_{15}{\mathit{\text{Treatment}}}_j+u_{1j} \end{gathered}$$ Level-2 Equations

Between-Person (i.e., Mean Total) Homework Effects on SHAPS

To investigate between-person effects of homework completion on symptoms, we included a cross-level interaction between time and the mean proportion of homework completion across therapy sessions, a time-invariant covariate (TIC), while also controlling for the total number of sessions attended. Cl-Hw and Pt-Hw completion were evaluated in separate models. If significant cross-level interactions were detected, we expanded the model to test a three-way interaction between time, homework, and treatment condition. In summary, these models investigated whether participants who completed more homework on average also improved at a faster rate across therapy sessions.

$${\mathit{\text{SHAPS}}}_{ij}={\beta }_{0j}+{\beta }_{1j}{\mathit{\text{Time}}}_{ij}+{\epsilon }_{ij}$$ Level-1 Equation

$$\begin{gathered} {\beta }_{0j}={\gamma }_{00}+{\gamma }_{01}{\mathit{\text{Mean Total Homework}}}_j+{\gamma }_{02}{\mathit{\text{Total Sessions}}}_j+u_{0j} \\ {\beta }_{1j}={\gamma }_{10}+{\gamma }_{11}{\mathit{\text{Mean Total Homework}}}_j+{\gamma }_{12}{\mathit{\text{Total Sessions}}}_j+u_{1j} \end{gathered}$$ Level-2 Equation

Within-Person (i.e., Session-to-Session) Homework Effects on SHAPS

To investigate within-person effects of homework completion on symptoms, we used a random-intercept multilevel model using change in SHAPS scores between successive therapy sessions (i.e., ΔSHAPS) as the outcome variable and session-by-session homework completion as a time-varying predictor. ΔSHAPS scores, rather than raw SHAPS scores, were the dependent measure for this analysis because we sought to assess whether homework completion predicted symptomatic improvement, rather than whether homework completion was related to the absolute level of anhedonia severity. Homework completion was participant-mean centered to provide a pure estimate of within-person effects. Participant means of homework completion were also included as a TIC in the model. Cl-Hw and Pt-Hw completion were once again evaluated separately. If significant effects of homework were detected, we expanded the models to include an interaction between participant-mean centered homework and treatment condition. In summary, these models examined whether completing relatively more homework between sessions was associated with relatively greater improvement in-between sessions, for a given participant.

$$\Delta SHAP{S}_{ij}={\beta }_{0j}+{\beta }_{1j}{\mathit{\text{Hom}}\mathit{ė}\mathit{\text{work}}}_{ij}+{\epsilon }_{ij}$$ Level-1 Equation

$$\begin{gathered} {\beta }_{0j}={\gamma }_{00}+{\gamma }_{01}{\overline{\mathit{\text{Homework}}}}_j+u_{0j} \\ {\beta }_{1j}={\gamma }_{10} \end{gathered}$$ Level-2 Equations

(Homėwork_ij = participant mean centered homework completion)

(${\overline{\mathit{Homework}}}_j$ = grand mean centered participant mean total homework completion)

Change in Homework Completion over Time

Given the possibility of a bidirectional relation between anhedonia severity and homework completion (i.e., not only could homework completion reduce anhedonia, but also the level of anhedonia could affect a participant’s propensity to engage with homework), we also sought to evaluate the trends in homework completion over time. If anhedonia levels sufficiently impacted homework completion, we might expect increases in homework completion over time, as we know participant’s symptoms generally improved (Cernasov et al., 2021). Thus, unconditional growth curve models were evaluated for Cl-Hw and Pt-Hw using the same procedures outlined with respect to SHAPS scores.

Results

Missing Homework Completion Ratings

The Pearson correlation between Cl-Hw and Pt-Hw across observations was .76 (p < .001). Given the strong correlation between variables, single predictor mixed effects models with random intercepts and random slopes were used to derive participant-specific regressions to estimate missing values of Cl-Hw and Pt-Hw from one another.

Treatment Engagement Metrics

The rates of attrition in MBCT and BATA did not differ, χ² (1) = 2.27, p = .13. The mean (median) number of therapy sessions attended was 9.4 (10) and did not differ between treatment conditions, (t(71) = .93, p = .35). On average, clinicians reported participants completed about 75% (SD = 21%) of their homework, while participants reported they completed about 78% (SD = 20%), a nonsignificant difference (p>.05). There were no differences between treatment conditions in mean total Cl-Hw (t(69) = .1, p = .92) or Pt-Hw completion (t(69) = .15, p = .88). We also evaluated the proportion of homework completed between participants who completed treatment and those who attritted, finding no significant differences for either Cl-Hw (t(69) = 1, p = .31) or Pt-Hw (t(69) = 1.4, p = .18). Lastly, there were no differences between treatment conditions in TAQ scores (t(59) = .28, p = .78), with a mean acceptability rating of 8.7 (SD = 5.1). See Table 1 for a summary of results by treatment.

Functional Form of SHAPS over Time

The histogram of SHAPS scores across all observations indicated a normal distribution of values. Visual inspections of spaghetti plots suggested a negative linear trend best reflected change over time across both treatment conditions. The random effects analysis of variance revealed the correlation between two observations of SHAPS scores from the same participant was .56, indicating a significant degree of clustering well-suited for multilevel modeling.

Model comparisons favored incorporating random intercepts (χ² (1) = 554.1, p < .001, ΔAIC = 552.1), random slopes (χ² (1) = 244.4, p < .001, ΔAIC = 242.4), a slope-intercept covariance (χ² (1) = 6.7, p = .01, ΔAIC = 4.7), and an autoregressive-1 error structure (χ² (1) = 43.04, p < .001, ΔAIC = 41.04). The quadratic effect of time was not significant (p = .6) and worsened model fit (χ² (1) = .27, p = .6, ΔAIC = −1.7). Additionally, the piecewise models did not converge during estimation with the knot at time = 3, 7, & 8, and worsened fit with the knot at time = 4, 5, & 6 (all p’s > .34). Model diagnostics for the final unconditional growth curve model suggested assumptions were met.

Table 2 summarizes results of the final unconditional growth curve model for SHAPS. Altogether these results indicated a constant, negative, linear trend best captured change in SHAPS over time, and that variability with respect to baseline SHAPS and rate of change in SHAPS between participants was significant. The mean SHAPS score at treatment onset was 36, with a standard deviation of 4.28 points. On average, SHAPS decreased .78 points between therapy sessions, with a standard deviation of .47. The correlation between random slopes and intercepts was −.37, indicating participants with higher baseline SHAPS improved at a significantly faster rate over time. Finally, the correlation between adjacent SHAPS observations was .29. See Figure 2 for a depiction of the unconditional model-implied growth curves.

Table 2.

Summary of Unconditional Growth Curve Model for SHAPS Scores

	Estimates (SE)	Confidence Interval	P
Fixed Effects
Intercept	36.04 (.53)	34.99 – 37.09	<.001
Time	−0.78 (.07)	−0.921 – −0.65	<.001
Random Effects
σ2	5.67
τ00	18.61
τ11	0.23
τ10/τ01	−0.77
ϕ	0.29
ICC	0.78
N	73
Observations	895
Marginal R2 / Conditional R2	0.259 / 0.838

Interpretation of fixed effects. Intercept – mean value of baseline SHAPS scores, Time – expected change in SHAPS scores with one session of therapy

Interpretation of random effects. σ² – variance in residuals for the participant level regression models, τ₀₀ – variance in baseline SHAPS scores, τ₁₁ – variance in rate of SHAPS score change over time, τ₁₀/τ₀₁ – covariance between baseline SHAPS scores and rate of change in SHAPS scores over time (participants with greater initial anhedonia severity tended to improve at a faster rate in treatment), ϕ – correlation between residuals one therapy session apart (decreases uniformly as the time gap increases), ICC – intraclass correlation coefficient representing the % of total variability in SHAPS scores attributable to differences between participants

N – the number of unique participants, Marginal R² – total variance explained by fixed effects, Conditional R² – total variance explained by combination of fixed and random effects

Figure 2.

Left: Spaghetti plot of raw change in SHAPS scores over time by treatment condition. Right: Unconditional growth curve model for SHAPS scores over time. Gray lines represent model-implied values from random effects (i.e., participant-specific regression equations). The black line represents the model-implied value from the fixed effects (i.e., the regression equation for the population). For detailed descriptions of results see Table 2. SHAPS scores significantly decreased over time. There was significant variability in baseline SHAPS scores and rates of change over time. Participants with higher initial SHAPS scores showed more rapid decreases. Observations closer in time were more closely related.

Age, Sex, Income, Total Sessions, and Treatment Effects on SHAPS

Table 3 summarizes results of the conditional growth curve model for treatment and demographic effects on SHAPS. Incorporating TIC predictors in the model revealed no significant effects of age, sex, income, total number of sessions attended, or treatment condition on either SHAPS intercepts or, when evaluated as cross-level interactions, on slopes (all fixed effects p’s > .12). Thus, there were no differences between BATA and MBCT in either baseline SHAPS or rate of change over time. Age, sex, and income were omitted from subsequent analyses.

Table 3.

Summary of Growth Curve Model for SHAPS Scores Conditional on Treatment and Demographics Factors

	Estimates (SE)	Confidence Interval	P
Fixed Effects
Intercept	35.95 (.84)	34.31 – 37.59	<0.001
Time	−0.76 (.11)	−1.58 – −0.31	<0.001
Age	−0.05 (.06)	−0.18 – 0.07	0.400
Sex [Male]	−0.83 (1.18)	−3.19 – 1.52	0.481
Income	−0.01 (.01)	−0.03 – 0.01	0.270
Total Sessions	−0.19 (.15)	−0.49 – 0.11	0.206
Treatment [MBCT]	0.79 (1.12)	−1.44 – 3.02	0.483
Time*Age	0.01 (.01)	−0.01 – 0.02	0.328
Time*Sex	0.17 (.15)	−0.11 – 0.46	0.236
Time*Income	0.00 (.00)	−0.00 – 0.00	0.361
Time*Total Sessions	0.02 (.03)	−0.03 – 0.08	0.470
Time*Treatment	−0.21 (.14)	−0.48 – 0.06	0.127
Random Effects
σ2	5.68
τ00	18.43
τ11	0.21
τ10/τ01	−0.60
ϕ	0.29
ICC	0.79
N	73
Observations	895
Marginal R2 / Conditional R2	0.27 / 0.85

Interpretation of fixed effects. Intercept – mean value of baseline SHAPS scores for female participants in BATA of average age, income, who attended an average number of total sessions, Time – expected change in SHAPS scores with one session of therapy for female participants in BATA of average age, income, and total sessions attended, Age – expected change in SHAPS score intercept with one year of age, Sex – difference in SHAPS score intercepts between males and females, Income – expected change in SHAPS score intercept for $1,000 increase in annual income, Toted Sessions – expected change in SHAPS score intercept for each additional session attended overall, Treatment – difference in SHAPS score intercepts between BATA and MBCT, Time*Age – difference in Time effect for each one year increase in participant age, Time*Sex – difference in Time effect between males and females, Time*Income – difference in Time effect for each $1,000 increase in participant annual income, Time*Total Sessions – difference in Time effect for each one additional total number of therapy sessions attended, Time*Treatment – difference in Time effect between BATA and MBCT

Interpretation of random effects. σ² – variance in residuals for the participant level regression models, τ₀₀ – variance in baseline SHAPS scores, τ₁₁ – variance in rate of SHAPS score change over time, τ₁₀/τ₀₁ – covariance between baseline SHAPS scores and rate of change in SHAPS scores over time (participants with greater initial anhedonia severity tended to improve at a faster rate in treatment), ϕ – correlation between residuals one therapy session apart (decreases uniformly as the time gap increases), ICC – intraclass correlation coefficient representing the % of total variability in SHAPS scores attributable to differences between participants, N – the number of unique participants, Marginal R² – total variance explained by fixed effects, Conditional R² – total variance explained by combination of fixed and random effects

Between-Person (i.e., Mean Total) Homework Effects on SHAPS

Table 4 summarizes results of the conditional growth curve models for between-person homework effects on SHAPS. There were no significant cross-level interactions between time and homework completion for either Cl-Hw (β=−.055, SE=.033,p=.10) or Pt-Hw (β=−.039, SE=.033, p=.39). There were also no significant three-way interaction effects with treatment condition. Model diagnostics suggested assumptions were met.

Table 4.

Analysis of Between-Person Effects of Mean Total Homework Completion on SHAPS Scores

	Clinician Reported Homework			Participant Reported Homework
	Estimates (SE)	CI	P	Estimates (SE)	CI	P
Fixed Effects
Intercept	36.26 (.52)	35.24 – 37.28	<0.001	36.25 (.52)	35.23 – 37.28	<0.001
Time	−0.81 (.08)	−0.96 – −0.66	<0.001	−0.81 (.08)	−0.96 – −0.66	<0.001
Homework	0.32 (.25)	−0.18 – 0.83	0.206	0.30 (.27)	−0.24 – 0.84	0.270
Total Sessions	−0.33 (.16)	−0.64 – −0.03	0.034	−0.31 (.16)	−0.63 – 0.01	0.056
Time*Homework	−0.06 (.03)	−0.12 – −0.01	0.099	−0.04 (.03)	−0.11 – 0.03	0.243
Time*Total Sessions	0.03 (.03)	−0.03 – 0.08	0.338	0.02 (.03)	−0.03 – 0.08	0.392
Random Effects
σ2	5.69			5.68
τ00	16.68			16.82
τ11	0.21			0.22
τ10/τ01	−0.55			−0.60
ϕ	0.29			0.29
ICC	0.78			0.78
N	71			71
Observations	891			891
Marginal R2 / Conditional R2	0.290 / 0.841			0.289 / 0.841

Interpretation of fixed effects. Intercept – mean value of baseline SHAPS scores for participants who completed an average amount of homework and attended an average number of sessions, Time – expected change in SHAPS scores with one session of therapy for participants with an average amount of homework completed and average number of sessions attended, Homework – expected difference in SHAPS score intercepts for participants who completed 10% more homework overall, Total Sessions – expected difference in SHAPS score intercepts for each additional session attended in total, Time*Homework – difference in Time effect for each 10% more homework completion overall, Time*Totcd Sessions – difference in Time effect for each additional session attended in total

Interpretation of random effects. σ² – variance in residuals for the participant level regression models, τ₀₀ – variance in baseline SHAPS scores, τ₁₁ – variance in rate of SHAPS score change over time, τ₁₀/τ₀₁ – covariance between baseline SHAPS scores and rate of change in SHAPS Scores over time (participants with greater initial anhedonia severity tended to improve at a faster rate in treatment), ϕ – correlation between residuals one therapy session apart (decreases uniformly as the time gap increases), ICC – intraclass correlation coefficient representing the % of total variability in SHAPS scores attributable to differences between participants

N – the number of unique participants, Marginal R² – total variance explained by fixed effects, Conditional R² – total variance explained by combination of fixed and random effects

To probe the reliability of these null findings we constructed 95% confidence intervals using parametric bootstrapping with 1,000 iterations using the lmeresampler package in R. Observations were resampled both within and between participants. Simulation results indicated the range of the confidence interval spanned 0 for both Cl-Hw (β = −.121 – .012) and Pt-Hw (β = −.101 – .025). Of the resultant values, 94.6% of parameter estimates for Cl-Hw were negative, as compared to only 88.3% of estimates for Pt-Hw.

The non-significant effect sizes observed for the cross-level interactions in both models were negligible by the standardized metric Cohen’s f² (Pt-Hw: f²<0.001; Cl-Hw: f²=0.002). This metric is a ratio of the difference in variances explained between models with and without the effect of interest, to the unexplained variance by the full model (Aiken et al., 1991). We estimated statistical power to detect cross-level interaction effects using Monte Carlo simulations (n=1,000) with the simr package (Green & MacLeod, 2016). These simulations substituted the observed value of the interaction term in the model to correspond with a “small” magnitude effect size (f²=.02), while holding constant all other observed values in the model for sample sizes, fixed effect estimates, and variance components. Results showed that we had 98% power (95% CI: 92.96 – 99.76) to detect a small effect for Cl-Hw and 97% power (95% CI: 91.48 – 99.38) to detect a small effect for Pt-Hw. This high power is likely related to our large number of observations at level-1 (n=891) and the significant variability in slopes for the effect of time.

Within-Person (i.e., Session-to-Session) Homework Effects on SHAPS

Table 5 summarizes results of the multilevel models for within-person homework effects on ΔSHAPS (i.e., change in SHAPS between successive therapy sessions). Model diagnostics suggested assumptions were met.

Table 5.

Analysis of Within-Person Effects of Homework Completion on ΔSHAPS Scores

	Clinician Reported Homework			Participant Reported Homework
	Estimates (SE)	CI	P	Estimates (SE)	CI	P
Fixed Effects
Intercept	−0.73 (.16)	−1.05 – −0.41	<0.001	−0.81 (.12)	−1.04 – −0.58	<0.001
Homework (CWP)	−0.27 (.09)	−0.44 – −0.09	0.003	−0.19 (.06)	−0.31 – −0.06	0.003
Homework (PM)	−0.07 (.09)	−0.24 – 0.10	0.391	−0.07 (.06)	−0.18 – 0.04	0.236
Treatment [MBCT]	−0.19 (.24)	−0.66 – 0.28	0.429	-	-	-
Treatment*Homework (CWP)	0.26 (.13)	0.01 – 0.51	0.039	-	-	-
Treatment*Homework (PM)	−0.02 (.12)	−0.26 – 0.22	0.853
Random Effects
σ2	7.98			7.96
τ00	0.00			0.00
ICC	0.00			0.00
N	71			71
Observations	586			586
Marginal R2 / Conditional R2	0.019 / 0.019			0.017 / 0.017

Note. The final model with participant reported homework showed no significant interaction effects and therefore values are reported from the model without interactions.

Interpretation of fixed effects. Intercept – the average expected change in SHAPS scores between therapy sessions for a participant completing an average amount of homework. Homework (CWP; Centered Within Participant) – the expected change in SHAPS scores between therapy sessions when a participant completes an additional 10% more homework than average between sessions (i.e., the within-person effect of homework). Homework (PM; Participant Means)– the average expected change in SHAPS scores between therapy sessions for participants who completed 10% more homework overall than the average participant. For clinician reported homework, the variables above are interpreted as the effect in BATA, while the Treatment effect is the difference in intercepts between BATA and MBCT and the interactions reflect the differences in Homework effects between BATA and MBCT.

Interpretation of random effects. σ² – variance in residuals for the participant level regression models, τ00 – variance in expected change in SHAPS scores between therapy sessions, ICC – intraclass correlation coefficient representing the % of total variability in SHAPS scores attributable to differences between participants

N – the number of unique participants, Marginal R² – total variance explained by fixed effects, Conditional R² – total variance explained by combination of fixed and random effects

There was a significant effect of participant-mean centered Cl-Hw completion on ΔSHAPS (p = .027). For a given participant, completing relatively more homework than average between sessions was associated with relatively greater than average reductions in SHAPS scores. Expanding the model to include an interaction with treatment condition, participant-mean centered Cl-Hw completion remained significant in the BATA group (p = .003) such that completing one standard deviation more homework than average between sessions was associated with a .15 standard deviation greater reduction in SHAPS scores. The interaction term between participant-mean centered Cl-Hw completion and treatment was also significant (p = .039). By summing the regression coefficients for the effect in BATA (β = −.27) and the interaction effect (β = .26) we estimate the effect in MBCT to approximate 0, indicating participant-mean centered Cl-Hw completion was unrelated to ΔSHAPS in this group.

There was also a significant effect of participant-mean centered Pt-Hw completion on ΔSHAPS (p = .003). For a given participant, completing relatively more homework than average between sessions was associated with relatively greater than average reductions in SHAPS. In the expanded model, the interaction with treatment condition was not significant, indicating the effect of participant-mean centered Pt-Hw completion was similar and significant across both BATA and MBCT groups. Thus, we interpreted the effect size from the simpler model without the interaction. Completing one standard deviation more homework than average between sessions was associated with .11 standard deviation greater reduction in SHAPS scores.

To probe the reliability of these significant results, we once again constructed 95% confidence intervals using parametric bootstrapping (1,000 iterations, observations resampled within and between participants) using the lmeresampler package in R. Notably, none of the confidence intervals for the relevant parameters spanned 0 (Cl-Hw: β_BATA = −.43 – −.1, β_MBCT = .022 – .512; Pt-Hw: β = −.314 – −.066). In fact, for Pt-Hw, not a single replicate out of 1,000 produced a positive parameter estimate, suggesting a robust within-person effect of homework on ΔSHAPS in our sample.

In summary, greater than average Cl-Hw and Pt-Hw completion between sessions were associated with greater than average reductions in SHAPS scores between sessions. For Cl-Hw this effect was only evident in the BATA group, while the effect of Pt-Hw was evident across the entire sample. These results are depicted in Figure 3.

Figure 3.

Homework completion effects on change in anhedonia severity between sessions (i.e., ΔSHAPS) disaggregated within & between-person. More negative ΔSHAPS values represent greater reductions in symptoms. Thinner, colored lines represent the estimated effects of homework unique to each participant (i.e., within-person effects). Thicker, black lines represent the estimated effects of mean total homework across participants (i.e., between-person effects). For a detailed description of the depicted results see Table 5. Left: For participant-reported homework, on occasions when individuals completed relatively more homework, they showed relatively greater reductions in anhedonia. Across participants, the between-person effect of mean total homework was not significant, indicating individuals who did more homework overall did not have greater overall reductions in anhedonia between sessions. Right: For clinician-reported homework, on occasions when individuals completed relatively more homework, they showed relatively greater reductions in anhedonia only within the BATA condition. Once again, the mean total effect of homework was not significant for either treatment condition.

Change in Homework Completion Over Time

Models for Cl-Hw and Pt-Hw showed a similar pattern of results. LRTs favored random intercepts and random slopes, zero slope-intercept covariance, and quadratic fixed effects of time. Model diagnostics indicated unequal level-1 residual variance across participants with respect to both dependent variables. To remedy the impacts of heteroscedasticity, we used the R package clubSandwich v0.5.6 (Pustejovsky, 2022) to implement a bias-reduced linearization correction for the standard errors and a Satterthwaite degrees of freedom adjustment to conduct hypothesis testing of the fixed effects (Pustejovsky & Tipton, 2018). The final unconditional growth curves model results for Cl-Hw and Pt-Hw completion are reported in Table 6. Overall, homework completion rates tended to slightly decrease across early sessions of treatment and then slightly increased beginning around session seven (see Figure 4).

Table 6.

Summary of Unconditional Growth Curve Models for Homework Completion

	Clinician-Reported Homework			Participant-Reported Homework
	Estimates (SE)	CI	P	Estimates (SE)	CI	P
Fixed Effects
Intercept	8.55 (.33)	7.89 – 9.22	<0.001	8.70 (.28)	8.13 – 9.26	<0.001
Time	−0.40 (.12)	−0.64 – −0.16	0.001	−0.32 (.11)	−0.54 – −0.11	0.003
Time2	0.03 (.01)	0.01 – 0.05	0.006	0.02 (.01)	0.00 – 0.04	0.025
Random Effects
σ2	3.47			3.59
τ00	3.22			2.65
τ11	0.03			0.03
ICC	.49			.43
N	71			71
Observations	612			612
Marginal R2 / Conditional R2	0.019 / 0.495			0.019 / 0.438

Note that due to the scaling of the homework variables one unit represents 10% homework completion in each week. Standard errors were corrected using bias-reduced linearization to account for variability in level 1 residuals among participants.

Interpretation of fixed effects. Intercept – expected value of homework completion at Time=0 which is not interpretable in this context because it would imply homework was assigned prior to the initial session, Time – slope of the tangent line of the curve at Time=0 indicating decrease in proportion of homework completion across initial sessions, Time² – change in the slope of the tangent line per session of therapy attended indicating decreases in homework completion are attenuated over time resulting in a U-shaped curve of homework completion

Interpretation of random effects. σ² – variance in residuals for the participant level regression models, τ₀₀ – variance in baseline homework completion, τ₁₁ – variance in initial rate of change over time, ICC – intraclass correlation coefficient representing the % of total variability in homework completion attributable to differences between participants

N – the number of unique participants, Marginal R² – total variance explained by fixed effects, Conditional R² – total variance explained by combination of fixed and random effects

Figure 4.

Changes in homework completion rates over time according to clinician-reported and participant-reported homework. For a detailed summary of the results see Table 6.

Discussion

Cognitive behavioral therapies operate under the framework that long-term psychological benefits are likelier when patients apply the skills and insights from therapy sessions in their daily life. Between-session homework is often assigned to facilitate the acquisition of these skills, for example, maintaining a daily thought record to enhance awareness of automatic thoughts. Research generally supports the notion that homework assignment and adherence is beneficial with respect to therapy outcomes (Kazantzis et al., 2016), although the effects of homework may not be as large or as consistent as theory would suggest (Mausbach et al., 2010). A notable limitation of prior research in this topic has been a limited attention to within-person processes. In other words, do changes in therapy outcomes track with homework assignment/adherence within an individual? We sought to address this gap in the literature by evaluating mean total homework effects as well as time-varying (i.e., session-to-session) homework effects on cognitive behavioral treatment outcomes.

We examined the association of homework completion and symptom severity in a transdiagnostic anhedonic adult sample receiving either BATA or MBCT. Despite differences in the purported psychological mechanisms of these treatments for anhedonia (i.e., BATA targets engaging in pleasurable activities while MBCT targets decentering and nonjudgmental acceptance), both interventions strongly encourage homework as part of their theoretical model. The effects of homework on symptom severity were examined separately between-person and within-person, and compared across clinician and participant report. Symptomatic improvement was measured by the SHAPS, a self-report instrument commonly used to assess anhedonia, though it is more accurately described as a measure of consummatory reward sensitivity. While we found no evidence that participants who completed a greater proportion of their homework improved more rapidly (i.e., a between-person effect), we found significantly greater reductions in SHAPS scores between therapy sessions in which participants completed more homework (i.e., a within-person effect). This result was evident across the sample for Pt-Hw completion and specific to BATA for Cl-Hw completion, underscoring the utility of tracking both perspectives in clinical trials.

Treatment Engagement and Outcomes

Outcomes in BATA and MBCT were similar across all measures of treatment engagement including attrition rates, the number of sessions attended, the proportions of homework completed, and treatment acceptability ratings. The pooled attrition rate observed, 30%, was similar to other recent transdiagnostic anhedonia treatment studies. For example, 75% of randomized participants completed post-treatment neuroimaging in the FAST-MAS trial evaluating a kappa-opioid antagonist (Krystal et al., 2020), and only 51% of randomized participants completed post-treatment assessment in a psychotherapy trial evaluating Positive vs Negative Affect Therapy (Craske et al., 2019). Moreover, a meta-analysis of randomized controlled trials for cognitive-behavioral therapies estimated an overall attrition rate of 36.4% during treatment for depression (Fernandez et al., 2015). When comparing participants who completed treatment and those who attritted, we found no significant differences in either mean Cl-Hw or Pt-Hw completion for the sessions attended. In fact, non-completers had nominally greater rates of both metrics indicating participants who dropped out could not be identified by early treatment non-compliance.

As reported in Cernasov et al. (2021), we found SHAPS scores were significantly and comparably reduced across BATA and MBCT. We used an alternative metric of time compared to our earlier report (i.e., sessions attended instead of weeks from the initial session) to evaluate piecewise models of change over time. Participants varied significantly in baseline anhedonia severity and in rate of change over time. Greater baseline severity was also associated with more rapid improvement. The correlation between SHAPS observations was greatest at adjacent observations, decreasing uniformly over time. Meanwhile, the total number of sessions attended, as well as demographic factors of age, sex, and income did not predict the rate of improvement with treatment.

Between-Person Homework Effects on SHAPS

To calculate the between-person effect of homework on symptoms, we tested whether mean total homework completion moderated the slope of SHAPS change over time in a multilevel growth curve model. Results showed neither models with Cl-Hw nor Pt-Hw reached significance. In one of the few other analyses disaggregating between-person and within-person homework effects on symptoms, Conklin and Strunk (2015) also reported nonsignificant between-person effects among a smaller sample of adults undergoing cognitive therapy for depression.

We considered the possibility that nonsignificant between-person effects could be driven by a small number of participants who completed their homework assignments at early sessions but quickly dropped out of treatment because of perceived lack of benefit. However, including the total number of sessions attended as a covariate and cross-level interaction in our models did not alter our findings. Moreover, we conducted post-hoc analyses using only the subset of participants who completed treatment. Once again, we found no significant interaction effects between time and homework completion indicating that a lack of between-person homework effects could not be explained by the number of sessions participants attended.

Within-Person Homework Effects on SHAPS

To calculate the within-person effect of homework on symptoms, we evaluated the significance of time-varying homework completion on ΔSHAPS (i.e., session-to-session change) in a multilevel model. Results showed that completing a greater-than-average proportion of homework between sessions was accompanied by greater-than-average reductions in anhedonia during that window of time. Stated otherwise, on occasions that participants completed more homework, a greater mood benefit was evident within individuals. This effect was observed across both treatments with respect to Pt-Hw, but specific to BATA for Cl-Hw completion. It is unclear what may drive differences between Cl-Hw and Pt-Hw effects in the MBCT condition. It may be that in MBCT, a participant’s estimate of practice engagement is a more sensitive predictor of clinical change than a listing of practices completed (as seen by the clinician). Relatedly, participants may have been more sensitive to the degree to which they brought mindful attention to everyday activities outside of the pre-specified informal practices and reflected that sense in their homework ratings.

Our significant within-person homework effects on symptoms parallel and extend findings from two other reports examining session-to-session changes. While Conklin and Strunk (2015) reported greater homework engagement was associated with greater reductions in depression, their analysis was limited to the first four sessions of a cognitive therapy protocol, purportedly because early treatment is associated with the most rapid recovery. In our sample, we found the rate of improvement in anhedonia was steady over time (i.e., piecewise growth curve models were nonsignificant) and time-varying homework completion predicted improvements across all treatment sessions. Additionally, Haller and Watzke (2021) reported time-varying homework engagement was associated with lesser depression in a telephone-based CBT study, however, their analysis did not separate variables for homework centered within-person and person-mean homework which would have disaggregated within-person and between-person effects.

Limitations

The present analyses are limited by a modest number of participants due to the temporary suspension of research activities during the SARS-CoV-2 pandemic. That said, given the frequency of data collection in the study design, we benefited from a large total number of observations. Simulations found that assuming all other components of our multilevel model were accurate, we had excellent power to detect even small magnitude cross-level interaction effects for the between-person effects of homework.

Another limitation of the present analyses is that all homework completion was treated equally despite the intensity, frequency, and duration of the goals within BATA being unique to each participant. For example, the homework assignment for one individual may have included going to the gym three times and cooking two meals during the week, while the assignment for another participant would be going to the gym twice and cooking one meal. While MBCT homework is consistent across participants, standardizing the homework assignments within BATA would be antithetical to the treatment philosophy given the focus on values-congruent behaviors which are personally unique. Clinicians in the BATA condition also scaled goals according to participants’ needs and abilities and modified the next week’s goals based on what was completed in the previous week (e.g., if the goal was to go the gym three times and the participant only went once, the clinician might scale back the goal in the next week to only go twice.) By comparison, all MBCT assignments were standardized in intensity and duration across participants. The focus on homework completion estimated broadly rather than on specific assignments obscures the possibility that some types of homework may be particularly important at different stages of therapy. Overall, methodological issues quantifying homework remains a challenge, particularly when comparing effects across types of therapy, as one intervention may emphasize duration whereas another may emphasize frequency or type.

Although we consider the explicit evaluation of within-person processes an important contribution of this study, we also recognize that an ABAB (i.e., reversal) design would be a superior approach to evaluate causal effects of therapy homework on outcomes. We cannot definitively exclude the possibilities that external factors such as life stressors were responsible for the covariance observed between homework completion and symptomatic improvement within given windows, or that fluctuating anhedonia levels determined weekly homework engagement. The reverse causation hypothesis is particularly salient given that within the BATA condition, the therapist’s decision about what homework to assign would be influenced by the participant’s functional status. That said, we evaluated changes in homework completion over time with the idea that if mood determined treatment compliance, we would expect parallel increases in homework completion rates as participants became less anhedonic. On the contrary, we found that while participants showed linear improvements in SHAPS scores, their homework completion rates decreased across the initial therapy sessions, before subsequently increasing. Overall, a bidirectional relation between anhedonia and homework is still plausible and should be considered when interpreting our findings.

Furthermore, our analyses do not address when and why participants were more likely to adhere to their homework assignments. Time-invariant covariates, such as perfectionism (Kobori et al., 2020) and executive functioning ability (Mohlman, 2013), or time-varying covariates, such as the strength of the therapeutic alliance (Zelencich et al., 2020), may account for these differences. Unfortunately, we did not collect the data necessary to test these hypotheses. Moderators and mediators of homework compliance remains an interesting avenue of research to explore.

Lastly, the assessment of anhedonia symptom severity in the present analyses was limited to the SHAPS which does not measure anticipatory reward functioning / motivational state. While other clinical self-report measures were included in the trial (assessing depression, anxiety, etc.), SHAPS was the only instrument used to define inclusion criteria and administered at each therapy session. Thus, time-varying, within-person effects of homework completion on symptoms could only be examined at a granular level with respect to the SHAPS. Treatment effects on other clinical outcomes will be reported in future manuscripts.

Summary

This study adds to the body of evidence supporting a beneficial role of homework in cognitive behavioral treatments (Kazantzis et al., 2010; Kazantzis et al., 2016; Mausbach et al., 2010). To our knowledge, this is the first study to evaluate therapy homework effects with respect to reward hyposensitivity, a transdiagnostic symptom of psychopathology, and one of the few explicitly examining within-person dynamics of therapy homework. We found that participants showed greater improvements in consummatory reward sensitivity between sessions in which they reported completing relatively more homework. This effect was evident across BATA and MBCT which differ in purported psychological mechanisms but share a strong emphasis on practicing specific behaviors outside of therapy (i.e., homework). We also found that participants who received BATA showed greater improvements in consummatory reward sensitivity between sessions in which clinicians assessed there was relatively greater homework completed. The disparate findings between participant and clinician reports with respect to the effects of MBCT underscore the utility of evaluating both sources of information in research addressing therapy homework effects. This study also highlights the utility of examining the influence of various potential modifiers on treatment outcomes in clinical trials using within-session analyses as reported here, providing that modifiers and treatment outcomes are assessed repeatedly during the trial.

Cognitive-behavioral theories posit that psychological changes occurs within a given individual following the application of new behaviors in daily life. These intraindividual processes can only be studied through repeated measures data (Curran & Bauer, 2011), as in the current analyses, which allow for proper disaggregation of between-person and within-person effects. Future research should analyze repeated measures of homework completion rather than exclusively aggregate metrics like total completion. Causal effects of homework completion on anhedonia (and psychopathology more generally) should be explored through ABAB treatment protocols in which symptomatic changes can be compared between sessions where homework was or was not assigned, within the same person. Notwithstanding present limitations, our findings show that change in homework completion between sessions is related to change in symptoms of anhedonia between sessions for patients receiving Behavioral Activation for Anhedonia and Mindfulness-Based Cognitive Therapy.

Highlights.

• Participants suffering from clinically significant anhedonia reported greater improvements in symptoms (i.e., SHAPS scores) between cognitive-behavioral treatment sessions in which they completed relatively more homework than usual.

• Relations between homework completion and consummatory reward sensitivity (i.e., SHAPS scores) were only evident when comparing session-to-session changes within participants and not when comparing total homework completed across participants.

• Parsing within-person and between-person effects in multilevel models of repeated measures is useful for investigating theoretical models of therapeutic change.