Original study: participants

Data for this secondary analysis was from the RAINBOW clinical trial, which took place in Northern California between September 2014 and January 2017 [7]. The original study included adults with elevated depressive symptoms, defined as a Patient Health Questionnaire (PHQ9) score 10, and co-occurring obesity, defined as Body Mass Index (BMI) 30, or 27 for Asian participants. The original study obtained written informed consent from participants and was approved by the Institutional Review Board at Sutter Health, North California. The original trial protocol was published [18]. Data was anonymized before use in this secondary analysis, which began January 26, 2024.

Original study: intervention

Participants were randomly assigned to the treatment group (n = 204) and received an integrated intervention including multiple sessions of Problem-Solving Therapy (PST) for depression and Group Lifestyle Balance (GLB) for weight loss for one year. PST for depression consisted of 15 one-on-one live coaching sessions with a trained professional, through an adapted version of the Program to Encourage Active, Rewarding Lives for Seniors [19]. The first 9 PST sessions were delivered in a 6-month intensive treatment phase, which were face-to-face 60-minute sessions at first weekly (4), then biweekly (2), then monthly (3). The remaining 6 sessions in the maintenance phase were monthly 15- to 30-minute telephone calls with brief mood and weight sessions. The GLB intervention was an adapted version of the Diabetes Prevention Program and included self-study videos at home [20]. The intensive treatment phase included 11 home-viewed GLB videos. No videos were watched during the maintenance phase.

More information on the integrated intervention is available in the original study [7] and accompanying articles [19,20]. The RAINBOW trial demonstrated significantly greater improvements in both depressive symptoms and weight loss in the treatment versus the usual care group at 12-month follow up [7].

Current study: data

Anonymized data from the RAINBOW treatment group participants were used for this post-hoc analysis. Three participants with fewer than two depression or weight measurements were removed. A sensitivity analysis was conducted removing individuals with two measurements or less, to determine whether the exclusion of subjects with fewer than three measurements meaningfully impacted the results. Data included repeated measures of depression symptoms and weight by self-report for trajectory classification, the baseline and 12-month depression symptoms and weight measures by trained research staff, and covariates as outlined below. The final analytic dataset for the trajectory modeling included one row for each unique participant-week with at least one observation for either depression or weight. For the 15 PST session weeks, depression symptoms and weight measurements were linked to the PST session number and anchored to the week they were expected to be performed. All other self-measured weight observations recorded their week number.

Current study: measures

Weight over time.

The longitudinal data included participants’ weekly self-monitored weight, measured in kilograms, for a maximum of 54 consecutive weeks. Each weekly weight measurement was transformed as a continuous percent change from baseline, with negative values indicating more “success” or greater weight loss, using the following formula:

Current study: statistical analysis

Descriptive statistics of mean, standard deviation (SD), frequencies, and proportions were calculated for the entire sample and all sub-groups. To compare differences in categorical demographic variables and comorbidities (e.g., sex, race, binge eating disorder), we performed Chi-Square or Fisher’s Exact tests (as appropriate based on expected cell frequencies). To compare differences in means of continuous, normally distributed demographic and clinical variables (e.g., age, blood pressure) across groups, we performed ANOVA tests. For all statistical tests, the identified trajectory group was treated as the independent variable of interest.

Group-Based Multi-Trajectory Modeling (GBMTM) was used to characterize latent groups among the treatment group participants. Group-Based Trajectory Modeling [32] is a maximum likelihood estimation technique that groups participants that follow similar trajectories over time. The multi-trajectory extension of this method allows for the identification of groups that follow similar trajectories for multiple outcomes (in our case, depression symptoms and weight) [32]. This approach is robust to missingness in one or both repeated measure variables, which is important in this analysis due to high missingness in the self-measured weight data. GBMTM can also account for inconsistent follow-up times. Both depression symptom scores and weight change were modeled as normally distributed, continuous variables. Though the PHQ-9 used to measure depression symptom scores is a discrete integer, our visual inspection of the distribution of the data supports the decision to model it as continuous for the purposes of these analyses. Further, the overall scale score has been commonly used as a continuous variable [25] and simulation studies have shown that when the number of discrete values is large (11 or more), the underlying distribution will approach normality [33,34]. The analysis was performed using the R multlcmm package [35] and R version 3.4.1 [36].

GBMTM models using one through five groups were assessed. Model selection was conducted using the Akaike Information Criterion (AIC) fit statistic and conceptual interpretation of the groups. In particular, the elbow test was applied to the AIC by creating a plot of the fit statistic values versus the number of trajectory groups in the model. Then, the “elbow” of the plot was identified, where increases in trajectory groups no longer corresponded to dramatic decreases in AIC. Participants were classified into the multi-trajectory group with the highest probability of group membership, and sensitivity analysis was performed by creating a subset of the data that only included individuals with group membership probability of at least 0.5 or 0.7. We investigated patterns of missingness for repeated measures and outcomes as additional sensitivity analysis.

To estimate the relationship between trajectory group membership and 12-month outcomes, two linear regression models were fitted to separately predict change in SCL20 and percent change in weight from baseline to 12 months. Models included one observation per participant, with the primary independent variable of interest being trajectory group membership, and controlled for baseline SCL20 or weight (respectively) and any demographic characteristics that were found to significantly differ between groups. Effect estimates from these linear regression models were calculated as beta coefficients with 95% confidence intervals (CIs).

To examine differences in clinically significant changes in outcomes across trajectory groups, two separate logistic regression models were fit. Models controlled for baseline SCL20 or weight (respectively) and the same demographic characteristics as the previous models. The binary outcomes of the two models were clinically significant change in SCL20 and weight from baseline to 12 months (as described in the “Secondary Outcomes” section above). Effect estimates from these logistic regression models were calculated as odds ratios (ORs) with 95% CIs.

Descriptive characteristics

Of the 204 participants in the treatment group, three participants were removed due to only having one measurement for PHQ9 and weight. This resulted in a final analytic sample of 201 participants. The mean age was 50.8 (SD = 12.2), 70.6% (n = 142) were female, and 72.6% (n = 146) of the sample was non-Hispanic White. The mean SCL20 score at baseline was 1.45 (SD = 0.53) and the mean weight was 104 kilograms (SD = 22.4). See Table 1 for further descriptive characteristics of participants.

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Table 1. Summary statistics of demographics and comorbidities across 3 identified groups.

https://doi.org/10.1371/journal.pone.0328715.t001

Multi-trajectory modeling

Based on the model fit statistics, two, three or four group models were examined as candidates for the final model because they had the lowest AIC values (S1 Fig, S1 Table). From these options, the three-group model was selected, as the two-group model missed granularity between groups and the four-group model created a small (n = 14) group that was a subset of one from the three-group model. S2 Table in the appendix shows the average assignment probability for each group. Sensitivity analyses excluding individuals with only two measurements (n = 7) yielded no meaningful differences in the identified trajectories.

From this model, three groups emerged (Fig 1, S2 Fig, S3 Fig). The first and largest group (n = 108) showed moderate depression symptom score reductions but almost no weight loss over the study period. The second group (n = 58) experienced substantial depression symptom score reductions and a moderate, steady weight loss. The third group (n = 35) experienced substantial depression symptom reductions – comparable to group 2 – and a substantial, steady weight loss. Based on these characteristics, the three groups were named as follows: Group 1 as “Moderate/Minimal” group, group 2 as “Substantial/Moderate” group, and group 3 as “Substantial/Substantial” group. For each group name, the first descriptor represents the change in depression symptom scores and the second descriptor represents the weight loss.

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Fig 1. Average trajectories of 3-group GBMTM.

PHQ and weight loss trajectories.

https://doi.org/10.1371/journal.pone.0328715.g001

Demographics across trajectory groups

The sociodemographic characteristics and comorbidities of the three groups were similar for all considered characteristics except for age. There was a statistically significant association between age and group membership (p = 0.024), with the Substantial/Substantial group having the oldest participants (mean: 54.3, SD: 12.9) and the Moderate/Minimal group having the youngest (mean: 49.2, SD: 12.6). Characteristics of all trajectory groups can be found in Table 1.

Relationship between trajectory groups and primary outcomes

All three groups saw an average reduction in depression symptomology from baseline to 12 months but differed in the magnitude of the change: the Moderate/Minimal group had a 0.08 reduction (SD = 0.81), the Substantial/Moderate group a 0.46 reduction (SD = 0.60), and the Substantial/Substantial group a 0.55 reduction (SD = 0.63; Table 2). In the multivariable model, trajectory group membership was found to be significantly related to change in depression symptomology, after controlling for baseline symptoms and age. Compared to the Moderate/Minimal group, the Substantial/Moderate group had an average additional 0.31 (95% CI: −0.54, −0.08) reduction in SCL20 at 12 months, and the Substantial/Substantial group had an average additional 0.47 (95% CI: −0.75, −0.19) reduction in SCL20 at 12 months.

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Table 2. Regression results for 12-month depression and weight changes.

https://doi.org/10.1371/journal.pone.0328715.t002

With regards to weight outcomes, only two of the three groups experienced an unadjusted weight reduction from baseline to 12 months; the Moderate/Minimal Group had an average 1.23-kilogram weight gain (SD = 5.00), the Substantial/Moderate Group had an average 3.53-kilogram weight loss (SD = 4.40), and the Substantial/Substantial group had an average 9.55-kilogram weight loss (SD = 4.70; Table 2). In the multivariable model, the Substantial/Moderate group had an average additional 4.64-kilogram decrease (CI: −6.25, −3.03) and the Substantial/Substantial group had an average additional 10.93-kilogram decrease (CI: −12.92, −8.95) compared to the Moderate/Minimal group.

Relationship between trajectory groups and clinically significant change

The proportion of participants achieving clinically significant change in depression symptoms (response or remission) ranged from 22% for the Moderate/Minimal group to 48% for the Substantial/Substantial group (Table 2). After controlling for covariates, only the Substantial/Substantial group, compared to the Moderate/Minimal group, was significantly associated with clinically significant change: the Substantial/Substantial group was 197% more likely (OR=2.97, CI: 1.23, 7.25) than the Moderate/Minimal group to achieve clinically significant SCL20 changes. The Substantial/Moderate group was more likely, but the results were not statistically significant (OR=1.55, CI: 0.71, 3.40).

For weight, only 6% of participants in the Moderate/Minimal group achieved clinically significant changes, compared to 33% in the Substantial/Moderate group and 87% in the Substantial/Substantial group (Table 2). After controlling for covariates, both the Substantial/Moderate group (OR=7.22, CI: 2.77, 21.37) and the Substantial/Substantial group (OR=94.56, CI: 27.30, 419.55) were significantly more likely to experience clinically significant weight loss at 12 months.

Sensitivity analyses

Sensitivity analyses that included only individuals with high probability of trajectory group membership (> 50%, > 70%) were conducted. Results of sensitivity analyses were consistent with those described above: group membership was associated with 12-month change in SCL20 and weight, the Substantial/Moderate group was more likely to achieve clinically significant weight loss, and the Substantial/Substantial group was more likely to achieve both clinically significant weight loss and clinically significant SCL20 reductions (S3 Table, S4 Table, S5 Table, S4 Fig, S5 Fig). Analysis of repeated measures missingness over time (S6 Fig, S6 Table), and demographics across participants with and without outcomes (S7 Table) are available in the supplement.

Limitations

There are several limitations to this analysis. First, the RAINBOW clinical trial was conducted in a single health system in Northern California; participants had high income and were mostly White and female, limiting generalizability to other geographic regions or demographic groups. In addition, we were limited to the information that the trial collected, so additional unmeasured confounders may exist. RAINBOW data collection concluded in 2017 (almost 8 years after the secondary analysis done in this study), so the analysis should be replicated in more recent clinical trials investigating both depression and obesity. PHQ9 score was modeled as a normally distributed, continuous variable, despite being a discrete integer and slightly skewed. We recognize that this may introduce some bias, particularly in the lowest range of the scale where the assumption of normality deviates most.

Finally, this study relied partially on self-report data which results in high missingness. GBMTM is robust to missingness; however, missing almost 50% of PHQ9 scores and almost 80% of weight measurements near the end of the trial may decrease the confidence in our group assignments. While this is an important limitation, the GBMTM probabilities for the three-group model are still relatively high for all groups (ranging from 72.3% to 92.7%), indicating that most individuals with missing data were still able to be assigned to trajectories with high confidence. The group with highest missingness was the group with the smallest weight changes that was used as the reference group for analyses examining 12-month outcomes. It is possible that the missingness in this group’s 12-month outcomes may have skewed the study’s findings in the direction of the null if individuals with missingness tended to have worse outcomes, which would make the true effect estimates larger than those observed herein. Because of this missingness and the wide confidence intervals on the odds ratios, results should be interpreted primarily for their directionality, and potential magnitude of increase in odds of clinically significant changes in weight or depression should be interpreted with caution.