Currently, there are several effective interventions to increase well-being, such as Cognitive-Behavioral Therapy (CBT), which focuses on reducing deficits, and Virtue-Based Interventions (VBI), which focus on encouraging actions that promote well-being. However, there is little research on the mechanisms by which these interventions work. The aim of this study is to analyze the specific and common mechanisms of change of two active treatments (CBT and VBI) for increasing well-being in patients with chronic diseases. This population will be used because of their low level of well-being compared to the general population. A randomized controlled trial will be conducted, with two experimental conditions (VBI and CBT) and four assessment points (pre- and post-intervention, and 6- and 12-month follow-up). We will primarily assess well-being, anxiety, depression, mechanisms specific to each intervention (e.g., dysfunctional thoughts in CBT, use of strengths in VBI), and mechanisms common to psychological interventions (e.g., trust in treatment). First, participants will be screened for eligibility according to the inclusion/exclusion criteria. Second, eligible participants will be randomized to a CBT or VBI condition and will complete baseline measures. Third, participants will receive the core intervention for 9 weeks. Finally, participants will complete measures after treatment and 6 and 12 months later. During treatment, they will answer some questions daily to assess well-being and well-being competencies using Ecological Momentary Assessment (EMA). The hypotheses are: (1) both participants in the CBT and VBI conditions will increase their levels of well-being and the changes will be mediated by the specific mechanisms of each intervention, (2) some of the changes in well-being that may exist in both interventions will be explained by the common factors, (3) all of these changes will be moderated by baseline levels of anxiety, depression and well-being, and (4) both participants in the CBT and VBI conditions will reduce levels of anxiety and depression. The study will be conducted following the principles stated in the Declaration of Helsinki.

Analysis plan:

A mixed approach between quantitative and qualitative methods was applied. Regarding the quantitative methods, differences between groups in demographics and other clinical variables will be tested with T-tests for continuous variables and χ2 tests for categorical variables. Assumptions will be tested and, if broken, non-parametric and robust alternatives will be applied. Relations between continuous variables will be screened and tested for differences between groups. In addition, reliability of self-report variables will be assessed to ensure good psychometric properties.

To test the impact of VBI and CBT across time, a two-way mixed Analysis of Covariance (ANCOVAs) will be implemented (group as between-subjects variable, time as a within-subjects variable). Main and interaction effects will be estimated, along with post hoc tests with correction of type I errors (Bonferroni and Šidák) and estimated marginal means with 95% confidence intervals. Assumptions for ANCOVA will be tested and corrections will be implemented if broken. All contrasts will count with effect sizes and 95% confidence intervals. Dropout and other missing data patterns will be assessed. More concretely, proportion of missing data will be screened and compared across groups. If relevant or non-ignorable missingness is found, multiple imputation of missing data will be applied. More concretely, a multilevel strategy will be implemented. Predictors will be selected by design and by sharing a relevant amount of variance with each outcome. In addition, sensitivity analysis will be implemented to test robustness of imputation models. To estimate the impact of sample size, all analysis will count with a sensitivity analysis will be implemented at 90% power and 95% confidence using G\*Power 3.1.

To analyze potential mechanisms of change in each program, structural equation models (SEM) will be implemented. Difference scores between times (post - pre intervention and follow ups - pre intervention) will be computed and implemented as outcomes. Following our framework, a series of proposals of mechanisms will be developed as theoretical models for the SEM. Given most or all variables will be continuous, Maximum Likelihood Robust will be used as the estimation method along with robust standard errors of estimates (this enables unbiasing estimates from deviations from normality). Missing data will be handled with the Full-Information Maximum Likelihood method. Fit will be assessed with indices and thresholds recommended by literature. Due to mediations present in our framework, indirect effects will be estimated with bootstrap techniques. In addition, a correction for multiple testing will be applied due to the proposal of several theoretical models. A power analysis revealed with 90% power, 95% confidence, and 210 degrees of freedom (20 variables), a minimum sample size of n = 100 able to differentiate between a population RMSEA = 0.5 with an alternative RMSEA = 0.08. However, sample size will be increased if available.

To analyze the EMA scores, multilevel longitudinal models will be implemented. More concretely, the specific time of assessment nested in the overall times (pre, post, and follow-ups), nested in individuals, and then nested in groups (VBI or CBT). Available models will be screened (e.g., cross-lagged growth modelling, GIMME models, dynamic SEM) and employed.

Descriptives, bivariate tests, and ANCOVAs will be estimated with JASP, while SEM and EMA analyses will be estimated with the R environment. Specific packages are lavaan, lme4 y EMAtools.

Regarding the qualitative methods, semi-structured interviews will be implemented with an inductive perspective to search for underlying categories to participants responses. Thematic analysis will be used as framework to locate and describe these categories. Two members of the team will develop the thematic analysis with the following phases: (1) reading and re-reading of open-ended responses and describe general ideas; (2) generation of first codes by extracting all relevant verbal information regarding research questions, assigning a brief description or code, and allocating them in a table; (3) organizing the codes in the search of themes; (4) review the proposed themes aiming for homogeneity and specificity of contents, and ensuring units of verbal meaning are adequately represented in the themes; (5) definition and description of themes.