All together 152 participants took part in the study, which was conducted anonymously online via the study website. Data came from an ongoing project assessing emotion dynamics and regulation in the context of suicide risk factors and protective factors in people with a diagnosis of AUD compared to HC.

The AUD sample consisted of n = 86 subjects aged between 24 and 67 years (M_age = 39.15; SD_age = 8.82), among whom n_m = 54 were men (62.8%) and n_w = 32 were women (37.2%). The majority of AUD respondents (46.5%) had a secondary education. Completed primary education was declared by 1.2% of people. Vocational school was completed by 8.1% of the respondents, while tertiary education was held by 38.4% of the respondents. Most people (67.4%) did not declare somatic diseases. The mean duration of abstinence in years among AUD subjects was M = 2.17, SD = 4.09. The AUD group was recruited from among those maintaining abstinence in inpatient wards and outpatient treatment addiction clinics. Inpatient treatment included an 8-week abstinence-based programme and intensive individual and group therapy. In contrast, outpatient treatment included patients in both partial and full remission. The diagnosis of AUD was based on the International Classification of Diseases and Health Problems (61) psychiatric diagnosis made on admission to the treatment unit. Due to the high overrepresentation of men in addiction treatment programmes, the AUD group in this study was predominantly male (62.8%). Patients were ineligible to participate in a treatment programme if they had a clinically significant cognitive deficit or met any of the following criteria: a history of psychosis, a co-occurring psychiatric disorder requiring current psychiatric treatment (e.g. history of psychosis, bipolar affective disorder) or the presence of acute alcohol withdrawal symptoms.

The HC group consisted of n = 66 people aged 18 to 57 years (M_age = 29.35; SD_age = 9.46), of whom n_m = 37 were men (56.1%) and n_k = 29 were women (43.9%). Exclusion criteria for the HC group was the presence of an alcohol related problem and other exclusion criteria were similar to those for the AUD group. The majority of subjects in the HC group (56.1%) had a tertiary education. Completed primary education was declared by 3.0% of subjects. Secondary school was completed by 22.7% of the respondents, while those currently studying accounted for 13.6% of the respondents.

The study was approved by the Ethics Committee at Cardinal Stefan Wyszynski University in Warsaw (Evidence: 6/2023).

Sociodemographic characteristics (e.g. age, biological sex, education) were obtained by means of a self-report questionnaire.

Audit (62). The tool is a screening tool to determine the extent to which a person surveyed consumes alcohol. It contains ten questions that address three areas of alcohol use: risky drinking, harmful drinking and alcohol dependence. Each question is assigned a set of answers to choose from. Each answer is assigned a score (from 1 to 4). Reliability for the total score Cronbach’s alpha = 0.972.

The Hospital Anxiety Depression Scale (HADS) (63), Polish validation (64). A screening tool used to assess the severity of medication and depression symptoms. It is not used for clinical diagnosis. It contains 14 items, of which 7 form the anxiety subscale (HADS-A) and 7 form the depression subscale. For the depression scale, Cronbach’s alpha reliability = 0.752.

Cognitive Emotion Regulation Questionnaire (CERQ) (65), Polish validation (66):. A 36-item questionnaire designed to assess individual differences in cognitive emotion regulation in response to stressful, threatening or traumatic life events. The tool assesses nine 4-item dimensions: blaming self, blaming others, acceptance, refocusing on planning, positive refocusing, rumination, positive refocusing, positive refocusing, perspective taking and catastrophising. Responses are given on a 5-point Likert scale from 1 ‘almost never’ to ‘almost always’. Therefore, subscale scores can range from 4 to 20, with higher subscale scores indicating greater frequency of use of a particular cognitive strategy. Cronbach’s alpha reliability for the ruminations scale = 0.763.

Perth Emotional Reactivity Scale (PERS) (67) Polish version (30): is a 30-item self-report questionnaire used to assess traits (dimensions) of emotional reactivity. PERS examines emotional reactivity as defined by Becerra (67); that is, it measures the typical ease/speed of activation, intensity and duration of emotional reactions, and allows the assessment of emotional reactivity in relation to positive (e.g. joy) and negative (e.g. sadness) emotions separately. Scores for the six subscales and the two composite subscales can be obtained by summing the respondent’s responses (i.e. the numbers to be circled on the 5-point response scale) for the respective items. The higher the score for the individual subscales and the two composite subscales, the higher the level of the dimensions of emotional reactivity; in other words, this means that the emotion in question can be more easily/quickly activated, more intense and lasts longer. Cronbach’s alpha reliability for PERS General Emotional Reactivity scale = 0.928.

Suicidal Behaviour Questionnaire Revised (SBQR) (68) pol. version (69). The questionnaire consists of four test items. The first three questions concern retrospective assessment: (1) “Have you ever thought about taking your own life or made an attempt to do so?”; (2) “How often have you had thoughts about taking your own life in the past year?”; (3) “Have you ever told someone about your intention to commit suicide or the likelihood that you might commit suicide”. The last, fourth question, concerns prospective assessment: (4) “How likely is it that one day you will attempt/attempt suicide?”. Responses are scored on a scale of 1 to 3 (questions 1-3) and 0 to 6 (question 4). Cronbach’s alpha reliability = 0.864.

In the first step of the analysis, a series of plots were generated to assess the relationships between the dependent variable, the mediator, and other variables. Both linear and quadratic functions were fitted to the observed data to evaluate their adequacy. This procedure was conducted separately for the alcoholic and healthy groups to assess the consistency of the relationships within each group. The series of plots and R-squared coefficients for both linear and quadratic functions, included in Supplementary Material A , demonstrated that linear relationships between variables were comparable to, or slightly weaker than, those for the quadratic function. However, the better fit of the quadratic function may have resulted from the small sample size and the presence of outliers, which could have significantly influenced the fit of both models. The visualised relationships confirmed the similarity in the fit of linear and quadratic functions; therefore, linear analyses were chosen for further investigation.

In the second step of the analysis, outliers were identified and smoothed. This smoothing procedure was performed using the statistical software SZTOS (70), designed to detect outliers in linear regression models testing moderation effects. The moderation procedure was applied because the slope-invariance procedure is a generalisation of simple interaction analysis.

The first step of the smoothing algorithm involved the random selection of the dependent variable, independent variable, and moderating variable, followed by the construction of a regression model. The randomness in selecting these variables aimed to minimise bias in the sequence of data imputation. Based on the specified regression model, the following influence measures were computed for each observation: studentised residuals, leverage values, and Cook’s distance (71). Observations with elevated values for these indicators were flagged, and missing values were inserted into the dependent variable columns of the identified rows. These missing values were then imputed using the random forests technique, which leveraged all available dataset information to predict the missing values. Additionally, if there were more than two independent, dependent, or moderating variables, the smoothed data from the first iteration were carried forward to subsequent smoothing analyses.

As mentioned earlier, missing data imputation via the random forests method was carried out using the missForest package from the CRAN repository (72) in R. This non-parametric method applies the random forests algorithm (73) to optimise the prediction of missing values. The random forests method involves randomly selecting observations (with replacement) to generate multiple decision trees containing different variables and observations from the dataset. When aggregated, these trees enable either regression-based prediction (for quantitative variables) or classification-based voting (for qualitative variables). The missing data imputation process using the random forests method consists of three iterative steps:

The entire dataset was randomly used in the missing value prediction process, and these steps were repeated until the prediction or classification error was minimised.

The results of the analysis are presented in Supplementary Material B , which includes a series of figures and tables. Figure a displays a plot of influential observations, Figure b presents the moderated relationships between variables in the model recalculated using raw data, and Figure c shows the moderated relationships recalculated using smoothed data predicted via the random forests technique. The analysis was performed on the full dataset, which consisted of N = 152 observations.

Based on both the raw and smoothed data, two structural equation models were estimated using the lavaan package (74). The estimator used was MLR (maximum likelihood estimation with robust Huber-White standard errors), which is recommended for small samples with non-normally distributed data (75). Model diagnostics for both datasets were evaluated using general Cook’s Distance in the influence.SEM package (76). The deltaChi method was omitted because the model demonstrated an almost ideal fit. These diagnostic procedures iteratively removed each observation (one at a time) and refitted the SEM model to the reduced dataset (N-1 cases). The recalculated general Cook’s Distance indicated that preprocessing the data resulted in fewer extreme observations. Even if an observation remained an outlier in the smoothed dataset, its influence was weaker than in the raw data. The results of the Cook’s Distance analysis are presented in Figures 1 and 2 .

To determine whether the groups were of equal size, a chi-square test for one variable was conducted (Pearson, 1900). The analysis revealed that the groups were statistically equal in size, χ² (1) = 2.63; p = 0.105. The homogeneity of variance in both groups was assessed using Levene’s test (Levene, 1960). If the assumption of homogeneity of variance was met, the result of Student’s t-test was reported; otherwise, Welch’s t-test was used (Welch, 1951). Effect sizes were assessed using Cohen’s d measure (Cohen, 2013). Analyses using Spearman’s correlation were performed to examine the relationship between the variables under study. A 95% confidence interval (CI) was used in both analyses.

Due to differences in the level of variables analysed across groups, and based on previous literature on the relationships examined, further analyses included the controlling co-variables: age (77), biological sex (47), current severity of alcohol use (78), severity of depressive symptoms (79, 80), and education (81).

First, intergroup differences were examined for the primary variables under investigation, namely rumination, emotional reactivity, and suicide risk. Subsequently, correlations between these variables were analysed both within the entire sample and across individual groups. Additionally, correlations between rumination, emotional reactivity, and suicide risk were assessed to evaluate the predictive validity of the structural model. The analyses also included depression severity, alcohol consumption, age, gender, and education as control variables. Table 1 below presents the descriptive statistics for the analysed variables.

Individuals diagnosed with AUD had significantly higher mean scores across all the variables listed below compared to the control group, except for rumination. Specifically, the AUD sample attained a mean SBQR score of 7.81 ± 2.74. The authors of the scale proposed a cutoff score of 8 points for individuals in clinical samples (68). Detailed results are presented in Table 2 .

Correlations between rumination, emotional reactivity, suicide risk, and control variables were computed separately for individuals with AUD and HC to identify significant associations and preliminarily confirm the validity of the proposed model. Table 3 presents the correlation coefficients for all variables in the entire sample, while Tables 4 and 5 display the correlation coefficients within each group.

In this study, the relationship between rumination (CERQ Rumination) and suicide risk (SBQR Score) was examined, with emotional reactivity (PERS General Emotional Reactivity) included as a mediator ( Figure 3 presents conceptual model). The analysis was conducted using structural equation modelling (SEM) in R (lavaan package), and the estimation was performed using the MLR method (maximum likelihood estimation with robust standard errors), which provides robust estimates and adjusted standard errors.

The model fit analysis demonstrated a very good alignment between the model and the empirical data. The chi-square statistic for one degree of freedom was not statistically significant (χ²(1) = 0.01; p > 0.05), and other fit indices also indicated a high level of model-data fit (CFI = 1.00; TLI = 1.18; NFI = 1.00; IFI = 1.01; RMSEA = 0.00, 90% CI [0.00–0.07], PCLOSE = 0.942; SRMR = 0.00; GFI = 1.00; AGFI = 1.00). These results suggest that the model adequately reflects the structural relationships among the examined constructs. A detailed overview of all structural model parameter estimates is presented in Table 6 .

In the path analysis, the examined model accounted for the effect of rumination on suicide risk through a single mediator - emotional reactivity. The model also controlled for the effects of age, sex, education, depression severity (HADS Depression), and alcohol use severity (AUDIT Score). Additionally, correlations between rumination and control variables were estimated, allowing for the consideration of their potential influence on the analysed relationships (see Table 1 in Supplementary Material C ). A significant positive association was found between rumination and emotional reactivity (β = 0.24; Z = 2.91; p < 0.01), indicating that higher levels of rumination were significantly associated with heightened emotional reactivity. Furthermore, elevated emotional reactivity significantly increased suicide risk (β = 0.25; Z = 3.33; p < 0.001). However, the direct effect of rumination on suicide risk was not statistically significant (β = 0.07; Z = 1.05; p > 0.05), suggesting that this relationship primarily occurs via emotional reactivity.

The mediation effects in the full sample revealed a statistically significant indirect effect (b = 0.060; s.e. = 0.030; Z = 2.003; p = 0.045). This finding suggests that rumination contributes to increased suicide risk through heightened emotional reactivity. Furthermore, the lack of a significant direct effect of rumination on suicide risk strengthens the hypothesis of full (or predominant) mediation. The R² values indicated that the model explained 45% of the variance in suicide risk (R² = 0.45) and 21% of the variance in emotional reactivity (R² = 0.21), highlighting the model’s substantial predictive capability.

Further analysis of path coefficient invariance revealed significant differences in model fit between models assuming equal versus varying regression slopes across groups (χ²(13) = 36.82; p < 0.001). The lower χ² value suggests that the model accounting for group differences in specific paths provides a better fit to the data.

A multi-group analysis was conducted to examine the potential moderate mediation effect by group status (AUD vs. HC). Table 7 presents the comparison of model parameter estimates between the AUD and HC groups. The overall mediation effect did not significantly differ between groups (Z = 1.05; p = 0.294). However, separate estimates of the indirect effect within each group indicated that in the HC group, the indirect effect (b = 0.048; s.e. = 0.032; Z = 1.493; p = 0.135) and in the AUD group (b = 0.010; s.e. = 0.017; Z = 0.585; p = 0.558) did not reach statistical significance.

These findings have important clinical implications. Therapeutic interventions and pharmacological treatment for people with AUD should specifically focus on reducing the severity of ruminative thoughts. Ruminations-focused interventions, such as metacognitive therapy and ruminations-focused cognitive behavioural therapy (89), have shown significant efficacy in the treatment of depression (90). In addition, there is some evidence to suggest that mindfulness-based cognitive therapy, which also places a strong emphasis on eliminating ruminative processes, is effective in therapy of patients with suicidal thoughts (91). More recently, forms of brief online interventions targeting ruminations have also emerged and have been found to be acceptable and effective in reducing symptoms of ruminations, worry anxiety and depression (92). For emotional reactivity, mindfulness meditation is a particularly promising intervention, as it has been found to simultaneously reduce physiological overreactivity and, in addition, reduce the severity of ruminations (93). Therefore, empirical studies on the effectiveness of such interventions in the AUD population are therefore scientifically proven and necessary in prevention and therapy of suicide risk. The aforementioned metacognitive therapy and cognitive-behavioural therapy focused on ruminations may be implemented into therapeutic programme for people with AUD representing a valuable form in reducing suicide risk. Certainly, these promising results require further exploration considering very limited research done in this field in AUD group. On the other hand, there is also research conducted on pharmacological interventions aimed at reducing the severity of ruminations. For example, combining amisulpride with antidepressant therapy in patients with treatment-resistant depression led to marked improvements in psychopathology in most patients, including those with severe ruminations (94). Aripiprazole monotherapy appears effective in reducing ruminations in cases of non-psychotic depression (95). Given that patients exhibiting increased ruminations are beneficiaries of treatment with antipsychotics (96), it is reasonable to focus future research on evaluating the efficacy of these therapies also in the AUD population who use this maladaptive emotion regulation strategy excessively.