This study employs an elaborate single-case design [33]. Through in-depth face-to-face sessions with the client and her family members, we aim to illustrate the analysis of psychosocial factors contributing to severe depression. Utilizing both qualitative and quantitative explorations across progressive sessions, we assess related depressive states and associated risk factors. The Beck Depression Inventory II (BDI-II) [34], a well-organized assessment tool, is utilized to evaluate and illustrate the gradual improvement in recovery within this context. The data used for this assessment was sourced from authentic diagnostic records provided by psychotherapists.

The process of utilizing the BDI-II framework can be time-consuming as it involves evaluating 21 criteria to identify the dominant psychological factor of depression. This delay in reaching a definitive diagnosis, which involves various psychotherapeutic intervention strategies, can adversely impact the mental and physical well-being of patients. To address this issue, we employ MOORA technique with conventional psychotherapeutic approach. By leveraging MOORA, we aim to expedite the convergence rate in identifying the dominating factors contributing to depression, thus facilitating the selection of appropriate intervention strategies by psychotherapists.

Our study utilizes a comprehensive dataset of 254 samples, divided into extreme (40.15%), severe (34.64%), and moderate (25.19%) depression categories. The results demonstrate that the application of the MOORA method accelerates the convergence process, enabling therapists to identify dominant psychological factors approximately 33–42% faster compared to traditional approaches. Additionally, average accuracy in detecting dominant psychological factors increased to 82.88–90.34%. This advancement has the potential to significantly enhance the efficiency and effectiveness of depression diagnosis and treatment planning in clinical settings.

Verifying the gap: psychological analysis vs. MCDM method

The dominant psychological factors responsible for severe depression problem based on out of 21 factors obtained from BDI-II analysis is solved in this paper following our proposed algorithm (Algo. 1) by employing MOORA method. In the case study the three alternatives psychotherapeutic strategies are addressed e.g., Individual Counseling, Couples Therapy and Group Therapy, respectively with respect to 21 psychological factors associated with depression analysis taken from BDI-II framework. The goal is to use MCDM methods to analyze and rank these alternatives, taking into account various criteria and their respective weights. The term normalized values implies that the values for each criterion have been adjusted or scaled to ensure consistency and comparability across the different criteria. For example, if the criteria include factors like Sadness, Guilty Feelings, and Crying, alternatives O1, O2, and O3 might represent different combinations or levels of improvement in these factors described in Table 2. The MCDM process would then involve assigning weights to these criteria and evaluating how well each alternative performs based on these weighted criteria, is shown in Table 3. Assign weights to each criterion based on their relative importance to the decision-making process and these weights can be determined through expert opinion, client discussions, and analytical techniques.

Algorithm 1

Identifying dominant psychological factors for depression analysis using MCDM MOORA method

Table 2 Normalized values for each criterionTable 3 Assigned weights for each criterion

For each alternative, the weighted normalized scores for each criterion is shown in Table 4.

Table 4 Weighted normalized scores for each criterion and alternative

Identify the best (maximum for benefit criteria) and worst (minimum for cost criteria) values for each criterion across all alternatives. Mathematically, let us denote the positive ideal solution for criterion i as PISi and the negative ideal solution as NISi. For a maximization criterion, the positive ideal solution is the maximum value across all alternatives for that criterion, and for a minimization criterion, it is the minimum value across all alternatives which is shown in Table 5.

Table 5 Positive and negative ideal solutions

The positive and negative ideal solutions are determined as follows:

$$}\;}\;}\;}\;i\;PIS_ = }(O_ ,O_ ,O_ ),\;NIS_ = }(Oj_ ,O_ ,O_ )$$

$$}\;}\;}\;}\;i\;PIS_ = }\left( _ ,O_ ,O_ } \right),NIS_ = }\left( _ ,O_ ,O_ } \right)$$

The performance scores (PS) help quantify the distance between each alternative’s performance and the best and worst solutions across all criteria, aiding in evaluating their relative performances is shown in Table 6. Rank the attributes based on their performance scores.

Table 6 Performance scores for each attributes and alternativeInference of MOORA

To infer the most effective criteria for each alternative, we can examine the performance scores for each criterion and alternative combination. The performance scores indicate the contribution of each criterion to the effectiveness or preference of an alternative. The analysis is based on the computed data shown in Table 6.

For Alternative O1

Most Effective Criteria: Loss of Interest in Sex (0.007632), Sense of Failure (0.005294), Self-Dislike (0.004784), Loss of Interest (0.0044672).

Least Effective Criteria: Worthlessness (0.001692), Suicidal Thoughts (0.0017528), Crying (0.001884), Pessimism (0.001968).

For Alternative O2

Most Effective Criteria: Sense of Failure (0.007396), Loss of Interest (0.0068864), Loss of Interest in Sex (0.006784), Self-Dislike (0.005936), Indecisiveness (0.0044672), Guilty Feelings (0.00424).

Least Effective Criteria: Worthlessness (0.001506), Pessimism (0.00182), Suicidal Thoughts (0.0018224), Loss of Pleasure (0.001968).

For Alternative O3

Most Effective Criteria: Self-Dislike (0.007632), Sense of Failure (0.006568), Indecisiveness (0.005248), Loss of Interest in Sex (0.005085), Guilty Feelings (0.004088).

Least Effective Criteria: Changes in Appetite (0.00124), Worthlessness (0.001776), Crying (0.0012672).

Overall Inference

Sense of Failure, Loss of Interest in Sex, Self-Dislike, and Loss of Interest are consistently among the most effective criteria across all alternatives. This suggests that addressing issues related to failure, sexual interest, and self-perception is crucial for all considered alternatives.

Worthlessness, Suicidal Thoughts and Crying are among the least effective criteria across all alternatives, suggesting that they have a smaller impact compared to other criteria.

Step 10 of Algo. 1 identifies the specific BDI-II parameters potentially contributing to the client’s vulnerability to relapse employing ordered statistics for all alternatives. Considering the parametric score range of 0 to 4, a mean value of approximately 1.5 can be estimated. We determined that parameters with average scores exceeding 1.5 after the final assessment are indicative of sustained vulnerabilities. Table 7 lists these seven vulnerable parameters i.e., key psychological factors (Akey), ∀i ∈ m.

Table 7 Critical psychological factors

It is important to note that not all vulnerable parameters i.e., key psychological factors (Akey) necessarily translate to key drivers of depression. Vulnerable parameters are empirically observed based on their individual mean scores. However within this group, critical parameters i.e., critical psychological factors (Acr) emerge as those exhibiting consistently high scores (≤ 2) throughout all 15 assessments. Table 7 shows three critical parameters (marked in bold) for our client, causing most vulnerability towards relapse, and those are not suppressed by the series of different intervention strategies.

Lemma 1

For any given critical parameter x and vulnerable parameter y, the relationship holds: x ⊆ y. The reverse implication (y ct x) is not universally true.

Proof

Let X =  and Y =  represent the BDI-II scores for parameters x and y over five assessments, respectively. The parametric means (X¯ and Y¯) for x and y are calculated as 1.6 and 2.4, respectively. Thus, X¯ > 1.5 and Y¯ > 1.5, classifying both x and y as vulnerable parameters. However, upon closer inspection of the BDI-II score patterns, it is evident that parameter x is suppressed in the final assessment, Xpost = , despite X¯ > 1.5. In contrast, parameter y remains unaltered in the post-assessment, Ypost = , with Y¯ > 1.5. Hence, x fails to be a subset of y in the post-assessment, highlighting the asymmetry in vulnerability. Consequently, the proof establishes the lemma.\(\square\)