# Probabilistic Decision Trees for Predicting 12-Month University Students Likely to Experience Suicidal Ideation

Efthyvoulos Drousiotis, Dan W. Joyce, Robert C. Dempsey, Alina Haines, Paul G. Spirakis, Lei Shi, Simon Maskell

► To cite this version:

Efthyvoulos Drousiotis, Dan W. Joyce, Robert C. Dempsey, Alina Haines, Paul G. Spirakis, et al. Probabilistic Decision Trees for Predicting 12-Month University Students Likely to Experience Suicidal Ideation. 19th IFIP International Conference on Artificial Intelligence Applications and Innovations (AIAI), Jun 2023, León, Spain. pp.475-487, 10.1007/978-3-031-34111-3_40. hal-05449810

HAL Id: hal-05449810

https://inria.hal.science/hal-05449810v1

Submitted on 9 Jan 2026

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons CC BY 4.0 - Attribution - International License
<figure><img src="image_2.png" /></figure>

ifip

International Federation for Information Processing

This document is the original author manuscript of a paper submitted to an IFIP
conference proceedings or other IFIP publication by Springer Nature. As such, there
may be some differences in the official published version of the paper. Such
differences, if any, are usually due to reformatting during preparation for publication or
minor corrections made by the author(s) during final proofreading of the publication
manuscript.
# Probabilistic Decision Trees for Predicting 12-Month University Students Likely to Experience Suicidal Ideation

Efthyvoulos Drousiotis¹(✉), Dan W. Joyce², Robert C. Dempsey³, Alina Haines⁴, Paul G. Spirakis⁵, Lei Shi⁶, and Simon Maskell¹

¹ Department of Electrical Engineering and Electronics, University of Liverpool, Liverpool L69 3GJ, UK

{E.Drousiotis,S.Maskell}@liverpool.ac.uk

² Institute of Population Health, University of Liverpool, Liverpool L69 3GJ, UK
D.Joyce@liverpool.ac.uk

³ Department of Psychology, Manchester Metropolitan University, Manchester M15 6BH, UK

r.dempsey@mmu.ac.uk

⁴ Department of Nursing, Manchester Metropolitan University, Manchester M15 6BH, UK

a.haines@mmu.ac.uk

⁵ Department of Computer Science, University of Liverpool, Liverpool L69 3BX, UK
spirakis@liverpool.ac.uk

⁶ School of Computing, Newcastle University, Newcastle NE4 5TG, UK
Lei.Shi@newcastle.ac.uk

**Abstract.** Environmental stressors combined with a predisposition to experience mental health problems increase the risk for SI (Suicidal Ideation) among college/university students. However, university health and wellbeing services know little about machine learning methods and techniques to identify as early as possible students with higher risk. We developed an algorithm to identify university students with suicidal thoughts and behaviours using features universities already collect. We used data collected in 2020 from the American College Health Association (ACHA), a cross-sectional population-based survey including 50,307 volunteer students. A state-of-the-art parallel Markov Chain Monte Carlo (MCMC) Decision tree was used to overcome overfitting problems and target classes with fewer representatives efficiently. Two models were fitted to the survey data featuring a range of demographic and clinical risk factors measured on the ACHA survey. The first model included variables universities would typically collect from their students (e.g., key demographics, residential status, and key health conditions). The second model included these same variables plus additional suicide-risk variables which universities would not typically measure as standard

**Supplementary Information** The online version contains supplementary material available at https://doi.org/10.1007/978-3-031-34111-3_40.
practice (e.g., students' sense of belonging at university). Models' performance was measured using precision, recall, F1 score, and accuracy metrics to identify any potential overfitting of the data efficiently.

**Keywords:** Bayesian Decision Trees · Suicidal Ideation (SI) · ACHA · Machine Learning

# 1 Introduction and Related Work

Suicidal thoughts, intent, plans, and attempts are concepts with varying definitions [18], resulting in variability of measurement and consequently difficulty establishing robust conclusions about which populations or individual-level clinical factors merit either screening or, at least, surveillance. Prediction for an individual's absolute risk of dying by suicide is difficult, not least because tools claiming to demonstrate predictive performance have significant caveats – for example, even in robustly developed, validated and calibrated suicide risk prediction tools [16], for thresholds of a 1% risk of suicide they display very low positive predictive value (i.e. they are poor at discriminating those who will commit suicide) but a significantly higher negative predictive value (i.e. the tool can reliably predict those who will *not* commit suicide). This pattern of relatively poor positive predictive performance alongside neglect of *how* these tools could augment human actors' work in helping people at risk of suicide [40] has led to some national guidelines recommending *against* using any structured assessment tools for managing the risk of suicide. For example, in the United Kingdom, the National Institute for Health and Care Excellence guidelines advise against using risk stratification tools [26].

The relationship between Suicidal Ideation (SI) to either attempting or committing suicide is complex. For example, the assumption of a straightforward 'linear progression' from SI to action is not empirically supported. Moreover, several key models of suicide, such as the Interpersonal Theory of Suicide [38], the Integrated Motivational-Volitional model [27], and the Three Step Theory of Suicide [21] separate the development of SI from the progression of ideation to an attempt. Given this complexity, locating individuals who might benefit from enhanced support and early intervention for both mental health problems and features associated with suicide may be logistically and practically more appropriate.

A study of UK university students designed to test the central tenets of the Three Step Theory [11] identified that SI develops in the presence of self-reported psychological pain and hopelessness cognitions. Further, “connectedness” (to others) appears to play a role in preventing the escalation of ideation to action, but also, a lack of social connectedness was independently associated with SI. University or college can be stressful for students, especially for those who are psychologically vulnerable and have poor support. University students are at an elevated risk for SI, planning, and attempts [15] potentially arising due to increased academic pressure, psycho-social stress, heavy workloads, and difficulties adapting to a new environment [5]. Around 16%–25% of students
have experienced some form of SI during university, and approximately 40% and 20% of students with SI reported that they have considered or attempted suicide respectively [25].

Early identification of at-risk students is important for effective suicide prevention and allows universities to refer students to appropriate well-being, counseling, and pastoral support. Various influences and predictors on the experience of suicidal ideation amongst university students have been identified in the existing literature. In terms of mental health-related variables, the experience of more severe depressive symptoms, psychosis, and greater perceived stress have been associated with higher suicide risk [1,32], with similar associations between increased mental health symptoms and past 12-month suicidal ideation reported [3,33]. Whilst there have been limited prospective studies, there is evidence that increased suicide risk over 12 months amongst students is associated with the experience of clinically significant mood and other common mental health conditions (e.g. generalised anxiety), stressful life events, childhood adversities, reporting of physical or sexual assault [6]. Various other risk factors for self-harm and suicidality amongst university students have been identified, including sleep difficulties [36], alcohol use problems [9,29], being of a younger age and/or status as an undergraduate student [32], as well as interpersonal difficulties, such as unsupportive family environments [42].

Theoretical models of suicide [21,38] suggest addressing SI as a potentially modifiable factor in preventing suicide. Identifying students with SI is, however, challenging as most of the studies [34] rely on information about an individual's mental health obtained from (e.g.) interactions with skilled pastoral support workers. Most of the previous studies [2,8,10], including those aiming to predict SI among different populations, focus on identifying predictors for SI using post-hoc, inferential statistical analyses, which may be helpful to inform predictive models. For example, inferential statistical methods also require a *priori* models describing the relationships between predictors and outcomes to test a specific hypothesis. As a result, there may be a number of different pathways to suicidality amongst at-risk university students considering the various risk factors that may interact to increase the vulnerability to suicidal thoughts and behaviours (i.e., suicide-related events).

The majority of the literature [5,15,20,22,23,37,41] uses traditional statistical and linear methods to analyse and identify putative factors that may be predictors of SI. Linear models and inferential statistical hypothesis testing often assume linearity of individual predictor's contribution to an outcome and very often, the models assume additivity of risk. Given the complexity of suicide in general, such approaches could hamper the ability to locate variables (or their combinations) that inform decision-making in a meaningful way [19,39]. Melissa et al. [24] conducted the only study that uses a non-linear machine learning (Random Forest) algorithm to identify possible predictors for students with SI considering 70 features. However, identifying factors associated with SI does not necessarily imply that they could help predict future students with SI [7].

The aforementioned studies were mainly conducted as explanatory analyses to help inform universities about the possible factors leading to SI in student
populations. In contrast, our study attempts to efficiently and effectively predict students with SI using data universities and colleges possess before a student starts their studies. Universities need understandable algorithms that are easily applied to data they already have, for example, to stratify students at risk of SI and to target resources appropriately to those who might most benefit.

Most of the papers in the literature tend to report analyses conducted on samples that contain relatively small amounts of data, with some large inconsistencies in sample sizes across previous studies. This problem is previously addressed [35], where the median number of participants across studies related to suicidal ideation was 79 and the mean 710. The features sample size in past studies have varied from 1085 to 5572 [15, 20, 22, 24, 37, 41]. To address this issue of inconsistent and relatively small sample sizes used in past research, we conducted machine learning-based analyses on a sample of 50,307 students from the American College Health Association (ACHA) survey to provide a more robust and reliable understanding of the predictors of suicidal ideation in university students. To achieve this aim, we conducted two separate analyses. Firstly, a machine learning model featuring data that universities are likely to collect as part of their normal operations was fitted to the data (e.g., information about the student's general health). Secondly, we tested a more comprehensive model featuring this information plus a variety of variables from the ACHA survey implicated in suicidality (e.g., social connectedness variables) which universities may not normally collect from their students. We ran these two models to investigate which offers the more robust and accurate predictive model of suicidal ideation in university students and identify possible important vulnerability factors for suicidality in students that universities may need to collect in the future. A scalable and transparent state-of-the-art machine learning algorithm, a parallel MCMC Decision Tree, processed the models.

# 2 Methods

## 2.1 Dataset and Data Preparation

The dataset used in this study is provided by ACHA<fnref n="1" /> (American College Health Association), a nationally recognised research survey that provides precise data about students' health habits, behaviours, and perceptions. The dataset contains information from 2020 of 50,307 students (68% females, 31% males, < 1% intersex) and 694 features including demographics, Likert scale questions, and multiple choice questions (MCQ).

The mean age of the sample was 22.5 years. Most students reported living either on campus or in university housing (39.6%) or off-campus or in non-university housing (46.4%). 12.8% of the students lived in their parents'/guardian' or other family member's house, 0.2% temporarily stayed with a relative, friend, or "couch surfing" until they found housing, < 0.1% did not

<footnote n="1">¹ https://www.acha.org/ACHA/Resources/Survey_Data/ACHA/Resources/Survey_Data.aspx.</footnote>
(currently) have a place to live, and 0.9% lived in other types of accommodation. 52% of the students were not in a relationship, 39.3% were in a relationship, and 8.7% were married or partnered. Of the 50,307 participants in the sample, 53.8% never thought about killing themselves, 25.7% had a brief passing thought about suicide/planning suicide, 15.3% had a plan at least once to kill themselves, and 5.2% had attempted to kill themselves. Specifically, 55.7% of girls, 57.8% of boys, and 44.4% of intersex students never thought about killing themselves, 27.3% of girls, 25.9% of boys, and 22.2% of intersex students had a brief passing thought about suicide/planning suicide, 11.1% of girls, 12.9% of boys, and 27.3% of intersex students had a plan at least one to kill themselves, and 5.9% of girls, 3.4% of boys, and 5.6% of intersex students had attempted to kill themselves. The main baseline characteristics did not significantly differ based on gender.

From the 694 available features, we used only the 16 features that universities already had (information asked during their UCAS application) to predict students' SI. For the secondary analysis, we used 182 features implicated in suicide risk which universities did not typically collect from students. Due to the large number of features we used for the secondary model, please find the table containing the features and the associated features' importance on the supplementary material. Our target variable asks the students if they thought about suicide in the past year, meaning that we predict students with suicidal ideation. For this particular question, there are five possible answers, never (1), rarely (2), sometimes (3), often (4), and very often (5). Participants who chose answers 2 to 5 were coded as positive for SI. We avoided any data pre-processing techniques (Oversampling, Undersampling, Principal Component Analysis, etc.), as we wanted our data to be as original as possible and keep the transparent nature of our algorithm, and allow practical conclusions to be drawn based on the raw data as collected on the ACHA survey. Table 1 demonstrates the imbalanced nature of our data, showing the number of students who reported SI compared to those who did not report SI. Specifically, 34,626 students didn't report any SI during the last year, while 15,681 students reported at least one SI during the last year.

<table><caption>**Table 1.** Percentage of students reporting SI</caption><thead><tr><td>Number of students</td><td>Percentage</td><td>SI</td></tr></thead><tbody><tr><td>34626</td><td>68.3%</td><td>No (0)</td></tr><tr><td>15681</td><td>31.17%</td><td>Yes (1)</td></tr></tbody></table>

## 2.2 Markov Chain Monte Carlo Decision Tree

A decision tree typically starts with a root node which branches into possible outcomes. Each of those outcomes leads to additional decision nodes, which branch off into other possibilities ending up in leaf nodes. This gives it a tree-like shape.

Our model describes the conditional distribution of *y* given *x*, where *x* is a vector of predictors [*x* = (*x*<sub>1</sub>, *x*<sub>2</sub>, ..., *x*<sub>*p*</sub>)]. The main components of the *tree*(*T*)
include the depth of the tree, ($d(T)$), the features, ($k(T)$), and the thresholds, ($c(T)$), for each node where $\theta = [k(T), c(T)]$, and the conditional probabilities $p(Y|T, \theta, x)$ for each leaf node, ($L(T)$). If $x$ lies in the region corresponding to the $i_{th}$ terminal node, then $y|x$ has distribution $f(y|\theta_i)$, where $f$ represents a parametric family indexed by $\theta_i$. The model is called a probabilistic classification tree, according to the quantitative response $y$.

As Decision Trees are identified by $(\theta, T)$, a Bayesian analysis of the problem proceeds by specifying a prior probability distribution, $p(\theta, T)$. Because $\theta$ indexes the parametric model for each $T$, it will usually be convenient to use the relationship

$$p(Y_1:N, T, \theta|x_1:N) = p(Y|T, \theta, x)p(\theta|T)p(T) \quad (1)$$

The Metropolis-Hastings (MH) algorithm for simulating the Markov Chain in Decision Trees (see Eq. 2) is defined as follows. Starting with an initial tree $T_0$, iteratively simulate the transitions from $T_i$ to $T_{i+1}$ by these two steps:

1. Generate a candidate value $T'$ with probability distribution $q(T_i, T')$.

2. Set $T_{i+1} = T'$ with probability

$$a(T_i, T') = \min(1, \frac{\pi(Y_1:N, T', \theta'|x_1:N) q(T, \theta|T', \theta')}{\pi(Y_1:N, T, \theta|x_1:N) q(T', \theta'|T, \theta)}) \quad (2)$$

Otherwise set $T_{i+1} = T_i$.

More information and a detailed explanation of the algorithm can be found here [14]

To evaluate our predictive model's performance, we used the following four metrics.

- Precision: the ratio of the correctly predicted positive observations to the total predicted positive observations.

- Recall: the ratio of correctly predicted positive observations to all observations in the actual positive class.

- F1-score: the weighted average of Precision row and Recall row. Therefore, this score takes both false positives and false negatives into account.

- Accuracy: the most intuitive performance measure and it is simply a ratio of correctly predicted observations to the total observations.

We also performed cross-validation by randomly splitting the initial dataset into 10 folds, where each fold was used as a test, and we repeated this process until all the folds were used as test sets.

The main advantage of the probabilistic machine learning (ML) models over conventional ML is that they are known to generalise better on imbalanced data and are less overfitting prone [12,13], allowing us to avoid data pre-processing techniques. We have further modified the algorithm to produce even more accurate results by adding special weights to the students with SI. Specifically, we instructed our algorithms to classify a student as a 0 (people with no SI) only
if it is more than 69% confident. This practice enabled us to further increase our performance metrics (accuracy, F1-score) and fight off overfitting due to the imbalanced nature of the dataset. In general, we believe that applying heavy data pre-processing techniques alters the dataset nature, leading us to solve a different problem, ending up having algorithms working only for the specific dataset and not being able to generalise. Our philosophy is to change and modify the algorithms to fit the problem, not vice versa.

# 3 Results

## 3.1 Predicting

For the students with SI using the features universities normally collect (e.g., through university application forms), the model had an out-of-bag error of 29.2% ± 0.9, leading to an accuracy of 70.8% ± 0.9. The predictive (0) values were 0.77, whereas the predictive (1) values were 0.55, meaning that 77% and 55% of predicted cases were actually cases. Table 2 shows the scores analytically for predicting students with SI. Specifically precision score is 65.33% ± 0.7, recall score is 64.16% ± 0.4, and f1-score 64.8% ± 0.4. Analyses of the importance of the variables for the prediction, measured by the times each variable is used on the predictive model, revealed that the following four variables were the most predictive, as shown in Table 3: Depression, Eating Disorder, Approximate Cumulative Average Grade, and Attending Classes, Discussion sections, or Labs.

## 3.2 Secondary Analysis

For the students with SI using the features universities might not ordinarily collect, the model had an out-of-bag error of 27.1% ± 3.96, leading to an accuracy of 72.9% ± 3.96. The predictive (0) values were 0.83, whereas the predictive (1) values were 0.58, meaning that 83% and 58% of predicted cases were actually cases. Table 2 shows the scores analytically for predicting students with SI. Specifically precision score is 70.30% ± 2.28, recall score is 71.3% ± 2.23, and f1-score 69.8% ± 2.99. Analyses of the importance of the variables for the prediction, measured by the times each variable is used on the predictive model, revealed that the following four variables were the most predictive, as shown in Table 3: Financial Problems, Bullying, Allergies to pets/animals, Gastroesophageal Reflux Disease/Acid Reflux.

<table><caption>**Table 2.** Metrics for predicting students with SI</caption><thead><tr><th></th><th>Precision</th><th>Recall</th><th>F1-score</th><th>Accuracy</th></tr></thead><tbody><tr><td>With Uni Features</td><td>65.33 ± 0.74</td><td>64.16 ± 0.37</td><td>65.83 ± 0.37</td><td>70.83 ± 0.89</td></tr><tr><td>Without Uni Features</td><td>70.30 ± 2.28</td><td>71.30 ± 2.23</td><td>69.80 ± 2.99</td><td>72.9 ± 3.96</td></tr></tbody></table>
<table><caption>**Table 3.** Features Importance for Variables Universities Collect from Students</caption><thead><tr><td>Features</td><td>Feature Importance(%)</td></tr></thead><tbody><tr><td>Age</td><td>1.6</td></tr><tr><td>Anxiety (Generalized Anxiety, Social Anxiety, Panic Disorder</td><td>6.8</td></tr><tr><td>Approximate Cumulative Average Grade</td><td>9.1</td></tr><tr><td>Attending Classes, Discussion sections, or Labs</td><td>8.0</td></tr><tr><td>Bipolar and Related Conditions (Bipolar I, II, Hypomanic Episode)</td><td>7.4</td></tr><tr><td>Biracial or Multiracial</td><td>5.5</td></tr><tr><td>Black or African American</td><td>4.2</td></tr><tr><td>Blind/Low Vision</td><td>5.2</td></tr><tr><td>Depression(Major Depression, Persistent Depressive</td><td>15.0</td></tr><tr><td>Diabetes or pre-diabetes/insulin resistance</td><td>2.7</td></tr><tr><td>Eating Disorder(Anorexia Nervosa, Bulimia Nervosa, Binge - Eating)</td><td>10.0</td></tr><tr><td>Enrollment Status</td><td>3.60</td></tr><tr><td>Insomnia</td><td>5.4</td></tr><tr><td>Middle Eastern/North African or Arab Origin</td><td>1.3</td></tr><tr><td>Parent or Guardian of a Child</td><td>7.6</td></tr><tr><td>Sex assigned at birth</td><td>5.6</td></tr></tbody></table>

# 4 Discussion

Predicting which university students are at higher risk of SI and potentially suicidal behaviours is a difficult task. Past studies in this area have been limited by using relatively small and unrepresentative samples of data and relying on researcher-led choices of which data to use in predictive models of suicidal ideation, meaning a lack of consistency and comprehensiveness in previous research [15, 22, 24]. To address these issues, we applied machine learning approaches to understand the variables associated with suicidal ideation amongst students based on an existing large survey of US students (over 50,000 participants) and the testing of predictive variables that universities routinely and seldom collect from incoming students.

Using a parallel MCMC Decision Tree model for the features universities already have, we found that four main baseline variables predicted SI: Depression, Eating Disorder, Approximate Cumulative Average Grade, and Attending Classes (Discussion sections, Labs) with a significance level of 15%, 10%, 9.1%, 8% accordingly. The model including those variables showed a good predictive performance (accuracy = 70.83 ± 0.89) estimated using cross-validation. In secondary analyses in a wider sample of (number of) features, the main predictive variables differed from the main analyses. Having Financial Problems contributed to a
4.13%, Bullying contributed to a 3.03%, Allergies to pets/animals contributed to a 4.13%, and Gastroesophageal Reflux Disease or acid reflux contributed to a 3.87%. The model, including the dataset with bigger feature space, had an improved predictive accuracy than the one using only the universities' typical features, with a predictive accuracy of 72.9 ± 3.96. We also achieved better results for both test cases (predicting students with SI, secondary analyses) compared to other studies predicting students with SI utilising a machine learning model(Random Forest). Specifically, [24] achieved 0.4 and 0.36 predicted (1) values for girls and boys, respectively, meaning that 40% and 36% of predicted cases were actual cases. In comparison, we achieved 0.55 and 0.58, which leads to a significant increase of 15% for girls and 19% for boys when we use features universities have, while 18% and 22% improvement achieved for our secondary analyses.

Machine learning approaches offer universities potentially powerful means of understanding the risk factors for suicidality amongst their student populations. There may be the potential for universities to use similar models at a local level considering risk factors that may be unique to their campuses, location, and student population. Understanding more local-level risk factors may be important for university health and wellbeing services to better identify those at risk for suicidal ideation and to provide more targeted early intervention support for students at a heightened risk.

There are some strengths and limitations to consider with the present study. As discussed earlier, previous studies of the risk factors associated with suicidal ideation amongst university students have been limited by their analysis of relatively small samples [20,37]. In contrast, our study drew on data from a large national sample of US university students (over 50,000 students) and applied machine learning approaches to develop predictive models of students' suicidal ideation. Based on a prior call [17], the present machine learning study has allowed for the modelling of numerous variables in a predictive model of suicidal ideation. Such models offer a more detailed understanding of university student suicidal ideation and accommodate the modelling of potentially hundreds of predictors and their complex inter-relationships, compared to the dominance of regression-based analyses in the literature, which only accommodate the testing of relatively simplistic models of suicidality [17]. In addition, the use of an existing, large, representative national survey to model potential predictors of suicidality amongst university students reduced potential research ethical issues associated with collecting suicide-related data from at-risk individuals.

There are, however, some limitations to the present study to consider. The study analysed data from an ongoing national US student survey from only one-time point. Given the complex and dynamic nature of suicidality, how these factors identified in the machine learning model influence suicidality over the longer term requires further exploration. It should also be noted that the specific predictors identified here may not be generalisable to students in other countries, where there may be more local and unique pressures on students implicated in suicidal ideation. We also focused on the experience of suicidal ideation as a broad outcome in the machine learning models and did not include detailed
assessments of the types of suicidal thoughts students experienced (such as active planning versus more passive ideation), and so care should be taken in assuming that these factors are similarly implicated in suicidal behaviours amongst students. Although, it is important to identify the potential factors implicated in the suicidal ideation-to-enaction process, particularly those associated with earlier suicidal thoughts where targeted interventions may be particularly effective. In addition, the survey data used in the machine learning approach here did not feature many key psychological variables implicated in the suicidality pathways, such as feelings of defeat and entrapment [17, 30, 31]. The factors in the models also tended to be more risk-focused in nature rather than encapsulate more protective factors against suicidality, and did not explicitly test existing models of suicidality which attempt to outline the ideation-to-enaction pathway [4, 27, 28]. Integrating factors associated with reduced suicidality, including more factors of a bio-psycho-social basis, may be promising for future machine learning approaches focusing on understanding suicidality in at-risk populations.

# 5 Conclusion

University students are a high-risk group for suicidal thoughts, feelings, and behaviours, but predicting which specific students are at higher risk is a difficult endeavour. Machine learning-based approaches offer a unique way of understanding suicide risk based on their ability to model a large and complex range of factors at the same time. Still, few machine learning approaches have been used to understand suicide risk in university students. Our study differs from most of the literature, as we discussed in Sect. 1. We trained a state-of-the-art MCMC Decision Tree with a large sample (over 50,000 participants) for the first time. We showed that such a machine learning-based approach could significantly contribute towards identifying and predicting suicidal ideation among university students. Unlike the other studies, we focused on the actual predictive model and how to produce optimal solutions instead of only identifying possible factors leading students to SI. Our approach can potentially help universities quickly identify and provide early interventions targeting students with these suicide-risk factors. Moreover, our model outperforms significantly any other similar implementation by an average of 17%, and 20% when a wider sample of features is used. This study, though, has some limitations. The study focused only on SI and not suicidal behaviours, as we should note that the results may not be generalisable to students in other countries.

# References

1. Akram, U.: Prevalence and psychiatric correlates of suicidal ideation in UK university students. J. Affect. Disord. **272**, 191–197 (2020)

2. Mohamad Ashari, Z., Liow, Y.E., Binti Zainudin, N.F.: Psychological risk factors and suicidal ideation among undergraduate students of a Malaysian public university. Jurnal Kemanusiaan **19**, 33–40 (2022)
3. Bantjes, J.R., Kagee, A., McGowan, T., Steel, H.: Symptoms of posttraumatic stress, depression, and anxiety as predictors of suicidal ideation among South African university students. J. Am. Coll. Health **64**(6), 429–437 (2016)

4. Barzilay, S., Apter, A.: Psychological models of suicide. Arch. Suicide Res. **18**(4), 295–312 (2014)

5. Blasco, M.J., et al.: Predictive models for suicidal thoughts and behaviors among Spanish university students: rationale and methods of the universal (university & mental health) project. BMC Psychiatry **16**(1), 1–13 (2016)

6. Blasco, M.J., et al.: First-onset and persistence of suicidal ideation in university students: a one-year follow-up study. J. Affect. Disord. **256**, 192–204 (2019)

7. Bzdok, D., Varoquaux, G., Steyerberg, E.W.: Prediction, not association, paves the road to precision medicine. JAMA Psychiatry **78**(2), 127–128 (2021)

8. Cong, C.W., Ling, W.S.: The predicting effects of depression and self-esteem on suicidal ideation among adolescents in Kuala Lumpur, Malaysia: Received 2019-10-10; Accepted 2020-01-06; Published 2020-04-17. J. Health Transl. Med. **23**(1), 60–66 (2020)

9. Coryell, W., et al.: Alcohol intake in relation to suicidal ideation and behavior among university students. J. Am. Coll. Health **1–5** (2021)

10. De Choudhury, M., Kiciman, E., Dredze, M., Coppersmith, G., Kumar, M.: Discovering shifts to suicidal ideation from mental health content in social media. In: Proceedings of the 2016 CHI Conference on Human Factors in Computing Systems, pp. 2098–2110 (2016)

11. Dhingra, K., Klonsky, E.D., Tapola, V.: An empirical test of the three-step theory of suicide in UK university students. Suicide Life-Threat. Behav. **49**(2), 478–487 (2019)

12. Drousiotis, E., Pentaliotis, P., Shi, L., Cristea, A.I.: Capturing fairness and uncertainty in student dropout prediction – a comparison study. In: Roll, I., McNamara, D., Sosnovsky, S., Luckin, R., Dimitrova, V. (eds.) AIED 2021. LNCS (LNAI), vol. 12749, pp. 139–144. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-78270-2_25

13. Drousiotis, E., Pentaliotis, P., Shi, L., Cristea, A.I.: Balancing fined-tuned machine learning models between continuous and discrete variables - a comprehensive analysis using educational data. In: Rodrigo, M.M., Matsuda, N., Cristea, A.I., Dimitrova, V. (eds.) Artificial Intelligence in Education. AIED 2022. LNCS, vol. 13355. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-11644-5_21

14. Drousiotis, E., Spirakis, P.G.: Single MCMC chain parallelisation on decision trees. In: Simos, D.E., Rasskazova, V.A., Archetti, F., Kotsireas, I.S., Pardalos, P.M. (eds) Learning and Intelligent Optimization. LION 2022. LNCS, vol. 13621, pp. 191–204. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-24866-5_15

15. Eskin, M., et al.: Suicidal behavior and psychological distress in university students: a 12-nation study. Arch. Suicide Res. **20**(3), 369–388 (2016)

16. Fazel, S., Wolf, A., Larsson, H., Mallett, S., Fanshawe, T.R.: The prediction of suicide in severe mental illness: development and validation of a clinical prediction rule (OxMIS). Transl. Psychiatry **9**(1), 1–10 (2019)

17. Franklin, J.C., et al.: Risk factors for suicidal thoughts and behaviors: a meta-analysis of 50 years of research. Psychol. Bull. **143**(2), 187 (2017)

18. Goodfellow, B., Kolves, K., De Leo, D.: Contemporary nomenclatures of suicidal behaviors: a systematic literature review. Suicide Life-Threat. Behav. **48**(3), 353–366 (2018)

19. Hedegaard, H., Warner, M.: Suicide mortality in the united states, 1999–2019 (2021)
20. Keyes, C.L.M., Eisenberg, D., Perry, G.S., Dube, S.R., Kroenke, K., Dhingra, S.S.: The relationship of level of positive mental health with current mental disorders in predicting suicidal behavior and academic impairment in college students. J. Am. Coll. Health **60**(2), 126–133 (2012)

21. Klonsky, E.D., May, A.M.: The three-step theory (3ST): a new theory of suicide rooted in the “ideation-to-action” framework. Int. J. Cogn. Therapy **8**(2), 114–129 (2015)

22. Knorr, A.C., Ammerman, B.A., Hamilton, A.J., McCloskey, M.S.: Predicting status along the continuum of suicidal thoughts and behavior among those with a history of nonsuicidal self-injury. Psychiatry Res. **273**, 514–522 (2019)

23. Liu, C.H., Stevens, C., Wong, S.H.M., Yasui, M., Chen, J.A.: The prevalence and predictors of mental health diagnoses and suicide among us college students: implications for addressing disparities in service use. Depression Anxiety **36**(1), 8–17 (2019)

24. Macalli, M., et al.: A machine learning approach for predicting suicidal thoughts and behaviours among college students. Sci. Rep. **11**(1), 1–8 (2021)

25. Mortier, P., et al.: The prevalence of suicidal thoughts and behaviours among college students: a meta-analysis. Psychol. Med. **48**(4), 554–565 (2018)

26. NICE. Self-harm: assessment, management and preventing recurrence. https://www.nice.org.uk/guidance/ng225

27. O'Connor, R.C., Kirtley, O.J.: The integrated motivational-volitional model of suicidal behaviour. Philos. Trans. R. Soc. B Biol. Sci. **373**(1754), 20170268 (2018)

28. O'Connor, R.C., Nock, M.K.: The psychology of suicidal behaviour. Lancet Psychiatry **1**(1), 73–85 (2014)

29. O'Neill, S., et al.: Socio-demographic, mental health and childhood adversity risk factors for self-harm and suicidal behaviour in college students in Northern Ireland. J. Affect. Disord. **239**, 58–65 (2018)

30. Owen, R., Dempsey, R., Jones, S., Gooding, P.: Defeat and entrapment in bipolar disorder: exploring the relationship with suicidal ideation from a psychological theoretical perspective. Suicide Life-Threat. Behav. **48**(1), 116–128 (2018)

31. O'Connor, R.C., Portzky, G.: The relationship between entrapment and suicidal behavior through the lens of the integrated motivational-volitional model of suicidal behavior. Curr. Opinion Psychol. **22**, 12–17 (2018)

32. Parker, M., et al.: Prevalence of moderate and acute suicidal ideation among a national sample of tribal college and university students 2014–2015. Arch. Suicide Res. **25**(3), 406–423 (2021)

33. Rahman, Md.E., Islam, Md.S., Mamun, M.A., Moonajilin, Mst.S., Yi, S.: Prevalence and factors associated with suicidal ideation among university students in Bangladesh. Arch. Suicide Res. **26**(2), 975–984 (2022)

34. Ream, G.L.: The interpersonal-psychological theory of suicide in college student suicide screening. Suicide Life-Threat. Behav. **46**(2), 239–247 (2016)

35. Ribeiro, J.D., et al.: Self-injurious thoughts and behaviors as risk factors for future suicide ideation, attempts, and death: a meta-analysis of longitudinal studies. Psychol. Med. **46**(2), 225–236 (2016)

36. Russell, K., Allan, S., Beattie, L., Bohan, J., MacMahon, K., Rasmussen, S.: Sleep problem, suicide and self-harm in university students: a systematic review. Sleep Med. Rev. **44**, 58–69 (2019)

37. Shim, G., Jeong, B.: Predicting suicidal ideation in college students with mental health screening questionnaires. Psychiatry Investig. **15**(11), 1037 (2018)
38. Van Orden, K.A., Witte, T.K., Cukrowicz, K.C., Braithwaite, S.R., Selby, E.A., Joiner Jr., T.E.: The interpersonal theory of suicide. Psychol. Rev. **117**(2), 575 (2010)

39. Walsh, C.G., Ribeiro, J.D., Franklin, J.C.: Predicting risk of suicide attempts over time through machine learning. Clin. Psychol. Sci. **5**(3), 457-469 (2017)

40. Whiting, D., Fazel, S.: How accurate are suicide risk prediction models? Asking the right questions for clinical practice. Evid. Based Ment. Health **22**(3), 125-128 (2019)

41. Wilcox, H.C., Arria, A.M., Caldeira, K.M., Vincent, K.B., Pinchevsky, G.M., O'Grady, K.E.: Prevalence and predictors of persistent suicide ideation, plans, and attempts during college. J. Affect. Disord. **127**(1-3), 287-294 (2010)

42. Zhai, H., et al.: Correlation between family environment and suicidal ideation in university students in China. Int. J. Environ. Res. Public Health **12**(2), 1412-1424 (2015)