Identifying suicide risk factors and evaluating it’s predictive value with the Bayes theorem
Inpatients at psychiatric hospitals are recognized to have a significant risk of suicide, but neither the risk factors nor the predictive power of those factors are well understood. A neural network model based on the Bayes theory of event probability and likelihood ratios was studied to identify suicide risk factors and evaluate its predictive value. The Bayes theorem predicts the likelihood of an event based on knowledge of prior circumstances that may be associated with it in probability theory and statistics. The suicide rate in psychiatric ward patients was 13.7 per 10 000 patients(British Journal of Psychiatry). On the basis of planned suicide attempts, actual suicide attempts, bereavement, delusionality, mental illness, and family history, only two of the patients who committed suicide had a risk of suicide above 5%. Although 2 patients were identified due to the associated predictive nature based on prior circumstances with suicide, but their clinical utility is limited due to the sensitivity, specificity, and rarity of suicide in these high-risk patients.
Bayes’ theorem and risk factor table(British Journal of Psychiatry)
Using the Bayes theorem a patient with all five of the aforementioned indicators has a probability of (0.137/100-0.137) ×4.9 ×3.9 ×2.2× 2.2 ×4.6=0.60, 37%(British Journal of Psychiatry). Only one patient in the data set had all five risk factors. This table depicts one of the clinical utility limits due to sensitivity. According to the table, only 2% of patients who committed suicide would have been predicted according to the algorithm of having a greater than 5% risk of suicide, which is the percentage at which you are considered high risk. The patients who had committed suicide were statistically only to have a 0.5% risk of suicide. Which showcases the other limit of specificity of a suicide case because even with these 5 risk factors, each person has their own set of factors and risk factor level for it. Based on this, if more research and risk factors were explored, using the Bayes’ theorem we may be able to identify additional suicide risk factors and have preventative measures put into place.
Citation
Powell, J., Geddes, J., Deeks, J., Goldacre, M., & Hawton, K. (2000). Suicide in psychiatric hospital in-patients: Risk factors and their predictive power. British Journal of Psychiatry, 176(3), 266-272. doi:10.1192/bjp.176.3.266
Copelan, Russell. “Opinion: The Little Suicide Construct That Could.” Medical News, MedpageToday, 11 Nov. 2022, https://www.medpagetoday.com/opinion/suicide-watch/101700.