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The Poisson distribution may reveal hidden public health problems masked by the Binomial distribution.

The occurrence of negative clinical and administrative outcomes in prehospital care, emergency departments, and hospitalizations is called the weekend effect (WE). ^{1, 2} The WE has been studied in the care of cardiovascular and cerebrovascular diseases, sepsis, and emergency surgeries, among others; however, there is little evidence regarding the WE in completed suicides (CS). ^{1– 3}

CS is the third leading cause of death among adolescents and young adults. Approximately 727.000 CS occur worldwide each year, with an estimated rate of 9 per 100.000 people. ⁴ In the Americas, the estimated annual rate is 6.2 per 100.000 people (65.000 CS). However, in Colombia, the rate increased from 4.6 to 6.0 (an increase of 30.4%) between 2011 and 2021. ^{5, 6}

A multicenter study analyzing more than 1.7 million CSs between 1971 and 2019 showed a higher risk on weekends in Central and South American countries, South Africa, and Finland, compared with countries in North America, Europe, and Asia, where CS occurred mainly on Mondays and Wednesdays. ⁷ In Colombia, ~25,000 CSs over eleven years were analyzed, and an average of 6.2 events per day was observed, increasing to 8 CS on holidays. Likewise, a higher risk of death was observed in the Eastern Plains, especially among young adults and older adults, as well as among residents of rural areas. ⁸

As mentioned, the WE has been studied in cardiovascular emergencies, obstetric complications, and both general surgical and trauma-related emergencies. However, it has been shown that the maturation of trauma systems and the 24/7 model of care are health determinants that can significantly reduce the WE, especially in injuries from external causes, such as CS. ^{1, 2, 7, 9– 11}

CS events during the week (n/5 days) and at weekends (n/2 days) may follow a Poisson distribution ( Poi(λ)), given that events occur in defined periods, in this case, asymmetric periods. ¹² In most studies, the statistical methods used to determine the WE in CS rely on logistic regression or comparisons of proportions using hypothesis tests for Binomial distributions (X ~ B(n, p)), and only rarely use multivariate methods or compare event frequency during the week and at weekends using Poi(λ). ^{1, 2, 7– 14}

The impact of the WE was first recognized in the commercial sector, and, contrary to the health sector, the effect is positive, with increases in visits to shopping centers, sales, alcohol consumption, among other financial indicators. ^{15, 16} In response to the WE, the economic sector makes logistical, administrative, and operational adjustments to meet the demand for services. Conversely, such strategies are not commonly seen within the health sector. This is often due to a lack of research or evidence regarding the WE, financial limitations, constraints on care, and various other factors that influence the reorganization or modification of health service delivery.

This study compared the frequency of suicides during the week and at weekends, using Binomial and Poisson distributions, to show the WE in the occurrence of CS in Colombia. The results will serve as academic support for adjusting and reorganizing the distribution of mental health services.

Using an analytical cross-sectional design and administrative data from the INMLCF, we demonstrated the usefulness of the Poisson distribution compared with the Binomial distribution to confirm the presence of the WE in CS events that occurred over nine years in Colombia.

Over the past three five-year periods, Colombia has faced socioeconomic challenges that may explain the progressive increase in CS frequency. One of these was the 2014 economic crisis, which significantly increased unemployment; in the most affected departments, the frequency of CS rose by approximately 50%. ²¹ Additionally, between 2016 and 2018, two out of three CS were related to domestic disputes or family crises, and 12% were related to economic problems. ²²

During the SARS-CoV-2 pandemic, CS frequency also increased, partly due to the effects of social isolation, such as anxiety, depression, domestic violence, and reduced access to mental health services. It is important to note that “social isolation” was often a misinterpretation of “physical distancing,” a non-pharmacological measure designed to minimize person-to-person transmission. ^{23, 24}

Reports suggest that mental health services often face serious problems on weekends, including insufficient specialized staff for psychiatric emergencies and administrative hurdles that limit access to necessary medications. ^{7, 25} In Colombia, these weekend access barriers have not been studied; however, increased alcohol consumption has been reported during this time, often combined with other psychoactive substances that may induce agitation, impulsivity, and impaired judgment-conditions that can contribute to interpersonal and intrafamilial violence. ^{26, 27}

Interpersonal and domestic violence are acute stressors that may increase the risk of CS on weekends. For example, in Colombia, 35% of CSs are associated with alcohol consumption, 20% with other psychoactive drugs, and 12% occur after episodes of domestic violence or aggression, particularly on weekends. ^{26, 28, 29}

In addition to the findings reported here, recent studies in various countries agree that the occurrence of suicides varies significantly by day of the week and contextual conditions associated with free time, leisure, or reduced institutional support. In Japan, Australia, and the United States, there has been a significant increase in suicides during weekends and holidays, a phenomenon that has been particularly marked in young age groups and working-age adults, with findings similar to those observed in this study. ³⁰ These patterns reinforce the hypothesis that the temporal structure of the week includes changes in routine, less work or formal supervision, greater availability of alcohol, and reduced access to health services modulate suicide risk.

In Latin American countries, several studies confirm this trend. In Peru, Roman-Lazarte et al. reported marked variations by department and documented a significant increase in suicides on Sundays, similar to that observed in Colombia and Brazil. ^{8, 31} In Argentina, Leveau et al. showed that social fragmentation increases suicide risk. ³² In Mexico, Borges et al. found a predominance of CS associated with acute alcohol consumption during weekends, especially among young men, highlighting the role of impulsivity and disinhibition in suicidal behavior. ^{26, 27, 33} Similarly, the combined use of alcohol and psychoactive substances increases the likelihood of a suicide attempt six- to eightfold. ^{34, 35} These findings are consistent with the results of this research and with Colombian reports in which alcohol consumption is related to about one-third of suicides and increases markedly on weekends. ²⁸

Furthermore, accumulated evidence suggests that the lack of mental health services with effective weekend coverage worsens this phenomenon. Studies in the United Kingdom, Canada, and South Korea have shown that suicide mortality is lower in regions with 24/7 community mental health services or crisis hotlines staffed by specialized clinical personnel. These interventions have reduced suicides related to periods of low care availability by 15% to 22%, supporting the need to reorganize service provision according to temporal patterns of risk. ^{3, 36, 37}

Finally, methodological evidence is also consistent with our findings. In analyses of rare events occurring independently over time, the Poisson distribution can provide more stable and sensitive estimates than the Binomial approach or simple proportional comparisons. Statistical studies in the temporal epidemiology of CS indicate that Poisson methods, or extensions such as multivariate Poisson models or Poisson regression with offsets, may better capture relative increases on specific days, particularly when the time windows are asymmetric, as in comparisons of two weekend days versus five weekdays. ³⁸

In conclusion, the Poisson distribution detected the weekend effect in CS more clearly than the Binomial distribution. The relative excess of suicides on weekends was more evident when analyzed using Poisson methods. These findings suggest that reorganizing mental health services according to temporal risk patterns could improve responsiveness to weekend demand.

Because the database was anonymized and data were obtained retrospectively, this research was classified as “without risk” and approved by the local ethical regulation in force by the Research Committee of the Juan N. Corpas University Foundation.

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