Binomial vs. Poisson distribution to determine the weekend effect on completed suicide.

Highlights

Introduction

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.

Materials and methods

Results

Suicide frequencies: Binomial vs. Poisson distribution.

Tables 1 and S1 compare the frequencies of CS on weekends and weekdays using a Binomial distribution (X ~ B(n, p)). Overall, no statistically significant differences were found in CS frequencies between weekdays and weekends over the nine years analyzed. Among the variables evaluated, four characteristics showed a higher frequency of CS on weekends: early adulthood, basic or high-school education, the Amazon region, and common-law marital status (p < 0.05). In addition, only 5 of 33 departments showed a higher frequency of CS on weekends (Fig. 1).

Fig. 1. Geographical Binomial suicide distribution.

Each table (Fig. 1a to Fig. 1f) shows the frequency (%, 95%, CI) of suicides on weekends and weekdays in the six geopolitical regions of Colombia. The departments are found by the abbreviations of the ISO-3166 system. Statistical differences between weekends and weekdays are identified with asterisks (P-Value <0.05*, <0.01**, <0.001***) and the absence of statistical differences with ns (not significant).

Tables 2 and S2 compare the frequencies of CS on weekends and weekdays using a Poisson distribution (X ~ Poi(λ)). For each year of the study period, the average number of CS per day on weekends (λweekends) was higher than the average number of CS per day on weekdays (λweekdays). Additionally, across the other dimensions analyzed, 17 characteristics showed higher λ_weekend than λweekdays (p < 0.05). Likewise, λweekends was higher in 16 of 33 departments (p < 0.05) (Fig. 2).

Table 2. Frequency of suicides in Poisson distribution.

Variables	Weekends		Weekdays		P-Value
	n: 3748.5	λ (95%, CI)	n: 3203.4	λ (95%, CI)
Age, life cycle
Early childhood	2.00	0.50–5.10	2.80	1.50–4.70	0.380
Middle childhood	11.0	6.90–16.70	8.40	6.10–11.4	0.185
Adolescence	356.0	330.3–383.1	341.6	325.6–358.2	0.185
Early adulthood	1020.5	1154.9–1251.5	919.2	892.8–946.2	0.001
Middle adulthood	1647.5	1591.7–1704.7	1389.0	1356.5–1422.1	0.001
Late adulthood	529.5	498.1–562.4	542.4	522.2–563.2	0.260
Sex
Male	3013.0	2937.4–3090.1	2575.4	2531.1–2620.3	0.001
Female	735.5	698.4–774.1	628.0	606.2–650.4	0.001
Education
Basic – High school	2793.0	2720.2–2867.2	2334.6	2292.4–2377.3	0.001
Technical - Universitary	108.0	94.1–123.4	107.6	98.7–117.1	0.495
Technical secondary	246.5	225.2–269.3	257.2	243.3–271.7	0.220
Nationality
Colombian†	3652.0	3568.7–3736.7	3128.2	3079.4–3177.6	0.001
Foreigner	79.5	67.6–92.9	62.6	55.9–69.9	0.008
Marital status
Single	1745.5	1688.1–1804.4	1521.0	1487–1555.6	0.001
Common-law marriage	919.5	878.0–962.5	703.0	679.9–726.6	0.001
Married	451.0	422.0–481.4	431.2	413.2–449.8	0.135
Separated, divorced	164.0	146.7–182.7	148.6	138.1–159.7	0.075
Widowed	62.5	52.0–74.5	64.4	57.6–71.8	0.410
Not applicable	3.00	1.10–6.50	4.00	2.40–6.20	0.355
Years
2015	317.5	293.3–343.2	280.6	266.1–295.7	0.005
2016	377.5	351.0–405.4	311.0	295.7–326.9	0.001
2017	403.0	375.7–431.8	353.0	336.7–369.9	0.001
2018	432.0	403.7–461.8	366.4	349.8–383.6	0.001
2019	410.5	382.9–439.6	364.4	347.9–381.5	0.002
2020	383.5	356.8–411.6	330.6	314.9–346.9	0.001
2021	422.0	394.0–451.5	369.0	352.4–386.2	0.001
2022	488.5	458.3–520.1	395.0	377.8–412.8	0.001
2023	514.0	483.1–546.4	433.4	415.3–452.0	0.001
Semiannually periods
January–June	1838.5	1779.6–1898.9	1593.8	1559.0–1629.2	0.001
July–December	1910.0	1849.9–1971.5	1609.6	1574.6–1645.2	0.001
Quarter of the year
January – March	908.5	867.2–951.3	778.2	753.9–803.0	0.001
April – June	930.0	888.2–973.2	815.6	790.8–840.0	0.001
July – September	949.5	907.3–993.2	794.8	770.3–819.9	0.001
October–December	960.5	918.0–1004.4	814.8	790.0–840.2	0.001
Geographical region
Andean	2335.0	2268.5–2402.9	2030.0	1990.7–2069.9	0.001
Pacific	580.0	547.1–614.4	474.6	455.7–494.1	0.001
Caribbean	560.0	527.7–593.8	483.2	464.1–502.9	0.001
Orinoco	167.0	149.6–185.9	139.8	129.6–150.6	0.004
Amazon	104.0	90.3–119.1	72.6	65.3–80.5	0.001
Insular	2.00	0.50–5.10	2.80	1.50–4.70	0.380

Figure 2. Geographical Poisson suicide distribution.

Each table (Fig. 2a to Fig. 2f) shows the average number of suicides per day (λ, 95%, CI) on weekends and weekdays in the six geopolitical regions of Colombia. The departments are found by the abbreviations of the ISO-3166 system. Statistical differences between weekends and weekdays are identified with asterisks (P-Value <0.05*, <0.01**, <0.001***) and the absence of statistical differences with ns (not significant).

Finally, Figure 3 shows the CS frequency ratio calculated using the Binomial (_{πweekends /πweekdays}) and Poisson (_{λweekends/λweekdays}) approaches to highlight the relative excess of CS in these two periods. Overall, and across each characteristic analyzed within the person, time, and place dimensions, the relative excess of CS estimated using the Poisson approach was greater than that estimated using the Binomial approach.

Figure 3. Relative excesses of suicides on weekends and weekdays.

The figure shows the suicide frequency rate calculated using Binomial distribution (light blue bars, πweekends /πweekdays) and Poisson distribution (black bars, λweekends/λweekdays), according to the characteristics analyzed in the dimensions of time, person, and place. On the far left, at the beginning, the global rate is highlighted in gray.

Discussion

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.

Ethics approval statement

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.

Patient consent statement

Not applicable.

Permission to reproduce material from other sources

Not applicable.

Clinical trial registration

Not applicable.