Reduction in the suicide rate during Advent—a time series analysis
Article Outline
- Abstract
- 1. Introduction
- 2. Methods
- 3. Results
- 4. Discussion
- 5. Conclusion
- Acknowledgment
- References
- Copyright
Abstract
Research has shown that there are different seasonal effects in suicide. The aim of this study is to demonstrate that the decrease in suicide rate at the end of the year is extended over the last weeks of the year and represents a specific type of seasonal effect. Suicide data were extracted from individual records of the Swiss mortality statistics, 1969–2003. The data were aggregated to daily frequencies of suicide across the year. Specifically, the period October–February was examined using time-series analysis, i.e., the Box–Jenkins approach with intervention models. The time series models require a step function to account for the gradual drop in suicide frequencies in December. The decrease in suicide frequencies includes the whole Advent and is accentuated at Christmas. After the New Year, there is a sharp recovery in men's suicide rate but not in women's. The reduction in the suicide rate during the last weeks of the year exceeds the well-recognised effect of reduced rates on major public holidays. It involves valuable challenges for suicide prevention such as timing of campaigns and enhancement of social networks.
Keywords: Seasonality, Prevention, Epidemiology, Switzerland
1. Introduction
Research and administrative statistics from the 19th century onwards have shown that suicide frequency peaks in the late spring and summer months and is least frequent during the winter (Kevan, 1980, Massing and Angermeyer, 1985). These well-known seasonal fluctuations are superimposed by additional temporal fluctuations such as the drop in suicides around major public holidays such as Christmas and New Year's eve (Phillips and Wills, 1987, Jessen and Jensen, 1999). Recent descriptive analyses have suggested that the decrease in suicide frequencies in December is not restricted to Christmas and New Year's Eve but extends across the whole Advent season and represents a specific type of seasonal effect (Ajdacic-Gross et al., 2003). This study aims to provide more detailed evidence on this phenomenon using intervention models within a Box–Jenkins modelling framework.
2. Methods
These analyses rely on suicide data extracted from computerised records of Swiss mortality statistics (Minder and Zingg, 1989). The individual records cover the period 1969–2003. Switzerland used the ICD8 coding system until 1994 and then switched to ICD10 coding in 1995. Suicide comprised the ICD8 codes 950–959 and the ICD10 codes X60–X84, respectively. Suicide is regularly registered as the main cause of death. The 35-year period included 49,763 suicides—35,079 (70.5%) men and 14,684 (29.5%) women.
The data were aggregated by day of death on the annual cycle, thus resulting in virtual time series. February 29th was excluded from the analyses. The range of the aggregated daily frequencies of suicide is between 183 (May 13th) and 80 (December 25th). To allow the modelling of time series across the turn of the year, the data were arranged by sequencing the year from July 1st to June 30th. The data used in these analyses were restricted to the period October 1st to February 28th. This 151-day time window comprised 19,963 suicides (14,037 men and 5926 women). Besides analysis of overall data, the analyses were differentiated by subperiods (1969–1985 vs. 1986–2003), by sex and age (−
29, 30–59 and 60+), and by religious affiliation (Catholics vs. Protestants). Below, we present results from sex-specific analyses.
The time series of aggregated daily frequencies of suicide in men and in women were analysed with the Box–Jenkins modelling approach, which is also known as Autoregressive Integrated Moving Average–ARIMA modelling (Box and Jenkins, 1970). A basic ARIMA(p,d,q) model may comprise an auto-regressive AR(p) process, a moving-average MA(q) process, and, for the purpose of transforming the series to a (mean-)stationary series, a differencing term d (see also Gottman, 1981, Diggle, 1990, Schmitz, 1989). However, ARIMA was interesting for our purposes mainly because it makes assessing temporary departures from the baseline possible. Two approaches are at our disposal:
While the first approach gives evidence on a general level whether a shift and/or a pulse might be relevant, the second approach provides more detailed information about the specific dynamics of change. We chose the second approach to model the suicide time series at the turn of the year.
The concrete procedure was to examine firstly basic ARIMA models in time series in men and women (for steps in identification of a transfer function model, see Helfenstein, 1996). Preliminary analysis was performed with the October/November series before extending the analysis on the whole series October–February. We used maximum likelihood estimation as default. The adequacy of the models was assessed by the Ljung–Box Q-test. In addition, Akaike's Information Criterium (AIC) values were consulted to choose a model among two or more well-working alternatives (Schmitz, 1989).
Pulse and step functions in intervention analysis were represented as usual by dummy variables, and thus implemented in transfer function models. The transfer functions applied to men's and women's series included:
Transfer functions, which did not turn out to be relevant, were excluded from finalizing the models. After introducing the transfer functions, we again took a look at the AR and MA parameters to perform final corrections, if necessary. Comparing the predicted values from models incorporating transfer functions and the baseline values without transfer functions led to calculating the numbers of saved suicides.
The analyses were conducted with SAS for Windows, Version 8.
3. Results
Aggregated daily frequencies of suicide between October and February are depicted in Fig. 1 (men) and Fig. 2 (women). In an eagle-eye perspective, there is a decline of suicide frequencies towards the end of the year, which is particularly clear in the men's series. The decline in the men's series is followed by a strong upswing in the first part of January. Moreover, Christmas Eve (women) and Christmas Day (men) show particularly low frequencies of suicide.
Fig. 1.
Aggregated daily frequencies of suicide, October–February, smoothed by 5-day moving averages; men, by age group; data derived from Swiss mortality statistics, 1969–2003.
Fig. 2.
Aggregated daily frequencies of suicide, October–February, smoothed by 5-day moving averages; women, by age group; data derived from Swiss mortality statistics, 1969–2003.
The ARIMA analyses of men's and women's time series required neither preliminary data transformations nor differencing to achieve stationarity of the series. The original series, the predicted values and the residuals in analyses of overall data are shown in Fig. 3 (men) and Fig. 4 (women). The analysis of men's suicide series was obtained without use of autoregressive or moving-average terms (Table 1). The December trough, modelled by a linearly decreasing step function, reached a maximum of 29.2 at the end of the year (a decrease of 30.6% compared with the baseline of 95.4 suicides daily). The starting point of the step function was determined as November 27th. The pulse function representing Christmas Day enhanced the reduction of suicide frequencies by a value of 20.8, i.e., 21.8%. The upswing after New Year's Eve was modelled as a pulse (of magnitude 25.9) followed by a gradual swing-back of the suicide frequencies to the baseline level. A second-order transfer function model provided the best fit. The optimal starting date of this transfer function was identified as January 4th. The Ljung–Box Q-test of the model shown in Table 1 yielded χ2=3.4 with 6 degrees of freedom (df) to lag 6 and χ2=6.6 with 12 df to lag 12.
Fig. 3.
ARIMA analysis of aggregated daily frequencies of suicide, October–February, men (frequencies (bold line), predicted values (grey line) and residuals); data derived from Swiss mortality statistics, 1969–2003.
Fig. 4.
ARIMA analysis of aggregated daily frequencies of suicide, October–February, women (frequencies (bold line), predicted values (grey line) and residuals); data derived from Swiss mortality statistics, 1969–2003.
Table 1. ARIMA analyses of aggregated daily suicide frequencies, October–February, by sex; data derived from Swiss mortality statistics, 1969–2003
| Parameter | Men estimate (S.E.) | Women estimate (S.E.) | |||
|---|---|---|---|---|---|
| Baseline | 95.4 (0.87) | 40.1 (0.45) | |||
| p, d, q parameters | p (auto-regressive) | – | – | ϕ6a | −0.25 (0.08) |
| d (differencing) | – | – | – | – | |
| q (moving average) | – | – | – | – | |
| Transfer function parameters | Decline during December (linearly decreasing step function order 0) | ω0b | −29.2 (9.5) | ω0c | −8.9 (1.9) |
| Christmas eve (pulse function order 0) | ⁎ | ⁎ | ω0 | ⁎⁎ | |
| Christmas Day (pulse function order 0) | ω0 | −20.8 (3.0) | ⁎ | ⁎ | |
| January upswing (pulse function order 2) | ω0d | 25.9 (0.19) | ω0 | ⁎⁎ | |
| δ1 | 1.15 (0.19) | δ1 | ⁎⁎ | ||
| δ2 | −0.49 (0.17) | δ2 | ⁎⁎ |
aAR(6). |
bStarting date November 27th. |
cStarting date December 5th. |
dStarting date January 4th. |
In modelling of the time series of women's suicide frequencies, the use of transfer functions was confined to the December trough (Table 1). Other transfer functions turned out to be of little use, i.e., there was no support for a pulse on Christmas Eve nor for any upswing after New Year's. The linearly increasing step function representing the decline in suicides had December 5th as its starting point and resulted in a maximum of 8.9, i.e., 22.2% compared with the baseline daily number of 40.1 suicides. An AR6 parameter was introduced in the final modelling step, which probably accounts for a sequence of outlying frequencies round Christmas and New Year's. The Ljung–Box Q-test of this model yielded χ2=3.0 with 5 df to lag 6 and χ2=7.5 with 11 df to lag 12.
Cumulating the differences between predicted values and the baseline indicates that the “Advent” between 1969 and 2003 was associated with 403 fewer male suicides (i.e., 12.2% reduction in the respective time period November 27th–December 31st), but the upswing after New Year's accounted for 78 extra suicides. In women, there were 121 fewer suicides (i.e., 12.6% reduction in the respective time period December 5–31).
Analyses by subperiod, by age, as well as by religious affiliation confirmed the main finding, i.e., the step function representing a continuous decline over several weeks, both in men and women. In the men's series, the upswing after New Year's is obvious mainly in the more recent subperiod, in Protestants and in young and middle-aged men. No upswing could be shown in Catholics and in older men.
4. Discussion
Many lay persons tend to believe that suicide is most frequent in winter months, notably in December (Granberg and Westerberg, 1999). Empirical research contradicts this notion. It has been shown consistently for more than 100 years that suicide is lowest in winter and highest in the spring and summer months (Durkheim, 2002/1897). December has been the least favored month for suicide for most of the time for which we have data (Ajdacic-Gross et al., 2005). While the amplitude of seasonality has smoothed down over the last 125 years, the December trough emerged as an outstanding phenomenon besides “regular” sinusoidal swings. This study documents that the December trough in suicides in Switzerland is due to a continuous decline of suicide frequencies which abruptly ends after the New Year.
Only recently, research has demonstrated that there is a variety of effects contributing to the seasonality in suicide. Firstly, the “regular” seasonal effect has been shown to result from superimposition of method-specific seasonal patterns, that is, it is itself a compound effect (Ajdacic-Gross et al., 2003, Ajdacic-Gross et al., 2005). Secondly, a holiday and festive day effect has been noted since suicide frequencies tend to be particularly low before or on such days (Bridges, 2004). The decline in suicides immediately before holidays is typically followed by an upswing shortly after (Phillips and Wills, 1987, Jessen and Jensen, 1999). Corresponding evidence has been shown also in suicide attempts and deliberate self-harm (Cullum et al., 1993, Jessen et al., 1999). The results depend in general on the specific holiday and on the cultural context. For instance, in Denmark, Christmas Eve has shown the most impressive maximum reduction of suicides of about 30% (Jessen and Jensen, 1999). Thirdly, a birthday effect has been discussed. In a short-term view of 3–5 days, suicides tend to be postponed until birthdays have passed (Jessen and Jensen, 1999).
4.1. A new type of seasonal effects in suicide
Formally, the prolonged decline of suicide frequencies, which takes place over several weeks towards the end of the year, represents a fourth type of seasonal effects in suicide. It clearly goes beyond any “regular” sinusoidal seasonal cycles as well as the known effects of holidays and festive days. The ARIMA analyses of Swiss data for 1969–2003 confirmed the preliminary evidence that had been outlined with regard to suicides (Ajdacic-Gross et al., 2003). A similar decline effect in December was shown by Masterton (1991), who investigated parasuicide admissions in Edinburgh, 1969–1987. However, the decline in Edinburgh was obvious only in women. Apart from possible divergences in seasonal effects between suicides and suicide attempts (or parasuicides), the findings indicate that cultural and social context should be considered in interpreting the findings.
In this study, ARIMA modelling made it possible to determine several details. Besides the gradual decrease in suicide frequencies towards the end of the year, a turbulent downswing and upswing at the turn of the year was confirmed in men's series, before the rates return to their baseline levels during January. The upswing phenomenon has been shown also by studies focussing on holiday effects in suicide (Phillips and Wills, 1987, Jessen and Jensen, 1999). In the women's series, and contrary to the Edinburgh data (Masterton, 1991), the return to the baseline levels appears to proceed directly, that is, without any upswings and after-effects.
The maximum magnitude of the “Advent drop” in suicides (about 30% in men's suicides and about 20% in women's suicides) is remarkable and exceeds the most optimistic hopes in any current suicide prevention strategy. In addition, the decline in suicides occurs despite increased alcohol consumption during this period, which is a well-known risk factor in suicidal behavior (Uitenbroek, 1996, Cherpitel et al., 2004).
The ARIMA models enabled us to calculate the net effect of the decrease in suicide frequencies at the turn of the year. Contrary to short-term holiday effects (Jessen and Jensen, 1999), the upswing in men's series after New Year counterbalances the previous decrease only marginally. Not only in women but also in men, there is a remarkable net effect.
4.2. Interpretation of the findings
Essentially, the December trough in suicide may be regarded as an extended holidays effect. Thus, the interpretational options are similar to such used in explaining the effect of holidays on suicide. The temporal elasticity of this effect is an interesting challenge in suicide prevention. Apart from suggestions of Jessen et al. (Jessen and Jensen, 1999, Jessen et al., 1999), which rely on Gabennesch's “broken promise” concept (Gabennesch, 1988) (that is, on Durkheim's anomy theory), two interpretations appear to be actually suitable.
Contrary to anomy theory, which was intended to explain paradoxical effects of rapid economic and social change, Durkheim's main concept, social integration, is much more promising to explain regular or recurrent effects (Durkheim, 2002/1897). Durkheim proposed that a higher degree of social integration (i.e., individuals sharing common values, hopes and beliefs) makes suicide less acceptable. In fact, social integration is closely associated with the density of social networks. Increased density of social networks not only provides a higher level of social integration and social control, but also a higher level of social support, the latter being a predictable modifier of suicidal behaviour (Gunnell et al., 2004). Interestingly, in Switzerland, the Advent has broadly lost its religious background and has become more and more a secular phenomenon. The increase in social contacts (visiting family and friends, workplace celebrations, performances in schools and kindergartens, etc.) is one of its most striking characteristics. The social agendas are never as full as in the last weeks of the year.
The agendas point also to the second interpretation of the December trough in suicides. This one relies on the role of temporal landmarks and the perception of the future, a hidden, however important, determinant of suicidal behaviour (Aish and Wasserman, 2001). On a cognitive level, temporal landmarks help us to see things in focus; they promote the temporary postponement of hopelessness. On a pragmatic level, temporal landmarks simply help to gain time and to tide over a crisis. Yet, many people who have called a help-line or have used a phone installed at a notorious high-risk scene have survived owing to a skillfully arranged recall or appointment.
Besides the December trough also the upswing in January which was found in men's suicide series requires an explanation. A promising approach might be derived from the classification of holidays which was proposed by Phillips and Wills (1987). They differentiated holidays with vs. holidays without a subsequent upswing of suicide frequencies. The latter typically involved families and longer visits, whereas the holidays with an upswing tended to involve friends and short visits. To draw an analogy to the interpretations from above, the first type of holiday is characterized by social contacts enhancing integration, whereas the second type is rather characterized by predominance of temporal landmarks. Therefore, we would hypothesize that the preventive effect of temporal landmarks is the main clue to understand the upswing phenomenon in January. It is no surprise to find this effect mainly in men, interpreting it by men's affiliations in working life, whereas women typically take more responsibility for social contacts in family and friendship networks.
4.3. Implications for suicide prevention
The December trough presents options for suicide prevention in two different ways. Seasonal timing might play a role in strategic planning of prevention programs. A reasonable option is to arrange a program at the turn of the year in order to benefit from the inertia in the change of suicide rates, that is, trying to keep the rates at the low level of December.
Besides pragmatism, it is striking that a timely limited natural experiment works better than any well-conceived prevention plan. The dynamics of suicide frequencies at the turn of the year is a challenge for suicide prevention. According to the interpretations above, activating family and friendship networks, and systematising the use of temporal landmarks, are strategies that have not been fully exploited up to now.
4.4. Strengths and limitations of this study
In this study, ARIMA modelling was applied to a series of aggregated daily frequencies, i.e., a virtual time series. The major advantage of this uncommon procedure is to open access to the flexibility of ARIMA modelling, that is, to incorporate transfer function models accounting for such complicated dynamics as the gradual decline of suicide frequencies towards the end of the year followed by after-effects after the New Year. In addition, ARIMA modelling enabled us to calculate the difference between predicted suicides and the hypothetical baseline level, thus providing distinct information about the net effect of the decline in suicides. However, the approach does not make allowance for the variability within the daily data.
There are some other limitations to this study. We used data from the official mortality statistics. The administrative statistics have well-known weaknesses, such as the under-reporting of suicides (Minder and Zingg, 1989). No seasonal variation in under-reporting was shown in previous research (Barraclough and White, 1978); however, this issue cannot be excluded definitively. The mortality statistics also lack determinants of the suicides (e.g., history of psychiatric disorders, concomitant life events). Lastly, the specific context of Switzerland, which is a little rich country in central Europe, might caution against generalisation. However, Switzerland represents at the same time “central Europe in miniature”: different regions and cantons belong to the German- or French- or Italian-speaking parts of the country, share either a Protestant or a Catholic tradition, and have either an industrial or rural tradition.
5. Conclusion
Despite these limitations, the decline in suicides during the Advent season in Switzerland is striking and hints at the potential for suicide prevention. Furthermore, it indicates that a combination of preventive features (social networks, time-related landmarks) may be distinctly more effective than the additive effect of any specific preventive strategy alone. Advent presents a renewed opportunity for suicide prevention every year.
Acknowledgment
The data were extracted from the Swiss mortality records with the authorization granted by the Swiss Federal Statistical Office in Neuchâtel, Switzerland.
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PII: S0165-1781(06)00213-7
doi:10.1016/j.psychres.2006.07.014
© 2006 Elsevier Ireland Ltd. All rights reserved.
