Statistical methodology
Suicide incidence rates
This report uses incidence rates to measure how often suicide occurs amongst the 3 Australian Defence Force (ADF) service groups, as well as in the Australian population. The incidence rate is the total number of deaths by suicide in a population over a specific period of time, divided by population time at risk during this time. In this study, the sum of the population at 30 June in each year of the relevant period is used as a proxy for population time at risk. Suicide incidence rates are expressed as the number of deaths per 100,000 population per year.
Rates based on small numbers
Rates based on small numbers of events can fluctuate from year to year for reasons other than a true change in the underlying risk of the event.
In this report, rates are not reported when there are fewer than 5 events, as rates produced using small numbers can be sensitive to small changes in counts of deaths over time.
In this report, rates denoted with an asterisk (*) should be interpreted with caution as the number of events is fewer than 20. These rates are subject to large fluctuations.
Standardised mortality ratios
Age-adjusted comparisons between the suicide rate in each of the 3 ADF service status groups and the Australian population were calculated using Standardised Mortality Ratios (SMR). The SMR is a widely recognised measure used to account for differences in age structures when comparing death rates between populations. This method of standardisation can be used when analysing relatively rare events, that is, where number of deaths is less than 25 for the analysed time period. The SMR is used to control for the fact that the ADF service status groups have a younger age profile than the Australian population, and rates of suicide vary by age in both the study populations and the Australian population. The SMRs control for these differences, enabling comparisons of suicide counts between the service status groups and Australia without the confounding effect of differences in age.
The SMR is calculated as the observed number of events (deaths by suicide) in the study population divided by the number of events that would be expected if the study population had the same age and sex specific rates as the comparison population. SMRs greater than 1.0 indicate a greater number of suicides in the ADF population than expected; and SMRs less than 1.0 indicate a lower number of suicides than expected in the ADF population.
Unlike suicide rates, SMRs only provide information about the 2 populations the statistic is based on. Comparing SMRs cannot be used to draw conclusions about the relative adjusted mortality rates of the study populations. This is because each SMR measure provides a comparison that is specific to the 2 populations involved.
Comparisons with the Australian population are not calculated for other breakdowns such as by length of service and rank as only adjusting for age and sex does not account for all the differences in the populations. In addition, it is considered more useful to compare between the different levels of these groups rather than with the Australian population.
Cox proportional hazards model
Survival analysis models the time it takes for an ‘event’ to occur after an ‘intervention’, termed ‘survival time’. The Cox proportional hazards regression model (Cox 1972) is the most common method for studying the dependency of survival time on one or more predictor variables.
In this report the event measured is death by suicide, and the intervention is separation from the ADF. Each individual enters the model on their separation date and is censored from further contribution at the point of their death (not by suicide) or at the analysis end date of 31 December 2022 for those alive.
The hazard ratio (HR) estimated via a Cox proportional hazards model measures the relative difference in hazard rates between comparison groups. Hazard rate is the instantaneous rate at which a particular event occurs at any point in time. For simplicity, hazard ratios are interpreted as rate ratios in this report.
The ‘survival’ package in the statistical computing software R was used to fit the Cox models presented in this study (Fox and Weisberg 2018).
An assumption of the Cox model is that the effect or hazard between groups within a variable remains approximately proportional over time (the proportional hazards assumption). Tests for proportional hazards were performed on the models presented for each variable and for the overall model. Where the assumption was not met and a time dependency was observed for a variable, adjustments were made to analyse the time-dependent variable in separate time periods where proportional hazards were observed (Therneau et al. 2024).
Statistical significance was determined when the hazard ratio 95% CI includes the value of 1.
Confidence Intervals
This report uses confidence intervals of 95% in the calculation of rates and SMRs. Broadly speaking wider CIs imply less certainty around a calculated value, and narrower CIs imply more certainty. Specifically, a CI at 95% suggests that repeated samples calculating the CI in the same manner would contain the true value 95% of the time.
Using confidence intervals to test for statistical significance
Statistical significance is based on a measure that indicates how likely it is that an observed difference, or a larger one, would occur under the conditions of the null hypothesis.
In this study, 95% confidence intervals (CIs) are provided for each standardised mortality ratio (SMR) and suicide rate to indicate the level of uncertainty around these estimates due to random fluctuations in the number of suicides over time. Estimates produced using low numbers can be sensitive to small changes in numbers of deaths over time and will therefore have wide CIs. CIs at 95% are provided within this report as they may account for the variation in absolute numbers of deaths by suicide over time (related to the small sample size). These assume that the suicide counts used in this analysis can be described by a Poisson distribution.
It is important to note that there are other sources of uncertainty, such as the linkage error, that are not captured by the provided CIs.
Use of CIs is the simplest way to test for significant differences between service groups and Australian comparison groups. For the purpose of this report, differences are deemed to be statistically significant if CIs do not overlap with each other (when comparing suicide rates) or 1.0 (in the case of an SMR). The CIs in this report cannot be used to determine the significance of differences between rates calculated for overlapping 3-year time periods.
Where the CIs are wide, for example in the case of the SMR for ex-serving females, sensitivity analysis was conducted. This analysis found that slight changes to the numbers of suicides did not significantly alter the result.
Population and suicide monitoring period
The population used in this report includes all ADF members who have served at least one day since 1 January 1985. As of 31 December 2022, around 392,000 Australians had served at least one day in the ADF between 1 January 1985 and 31 December 2022. Of these, 373,000 were still alive, comprising 58,800 permanent, 38,800 reserve, and 274,000 ex-serving.
Box 2 above gives more information on the ADF population used in this report and how it compares to the Australian population. Last year’s report was based on ADF members with at least one day of service since 1 January 1985 who died by suicide between 1 January 1997 and 31 December 2022. The current report uses the same ADF cohort, plus the 2022 data.
For more information on the demographics of this population, see the report: Serving and ex-serving Australian Defence Force members who have served since 1985: population characteristics 2019
Cox DR (1972). ‘Regression models and life‐tables’, Journal of the Royal Statistical Society: Series B (Methodological), 34(2):187-202, doi.org/10.1111/j.2517-6161.1972.tb00899.x.
Fox, J and Weisberg S (2002). Cox proportional-hazards regression for survival data, An R and S-PLUS companion to applied regression, accessed 27 June 2024.
Therneau T, Crowson C and Atkinson E (2024) Using Time Dependent Coefficients in the Cox Model, accessed 27 June 2024.