# Drowning Risk Analysis Comparing Surf Bather Subgroups
## 2 Materials and Methods
### Risk Analysis Calculations  
The technical risk analysis procedure with formulas is presented in Appendix A. Appendix B provides a worked example of the method. An online Supplementary Materials provides spreadsheet calculations (BackMatter). A descriptive overview of the method consistent with Table 2 is given below. Step 1 provides a mean rating of total drowning risk contribution from swimming ability, surf swimming experience and wave height for selected surf bather subgroups (e.g., risk marker _age_ was sub-grouped as <30 years or \(\geq\)30 years) [26]. A unique bather risk score was derived from self-report data (N = 403) [22]. Scores were then weighted by each risk factor's modelled contribution (including interactions) to surf bather drowning, derived from specialist assessment based on repeated measures ANOVA [7]. From tallied risk scores, an average score represented the subgroup population's drowning risk. Step 2 provided a ratio of total person-time crude water exposure between comparison subgroupings (e.g., males vs. females) derived from direct observation [23]. (The term _crude_ here indicates that the measure of water time exposure does not capture individual variations in drowning risk associated with factors such as water depth or distance from \begin{table}
\begin{tabular}{c} \hline \hline
**Step 1** \\ To specify total drowning risk factor contribution for each subgroup \\
**Information sources and analysis:** Mean subgroup score derived from bathers’ self-reported \\ swimming abilities, surf swimming experience and prevailing wave size (on day surveyed), \\ weighted by each measured variable’s modelled contribution to drowning risk [7; 22] \\
**Outcome:** Subgroup score representing average total drowning risk from selected factors \\ \hline \hline
**Step 2** \\ To specify comparative total water exposure time between subgroups \\
**Information sources:** Total time in minutes exposed to water by subgroup [23] \\
**Outcome:** Ratio of water exposure for selected subgroups \\ \hline \hline
**Step 3** \\ To specify comparative subgroups drowning risk accounting for water exposure \\
**Information sources and analysis:** Subgroup total drowning risk (**step 1**) weighted by \\ comparative water exposure (**step 2**) \\
**Outcome:** Derived ratio of total drowning risk for selected subgroups \\ \hline \hline
**Step 4** \\ To specify comparative drowning rate between subgroups as the _gold standard_ \\
**Information sources:** Ratio of drowning frequency for subgroups from mortality data for a \\ defined period [25] \\
**Outcome:** Comparative rate of drowning frequency between selected subgroups \\ \hline \hline
**Step 5** \\ Comparison of derived drowning ratio with comparative drowning rate \\
**Information sources:** Derived subgroup drowning ratio (**step 3**) and comparative subgroup \\ drowning rate (**step 4**) \\
**Outcome:** Derived ratio from inferential data assessed against _gold standard_ from mortality data \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Conceptual summary of study method. shore.) Recorded person-time in water summed for each subgroup was recorded in minutes. The comparative total person time-in-water between subgroups was reduced to a ratio in the simplest form (i.e., \(\eta\):1) for convenience. The _antecedent_ term (\(\eta\)) applied to the first subgroup and the _consequent_ term (1) applied to the second subgroup. Step 3 combined subgroup drowning risk (step 1) and the comparative ratio of total person-time water exposure (step 2) to produce a ratio of derived drowning risk. The calculated antecedent term in this ratio is obtained from the first subgroup's product of drowning risk and antecedent (\(\eta\)) ratio result for water time exposure. The ratio consequent term representing the second subgroup is the product of that subgroup's drowning risk and the unitary consequent from step 2. This calculation produced a relative ratio of drowning risk between subgroups, accounting for exposure to water.