# Drowning Risk Analysis Comparing Surf Bather Subgroups
## Appendix B  
Worked example of method in five steps (see also online Supplementary Materials). Subgroup comparison within gender for males vs. females. **Step 1--subgroup drowning risk (grouped by a specified risk marker variable)**  
\[ \begin{array}{c}\text{{Trc}}[sg\#]=\frac{\sum_{i=1}^{\text{all}}0.82 sa+0.885 ser+0.93 wh+0.15(se\times\text{{inf}})}{\sum_{i=1}^{\text{all}}3}\\ \text{{Trc}}[sg1]-\text{{Males}}=\frac{923.90}{239}=5.02\\ \text{{Trc}}[sg2]-\text{{Females}}=\frac{1280.31}{209}=5.74\end{array} \]  
Result: Males (_sg_1) had relatively lower mean contribution to drowning risk from selected factors (_Trc_) compared to females (_sg_2). **Step 2--Ratio of total person time exposure to water**  
\[ \begin{array}{c}\text{{Awe}}[sg1]\text{: }C\text{{Cwe}}[sg1]=\frac{\sum_{i=1}^{ \text{all}}sg1}{\sum_{i=1}^{\text{all}}s2}\text{: }1\\ \text{{Males}}:\text{{Females}}=\frac{5668\text{{min}}}{1388\text{{min}}}:1=4.24 \text{:}1\end{array} \]Result: Males (sg1) have relatively higher water exposure (_Awe_) compared to females (_Cave_). **Step 3--Derived drowning risk**  
\[ \begin{array}{c}Addr[sg1]:Cddr[sg2]=\frac{\texttt{Tr}[sg1]\times\texttt{A}r[sg1 ]}{\texttt{Tr}[sg2]}:1\\ Males:Females=\frac{5.02\times 4.24}{5.74}:1=3.71:1\end{array} \]  
Result: Males (sg1) have relatively higher derived drowning risk (_Addr_) compared to females (_Cddr_), accounting for differences in water exposure (_Awe_) and total contributed drowning risk from factors (_Trc_). **Step 4--Specific drowning rate and 95% CI for antecedent**  
\[ \begin{array}{c}Asdr[sg1]:Csdr[sg2]=\frac{\texttt{Ag}1}{\texttt{Ag}g2}:1\\ Males:Females=\frac{110}{18}:1=6.11:1\end{array} \]  
Result: Males (_sg1_) have relatively higher specific drowning rate (_Asdr_) compared to females (_Csdr_). This rate of 6.11 is higher than the derived drowning risk ratio for males (_Addr_) of 3.71. \[\begin{array}{c}95\% CI\text{ for antecedent }(Asdr[sg1])=6.11(proportion\text{ }of\text{ }0.8594)\\ \text{Adjusted Wald bimomial test for confidence intervals :}\\ \text{lower limit }=\text{ }0.7878\\ \text{upper limit }=\text{ }0.9100\\ \text{ }\  
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