# Drowning Risk Analysis Comparing Surf Bather Subgroups
## Appendix A  
Technical procedure in five steps. The five steps described in Table 2 are detailed here in mathematical form. _Step 1_ Estimation of total drowning risk for a surf batter subgroup from selected factors (based on self-report dataset):  
\[\mathit{Trc}[sg\#]=\frac{\sum_{ki=1}^{ni}(Es[sa]*sa)+(Es[se]*se)+(Es[wh]*wh)+( Es[se\times wh]*(se\times wh))}{ni}\]  
_Trc_--total risk contribution from selected drowning factors  
_Es[sa, se or \(wh\)]--_effect size for selected drowning factor calculated by partial \(\eta^{2}\)  
_k_--respondent score in subgroup  
_i_--dataset employed  
_n_--subgroup sample size  
_sa_--swimming ability drowning factor  
_sg#_--subgroup  
_se_--surf experience drowning factor  
_wh_--wave height drowning factor  
The equation in step 1 combines linear summated terms plus a multiplicative term representing factor interaction [36] (pp. 3-7). All terms in the equation were found to be statistically significant contributors to drowning risk in a linear (or close to linear) pattern, based on specialist ratings [7]. Including a configural term in predictive equations had the advantage of better differentiating an individual bother's patterns of scores [37] (p. 122). Effect sizes calculated by partial \(\eta^{2}\) were used as coefficients (weights) for the three candidate risk factor variables and a single interaction of two factors found to be significant predictors of surf bather drowning in the repeated measures ANOVA model [7]. The weights were: 0.82 for swimming ability, 0.85 for surf swimming experience, 0.93 for wave height and 0.15 for the interaction of surf swimming experience and wave height. The significant interaction in the model was represented by the product of the included two variables [38] (p. 445). _Step 2_ Calculation of the comparative ratio of total person time water exposure for surf bather subgroups (based on direct observation dataset):  
\[\mathit{Awe}[sg1]\text{: }\mathit{Cwe}[sg2]=\frac{\sum_{ki=1}^{ni}sg1}{\sum_{ki=1 }^{ni}sg2}:1\]  
_Awe_--antecedent in ratio of total person time (minutes) water exposure-subgroup 1  
_Cwe_--consequent in ratio of total person time (minutes) water exposure-subgroup 2  
_k_--respondent score in subgroup  
_i_--dataset employed  
_n_--subgroup sample size  
_sg#_--subgroup  
_Step 3_ Prediction of comparative drowning risk for surf bather subgroups by combining results for step 1 (drowning risk contribution) and step 2 (relative water exposure):  
\[\mathit{Addr}[sg1]\text{: }\mathit{Cddr}[sg2]=\frac{\mathit{Trc}[sg1] \times\mathit{Awe}[sg1]}{\mathit{Trc}[sg2]}:1\]  
_Addr_--antecedent in ratio of derived drowning risk-subgroup 1  
_Awe_--antecedent in ratio of total person time (minutes) water exposure-subgroup 1_Cddr_--consequent in ratio of derived drowning risk-subgroup 2 _sg_#-- subgroup _Trc_--total risk contribution from selected drowning factors _Step 4_ Calculation of comparative specific drowning rate for selected subgroupings (based on mortality dataset) and 95% CI for antecedent:  
\[Asdr[sg1]\text{: }Csdr[sg2]=\frac{\#sg1}{\#sg2}\text{: }1\]  
_Asdr_--antecedent in ratio of specific drowning rate-subgroup 1 _Csdr_--consequent in ratio of specific drowning rate-subgroup 2 _sg_#--subgroup #--frequency within subgroup  
95% _CI_ for antecedent \((Asdr[sg1])-\)Adjusted Wald bimomial test for confidence intervals \(i\) Enter numerator frequency and subgroup total frequency into online calculator to find \(Low\) 95% _CI_ and \(High\) 95% _CI_  
_ii_\(Asdr[sg1]\) _lower boundary_ : \(Csdr[sg2]=\frac{Low95\%CI*(\#\text{{sg}}1+\#\text{{sg}}2)}{(1-Low95\% CI)*( \#\text{{sg}}1+\#\text{{sg}}2)}\): 1 _iii_\(Asdr[sg1]\) _upper boundary_ : \(Csdr[sg2]=\frac{High95\%CI*(\#\text{{sg}}1+\#\text{{sg}}2)}{(1-High95\% CI)*( \#\text{{sg}}1+\#\text{{sg}}2)}\): 1  
Specific comparative rates calculated in step 4 are a time-bound subset of ratios [39] (p. 152). For the calculations here, the period was four years (2001 to 2005).