## 3 Results
### Objective 1  
Using the independent variables from Table 1 as the individual predictors and the post-incident state binary levels of disability and medical state as the dependent (output) variable, a nominal LR model was fit to the data. In order to evaluate the effectiveness of the LR model in estimating the probability of a disability post-incident state, the overall model evaluation (Table 2), statistical significance of individual independent variables (Table 3), and predicted probabilities' validation (Table 4) were extracted from the model outputs. A logistic model provides a better fit to the data if it demonstrates an improvement over the intercept-only model (reduced model). The whole model tests the difference between the complete model that includes the intercepts and all effects versus the reduced model, and is used to measure the significance of the repressors as a whole to the fit [34]. The whole model test chi-squared value of 1168.84 showed the significance of the LR model versus the intercept only model (\(p\)-value \(<\) 0.05). The likelihood ratio test also yielded the same result as the whole model test regarding the effectiveness of the LR model. The LR model is helpful in demonstrating the relationship between the input and output variables. To examine the effects of the independent variables on the probability of disability post-incident state versus medical, the Wald chi-squared and their corresponding \(p\)-values were measured. For a \(p\)-value less than 0.05 (\(\alpha\) = 0.05 at 95% confidence interval), the independent variables were considered statistically significant in the model, which meant it was likely to affect the probability of the binary outcome [35]. Table 3 shows the Wald chi-squared values and their corresponding \(p\)-values for individual predictors in the model. It indicates that all model input variables are statistically significant on estimating the probability of post-incident state. Using the LR model formula, the probability of disability vs medical post-incident state was calculated per case. Comparing the probability of medical vs disability post-incident state, the one with higher probability was labeled as the predicted class. The predicted post-incident states were compared with the actual post-incident states from the data. The degree to which the predicted probabilities agree with the observed outcomes from the original data is expressed as a classification table [28]. Using the LR output classifications, the frequency of actual versus predicted outcomes are given in Table 4. According to the percentage of correct predictions, the prediction of the medical post-incident state was more accurate than that of the disability state. This observation was also supported by the magnitude of sensitivity (2.04%) compared to that of specificity (99.08%). Sensitivity measures the proportion of correctly classified events (disability post-incident state in this study), whereas specificity measures the proportion of correctly specified nonevents (medical post-incident state in this study) [28]. The LR model could predict the post-incident state of similar occupational injuries with an accuracy rate of 77% (gained by dividing the total number of accurately classified outcomes over the total number of cases). The overall correct prediction of 77% is an improvement over the chance level [27]. \begin{table}
\begin{tabular}{c c c c} \hline \multirow{2}{*}{**Actual Post-Incident State**} & \multicolumn{3}{c}{**Predicted Post-Incident State**} \\ \cline{2-4}  & **Disability** & **Medical** & **\% Correct** \\ \hline Disability & 65 & 3123 & 2.04\% [65/(65 + 3123)] \\ Medical & 90 & 10,579 & 99.08\% [10,579/(90 + 10,579)] \\ \hline Overall \% correct (n = 13,867) & & 76.75\% [(10,579 + 65)/n] \\ \hline \end{tabular}
\end{table} 
Table 4: Classification table for the LR model.