## 4 Results for East Japan  
In Figure 6, the red line represents the KM curve of all of the panels. Survival probability declined to 50% after approximately 25 years, implying that the deterioration rate is faster than in the Tokyo region, as shown in Section 5. The representative KM of some category variables with very different survival probability declinations are shown in Figure 8. Figure 8a shows results based on whether panels are on the edge. Figure 8b shows results based on whether the panels are positioned near the expansion joint. Figure 8c presents the survival probability of two de-icing groups, below and above 20 t/km. The survival probability declination of these variables was found to be very different, indicating that these factors could strongly affect the deterioration rate. Figure 8: Survival probability of some category variables in East Japan; (**a**) edges; (**b**) near expansion; (**c**) de-icing salt. The univariate analysis gave us a general understanding of the explanatory variables, separately and on one side. The KM curve confirmed the basic information of each category description variable and roughly plotted the deterioration rate. However, to evaluate the effect of all of the factors and determine the relationship between all of the explanatory variables, a multivariate analysis was performed; the result is shown in Table 3.  
The hazard ratio is interpreted as the ratio of the possibility of degradation over any time duration. The \(p\) value is from the Wald test, and determines the significance of the results. The equation is as follows:  
\[p\ Value=\frac{(\hat{\beta}-\beta_{0}\ )}{\hat{se}(\hat{\beta})}\sim\mathcal{N}(0,1) \tag{10}\]  
Essentially, it tests whether \(\hat{\beta}\) is statistically equal to \(\beta_{0}\). In this analysis, \(\beta_{0}\) always equals 0 because the hazard ratio is calculated using \(exp(\hat{\beta})\). Therefore, the \(p\) value indicates whether \(\hat{\beta}\) significantly contributes to the hazard ratio. For numerical explanation variables, an increase in traffic volume slightly increased the hazard ratio. Moreover, the average slab thickness in East Japan was 22.4 cm, and the hazard ratio of the slab thickness was close to 1; the \(p\) value also showed that \(\hat{\beta}\) did not make a significant contribution to the hazard ratio. This result implies that fatigue damage was not a major reason for the deterioration of the bridge slabs. However, winter precipitation and high de-icing salt usage greatly increased the risk of deterioration. The reason is shown in Figure 9. Due to heavy snowfall and snow removal, snow accumulated at the edge of the slab and became a snow mound. The snow mound melted little by little, and during this process, snowmelt with a large quantity of de-icing salt penetrated the crack, keeping the slab in a condition of consistently high humidity and salinity and resulting in further cracking and steel corrosion. Therefore, deterioration greatly accelerated. \begin{table}
\begin{tabular}{c c c c c} \hline  & **Hazard Ratio** & **Lower 0.95** & **Upper 0.95** & \(p\)**Value** \\ \hline Traffic & 1.119 & 1.078 & 1.161 & 0.000 \\ Span Length & 0.907 & 0.877 & 0.938 & 0.000 \\ Slab Thickness & 0.966 & 0.931 & 1.002 & 0.067 \\ Winter Rain & 1.305 & 1.253 & 1.359 & 0.000 \\ \hline De-icing Salt & & & & \\ Below 20 & 1.000 & & & \\ Over 20 & 1.331 & 1.236 & 1.434 & 0.000 \\ \hline Crossing Condition & & & & \\ River & 1.000 & & & \\ Overpass & 0.951 & 0.880 & 1.028 & 0.209 \\ Unknown & 0.852 & 0.726 & 0.999 & 0.049 \\ \hline Edge & & & & \\ No & 1.000 & & & \\ Yes & 3.840 & 3.467 & 4.254 & 0.000 \\ \hline Near Expansion & & & & \\ No & 1.000 & & & \\ Yes & 1.645 & 1.532 & 1.766 & 0.000 \\ \hline Slope & & & & \\
0.0–1.0 & 1.000 & & & \\ Over 1.0 & 0.798 & 0.740 & 0.861 & 0.000 \\ Unknown & 3.730 & 3.076 & 4.521 & 0.000 \\ \hline Waterproof & & & & \\ Yes & 1.000 & & & \\ No & 1.377 & 1.259 & 1.505 & 0.000 \\ \hline \end{tabular}
\end{table} 
Table 3: Multivariate Cox regression analysis result for East Japan.