## Survival Model Development  
### NBI Data Extraction  
Numerical ratings given for the condition of major bridge components form some of the 117 data entries in the NBI records used in this study. The following procedures were used to extract data for this study. Further details on the data extraction and analysis are presented in a thesis by [PERSON] [39]. A list of extracted data and the software code used to analyse the data are provided as Supplementary Materials accompanying this paper.  
* Bridge records without a superstructure rating (NBI item 59) and/or construction date (NBI item 27) were removed.
* All reconstructed or rehabilitated superstructures (NBI item 106) were removed.
* Uncommon bridge types and superstructures were excluded. Steel superstructures (NBI item 43A, code 1, 2, 5, or 6) as well as concrete and pre-stressed concrete superstructures (NBI item 43A, code 3 or 4) were retained for analysis. All other structural materials and superstructures were excluded from the data.
* Bridges with more common structural systems such as slab, multi-beam, girder, tee beam, floor beam, and box beam (NBI item 43B, code 1 to 6) were retained for analysis. Data from bridges with less common structural systems such as truss, arch, and cable-stayed were removed.
* Bridges with superstructure ratings other than 5 were excluded from the dataset.
* The retained bridge records were then classified based on their superstructure material type (NBI, item 59) (steel or concrete).  
There are several NBI parameters that may potentially affect the bridge superstructure reliability. These include bridge age, deck area, Average Daily Traffic (ADT), maximum span length (MSL), and superstructure type (steel or concrete).  
[PERSON] et al. [18] showed that the deck area was an important factor in reliability of bridge decks. This parameter was initially considered as a covariate in this study. In a multi-beam bridge, a large deck area may indicate a large superstructure member length, a large deck width (more beams), or both. With a larger overall superstructure member length, the probability of appearance of defects would increase. The maximum span length could also be a relevant parameter as it has direct influence on bending moments. The ADT was included as a covariate because of its influence on load and \"wear and tear\" on the bridge. The Average Daily Truck Traffic (ADTT) could also be considered but was not selected because ADT and ADTT are not independent of each other (i.e., one must be selected). ADT may also be related to usage of corrosion-inducing de-icing salts. Finally, the type of superstructure (steel or concrete) may also be relevant to superstructure reliability. For the superstructure type parameter, a discrete variable was assigned. The results of survival analyses can be used to assess whether a covariate is statistically significant.  
A correlation analysis was first performed among considered covariates to determine if they were correlated. Results of this analysis are shown in Table 1.  
The correlation analysis indicated that there was moderate correlation between deck area and maximum span length parameters (Pearson correlation coefficient of 0.665), and therefore, the two parameters are not independent of each other. This indicates that both parameters cannot be used simultaneously and only one should be selected. The maximum span length can significantly affect the overall structural response of the bridge. Therefore, in this study, the maximum span length is included as a parameter (in lieu of deck area) for the survival analysis of bridge superstructures.