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Lifetime assessment of structural concrete: Multi-scale and multi-chemo-mechanistic approach
Published in Airong Chen, Xin Ruan, Dan M. Frangopol, Life-Cycle Civil Engineering: Innovation, Theory and Practice, 2021
Appearing of efflorescence and leakage of the rust is defined as ‘event' for survival analysis (Fang et al. 2018; Yamazaki & Ishida 2015). The Kaplan–Meier curve (non-parametric univariate analysis) which is shown in Figure 19 indicates that half of bridges decks have experienced the ‘event' after 50 years of use. COX regression (semi-parametric multivariate method) which can quantify the effect of all deterioration factors is shown in same Figure. Risk increases as a variate increases when hazard ratio is higher than 1, and vice versa. It can be seen that winter precipitation and high de-icing salt usage greatly increase the risk of deterioration, indicating that severe environment is an important factor causing slab deterioration. This statistical analysis was conducted only based on the inspection data. Thus, this is the knowledge earned from the documentation alone.
Data driven maintenance cycle focusing on deterioration mechanism of road bridge RC decks
Published in Hiroshi Yokota, Dan M. Frangopol, Bridge Maintenance, Safety, Management, Life-Cycle Sustainability and Innovations, 2021
Tetsuya Ishida, Jie Fang, Eissa Fathalla, Tomoya Furukawa
The hazard ratio is interpreted as the ratio of mortality or failure for two samples at any duration of time. Hazard ratio higher than one reveals increased risk, and vice versa. In order to give a better comparison various factors for the degradation of the bridge decks, all covariates are standardized by using Equation 4. zi=xi−μσ
Hazard Characterization and Dose–Response Assessment
Published in Ted W. Simon, Environmental Risk Assessment, 2019
The odds of having the disease in a given quantile is P(risk)/(1–P(risk)). The odds ratio is the ratio of the odds in a given quantile and the odds in the reference quantile. The uncertainty in the number of cases is binomially distributed and can be modeled as random binomial variable. Hazard ratio differs from relative risk only in the inclusion of time in the denominator; hence, for a given exposure bin, instead of the total number of persons at risk, a value such as person-years at risk is used.
Modeling lane-change-related crashes with lane-specific real-time traffic and weather data
Published in Journal of Intelligent Transportation Systems, 2018
Zhi Chen, Xiao Qin, Md. Razaur Rahman Shaon
The hazard ratio of each variable describes the ratio of change in the probability of a crash with one unit change in that variable. A hazard ratio greater than 1 means that the chance of a crash increases as the value of that variable increases. The noncrash events happening at the same location and same time on the same day of the week were chosen for data collection. Thus, each crash and its corresponding noncrash events form one stratum, and the whole data set are stratified based on the location, time, and date of each crash. This stratification feature suggests that it may be questionable to apply popular variable selection methods (e.g. decision tree, random forest) to narrow down the number of variables, as they may not be able to handle stratified data.
Competing risks models for the deterioration of highway pavement subject to hurricane events
Published in Structure and Infrastructure Engineering, 2019
Sylvester Inkoom, John O. Sobanjo
The hazard ratio on the other hand is the ratio of the hazard rates corresponding to the conditions described by two levels of an explanatory variable (Jeong & Fine, 2007; Kleinbaum & Klein, 2012; Latouche, Allignol, Beyersmann, Labopin, & Fine, 2013; Wellek 1993; Zhao & Sun, 2004). The hazard ratio compares the hazard rates of the competing events based on the age covariate. The mean estimate and the confidence intervals are used to describe the extent or impact of one risk compared to the other. The crack deterioration is considered as the main event and the other hurricane categories as the competing events of failure.
Statistical modelling for cancer mortality
Published in Letters in Biomathematics, 2019
The Cox model is expressed by the hazard function denoted by . Briefly, the hazard function can be interpreted as the risk of dying at time t. The Cox model can be written as a multiple linear regression of the logarithm of the hazard on the variables , with the baseline hazard being an ‘intercept’ term that varies with time. The quantities are called hazard ratios (HR). A value of is greater than zero, or equivalently a hazard ratio greater than one, indicates that as the value of the covariate increases, the event hazard increases and thus the length of survival decreases. Put another way: a hazard ratio above 1 indicates a covariate that is positively associated with the event probability, and thus negatively associated with the length of survival. A positive sign means that the hazard (risk of death) is higher, and thus the prognosis worse, for subjects with higher values of that variable. For good prognosis means the negative sign that the hazard is lower. When hazard ratio is equal to 1, then there is no effect. Therefore, A covariate with hazard ratio (i.e. when ) is called bad prognostic factor.A covariate with hazard ratio < 1 (i.e. when ) is called good prognostic factor.