China
Africa
Explore chapters and articles related to this topic
Duration Models
Published in Simon Washington, Matthew Karlaftis, Fred Mannering, Panagiotis Anastasopoulos, Statistical and Econometric Methods for Transportation Data Analysis, 2020
Simon Washington, Matthew Karlaftis, Fred Mannering, Panagiotis Anastasopoulos
A nonparametric approach for modeling the hazard function is convenient when little or no knowledge of the functional form of the hazard is available. Such an approach was developed by Cox (1972) and is based on the proportional hazards approach. The Cox proportional hazards model is semi-parametric because EXP(βX) is still used as the functional form of the explanatory variable influence. The model is based on the ratio of hazards—so that the probability of an observation i exiting a duration at time ti, given that at least one observation exits at time ti, is given as () EXP(βXi)/∑j∈RiEXP(βXj),
Radiomics and quantitative imaging
Published in Jun Deng, Lei Xing, Big Data in Radiation Oncology, 2019
Dennis Mackin, Laurence E. Court
In model building and in radiomics, there is often a trade-off between the accuracy of the prediction and the interpretability of the model. To understand this trade-off, it helps to first consider the three categories of models common in radiomics: regression, classification, or survival analysis. Regression models predict a continuous outcome value. Classification models assign data observations to one or more groups. Survival analysis predicts the time until an event, such as a local recurrence of a tumor or death, from data that are censored. In censored data, the time of the event of interest is unknown for some observations. Each of these three types of model is associated with a commonly used statistical model: the linear model for regression, logistic regression model for classification, and Cox proportional hazard model for survival analysis. The popularity of these models is due in a large part to the interpretability of the model coefficients. The coefficients in linear models are the expected change in the predicted value for a unit change in the corresponding data feature. For logistic regression, the coefficients estimate the change in the log odds ratio of classes for a unit change of the date features. The coefficients in a Cox proportional hazards model scale the likelihood of the occurrence of the event, or “hazard.” These models can be explained to caregivers and patients, perhaps making them more likely to gain acceptance in the clinic (Caruana et al. 2015; Breiman 2001b).
Marginally and Conditionally Specified Multivariate Survival Models: A Survey
Published in Donald B. Owen, Subir Ghosh, William R. Schucany, William B. Smith, Statistics of Quality, 2020
A very popular survival model is the proportional hazards model. In this case we set μ = 0, σ = 1, γ = 1 in Eq. (5) to obtain what might be called a “Lehmann alternatives” model: () F¯X(x)=[F¯0(x)]δ
Condition-based maintenance for a degradation-shock dependence system under warranty
Published in International Journal of Production Research, 2023
We use a proportional-hazards model (Cox 1992) to estimate the extra effects of the degradation-rate acceleration. A regression-based model that is widely used is the proportional-hazards model. The time-dependent proportional-hazards model is generally expressed as (Elsayed 2012; Shyur, Elsayed, and Luxhøj 1999) where and denote the regression coefficient and stress function, respectively; is modified multiplicatively by covariates and is referred to as the baseline failure-rate function (Elsayed 2012; Shyur, Elsayed, and Luxhøj 1999). The degradation path is any unknown function, which can be either monotonically decreasing or monotonically increasing. The function for degradation is considered to endure item-to-item deviation by including the random variable X, and it is given by