Abstract
Cox regression is the method for investigating the effect of several variables upon the time a specified event takes to happen. It is also known as the proportional hazards regression because it is all revolved around survival analysis. The Cox proportional hazards (CPH) model is the most frequently used approach for survival analysis in a wide variety of fields. This article summarizes current research, especially its applications in the area of diagnosis and treatment of coronavirus disease 2019 (COVID-19). Also, the pros and cons of competitive machine learning (ML) models for targeting the same object will be presented.
TopBackground
The Cox Proportional Hazards Regression Model, or the Cox regression model for short, was discovered by David Roxbee Cox in 1972. It is commonly used for survival analysis, as it is concerned with the amount of time that passes until a particular event occurs, such as a death of a patient. Hazard function is the term for the rate at which a patient's death is known. Being a semiparametric model, it is a regression model with both a finite- and an infinite-dimensional component. This means there are no assumptions on the shape of the baseline hazard function and the measure of effect is the hazard rate. The hazard represents the anticipated number of events per a single unit of time. Consequently, the hazard in a group can exceed 1 at times. The three main uses for Cox regression are independence of survival times between separate individuals of a sample, a multiplicative relationship between independent variable predictors and the hazard (as opposed to a linear relationship like of a multiple linear regression analysis can give), and a constant hazard ratio over time progression (LaMorte, 2016).
Key Terms in this Chapter
Proportionality Assumption: Proportionality assumption in Cox Regression means that the ratio of the hazards for any two individuals is constant over time. If we don't have proportional hazards, the regression coefficient should be modeled over time and referred to as a time-varying coefficient.
Concordance Index (C-Index): The c-index is a measure of rank correlation between the models’ predicted risk scores and the observed time points (in the test data). It can be thought as a generalization of Kendall’s correlation t tailored specifically for right-censored survival data.
Prediction Models: Predictive modelling uses statistics to predict outcomes. Most often the event one wants to predict is in the future, but predictive modelling can be applied to any type of unknown event.
Medical Decision-Making: Refers to the complexity of establishing a diagnosis and/or selecting a management option.
Survival Analysis: Survival analysis is a collection of statistical procedures for data analysis where the outcome variable of interest is time until an event occurs.
Cox Regression (or Proportional Hazards Regression): A method for investigating the effect of several variables upon the time a specified event takes to happen.