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Analyzing time to event outcomes with a Cox regression model

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Abstract Survival analysis is concerned with studying the time between entry to a study and a subsequent event (such as death). Survival times now often refer to the development of a particular symptom or to relapse after remission of a disease, as well as to the time to death. A Cox regression model is a statistical technique for exploring the relationship between the survival of a patient and several explanatory variables. A Cox regression model provides an estimate of the treatment effect on survival after adjustment for other explanatory variables. Also, it allows us to estimate the hazard or risk of death for an individual given their prognostic variables. A Cox regression model must be fitted using an appropriate computer program (such as R, S‐Plus, SAS, STATA, or SPSS). The final model from a Cox regression analysis yields an equation for the hazard as a function of several explanatory variables. Interpreting the Cox regression model involves examining the coefficients for each explanatory variable. A positive regression coefficient sign for an explanatory variable means that the hazard is higher and thus the prognosis worse. Conversely, a negative regression coefficient implies a worse prognosis for patients with higher values of that variable. WIREs Comput Stat 2012, 4:310–315. doi: 10.1002/wics.1197 This article is categorized under: Applications of Computational Statistics > Clinical Trials Statistical and Graphical Methods of Data Analysis > Reliability, Survivability, and Quality Control

Kaplan estimate of the survival function for 10 patients with malignant melanoma skin cancer.

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A plot of the logarithm of the negative logarithm of the estimated survivor function against the logarithm of survival time by randomized group for the AIM HIGH trial data (n = 674).

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Kaplan–Meier survival curve estimates for 338 malignant melanoma cancer patients on interferon treatment, compared to the survival of 336 controls.

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Statistical and Graphical Methods of Data Analysis > Reliability, Survivability, and Quality Control
Applications of Computational Statistics > Clinical Trials

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