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Lecture

Survival Analysis: Cox Proportional Hazards Model

In courses (2)

MATH-474: Statistics for genomic data analysis

After a short introduction to basic molecular biology and genomic technologies, this course covers the most useful statistical concepts and methods for the analysis of genomic data. ...

MATH-493: Applied biostatistics

This course covers topics in applied biostatistics, with an emphasis on practical aspects of data analysis using R statistical software. Topics include types of studies and their design and analysis, high dimensional data analysis (genetic/genomic) and oth ...

Description

This lecture covers the Cox proportional hazards model, a widely used method in survival analysis. It explains how to estimate hazard functions, assess model assumptions, and interpret results using residuals. Parametric and non-parametric estimation methods are discussed, along with practical examples and tools in R.

Instructor

Darlene Goldstein

Official source

Related concepts (32)

Survival analysis

Survival analysis is a branch of statistics for analyzing the expected duration of time until one event occurs, such as death in biological organisms and failure in mechanical systems. This topic is called reliability theory or reliability analysis in engineering, duration analysis or duration modelling in economics, and event history analysis in sociology.

Survival function

The survival function is a function that gives the probability that a patient, device, or other object of interest will survive past a certain time. The survival function is also known as the survivor function or reliability function. The term reliability function is common in engineering while the term survival function is used in a broader range of applications, including human mortality. The survival function is the complementary cumulative distribution function of the lifetime.

Proportional hazards model

Proportional hazards models are a class of survival models in statistics. Survival models relate the time that passes, before some event occurs, to one or more covariates that may be associated with that quantity of time. In a proportional hazards model, the unique effect of a unit increase in a covariate is multiplicative with respect to the hazard rate. For example, taking a drug may halve one's hazard rate for a stroke occurring, or, changing the material from which a manufactured component is constructed may double its hazard rate for failure.

Hazard ratio

In survival analysis, the hazard ratio (HR) is the ratio of the hazard rates corresponding to the conditions characterised by two distinct levels of a treatment variable of interest. For example, in a clinical study of a drug, the treated population may die at twice the rate per unit time of the control population. The hazard ratio would be 2, indicating higher hazard of death from the treatment. A scientific paper might utilise a Hazard Ratio (HR) to state something as follows.

Nonparametric statistics

Nonparametric statistics is the type of statistics that is not restricted by assumptions concerning the nature of the population from which a sample is drawn. This is opposed to parametric statistics, for which a problem is restricted a priori by assumptions concerning the specific distribution of the population (such as the normal distribution) and parameters (such the mean or variance).

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