# What is a Cox model?

A Cox model, also known as a proportional hazards model, is a statistical model used to analyze the relationship between the occurrence of an event (such as death or disease) and one or more predictor variables (such as age, gender, or treatment). It is commonly used in medical research to evaluate the effect of risk factors on the risk of a particular outcome, such as the effect of a particular treatment on the risk of death or disease progression.

In a Cox model, the hazard ratio (HR) is used to measure the effect of a predictor variable on the risk of the event. The HR represents the relative risk of the event occurring for a given unit change in the predictor variable, with a HR greater than 1 indicating an increased risk and a HR less than 1 indicating a decreased risk.

The Cox model is a semi-parametric model, meaning that it does not make assumptions about the specific functional form of the relationship between the predictor variables and the event, but it does assume that the hazard function is proportional across different levels of the predictor variables. This allows the model to be flexible in modeling complex relationships between the predictor variables and the event, while still allowing for statistical inference to be made about the effect of the predictor variables on the event.

The Cox model is widely used in medical research to analyze data from clinical trials and observational studies, and it has become an important tool for evaluating the effectiveness of treatments and interventions in reducing the risk of adverse outcomes.

# How to perform a Cox model on EasyMedStat?

First, you need to have appropriate data to perform a Cox model. You will need at least 3 date-formatted variables:

- The date of inclusion, ie, the date at which the survival analysis is started. It could be the date of surgery, the date of the initiation of the treatment, ...
- The date of the last follow-up which is the date at which the latest news are known for a given patient
- The date of the event to be studied

Then, to perform your analysis:

- Open the menu "Statistics" and click on "Predictive factors (multivariate)"
- In the variable to explain, choose the date of the event to be studied
- In the predictive variables panel, choose the variables that are likely to predict your event

If your Cox model is not calculated, it is most likely that you did not provide the appropriate data in order to perform survival analyses. You may find more information here: Kaplan-Meier Survival Analysis

# How to pick predictor variables?

There are a few general principles to consider when selecting predictor variables for a Cox model:

- Relevance: The predictor variables should be relevant to the outcome of interest. For example, in a study evaluating the effect of a particular treatment on the risk of death, age and underlying health conditions would be relevant predictor variables, but hair color would not. It is therefore important to consider the findings of other authors in the scientific literature on the subject of your research.
- Clinical significance: In addition to statistical significance, it is important to consider whether the effect of the predictor variable is clinically significant. For example, a predictor variable may be statistically significant but have a small effect size, which may not be clinically meaningful.
- Multicollinearity: It is important to avoid selecting predictor variables that are highly correlated with one another, as this can lead to unstable estimates of the effect of each variable.
- Parsimony: It is generally recommended to include only a small number of predictor variables in a Cox model, as adding too many variables can make the model more difficult to interpret and may increase the risk of overfitting.

Overall, it is important to carefully consider the research question and the available data when selecting predictor variables for a Cox model and to use statistical tests to evaluate the significance and importance of each variable.

# How to interpret the hazard ratios?

The hazard ratio (HR) is a measure of the effect of a predictor variable on the risk of an event, such as death or disease progression. In a Cox model, the HR represents the relative risk of the event occurring for a given unit change in the predictor variable, with a HR greater than 1 indicating an increased risk and a HR less than 1 indicating a decreased risk.

For discrete variables, such as gender or treatment group, the HR can be interpreted as the relative risk of the event occurring in one group compared to another. For example, if the HR for gender is 2.0, this means that the risk of the event occurring is twice as high in one gender compared to the other.

For numeric variables, such as age or blood pressure, the HR can be interpreted as the relative risk of the event occurring for a given unit change in the predictor variable. For example, if the HR for age is 1.2, this means that the risk of the event occurring increases by 20% for each unit increase in age.

It is important to note that the interpretation of the HR depends on the scale of the predictor variable. For example, a HR of 1.2 for age might indicate a small increase in risk for a small change in age, but a much larger increase in risk for a large change in age. It is also important to consider the confidence interval (CI) for the HR, as this provides information about the precision of the estimate and the degree of uncertainty around the estimate. A narrow CI indicates a more precise estimate, while a wide CI indicates a less precise estimate.

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