General information

Cox Regression is one of the most popular regression techniques for survival analysis, which is used to connect several risk factors or exposures, considered simultaneously, to survival time.

The response variable is the hazard function $\lambda(t)$, which assesses the probability that the event of interest occurred before $t$. The equation models this hazard as an exponential function of an arbitrary baseline hazard ($\lambda_0$) when all covariates are null, and $\beta$ is the regression coefficient of the covariate, $x$.

$$ \lambda(t) = \lambda_0(t)\,exp(\beta_1x_1+...+\beta_kx_k) $$

The Cox proportional hazards model makes two assumptions:

1. Survival curves for different strata must have hazard functions that are proportional over the time t.
2. The relationship between the log hazard and each covariate is linear, which can be verified with residual plots.

Description

Brick Locations

Bricks → Machine Learning → Cox Regression

Brick Parameters

• Duration column

  The column that contains the subjects’ lifetimes.

• Event column (optional)

  The column that contains the event occurrence observation. If not specified, all cases are considered to be uncensored.

• Strata column (optional)

  The column that is used for stratification.

• Cluster column (optional)

  The column that has unique identifiers for clustering covariances.

• Filter Columns

  Dataset columns that are ignored during the model training. However, they will be present in the resulting set. Multiple columns can be selected by clicking the ‘+’ button.

  If you want to remove many columns, you can select the columns to keep and use the flag “Remove all except selected”.

Brick Inputs/Outputs

• Inputs

  Brick takes the dataset with the duration target column

• Outputs

  • Brick produces the dataset with an extra column ‘duration_expectation’ for model predictions
  • A trained model that can be used in other bricks as an input

Example of usage