# Cox Proportional Hazards Model

The Cox proportional hazards model is a semiparametric regression model used to fit survival models without knowing the distribution. It is based on the assumption that covariates affect the hazard function multiplicatively. That is,

\[\lambda(t | X_i) = \lambda_0(t) \exp(X_i \cdot \beta)\]

where $\lambda(t|X_i)$ is the estimated hazard for sample $i$, $\lambda_0$ is the baseline hazard, $X_i$ is the vector of covariates for sample $i$, and $\beta$ is the vector of coefficients in the model.

## API

`StatsBase.fit`

โ Method.`fit(::Type{CoxModel}, M::AbstractMatrix, y::AbstractVector; kwargs...)`

Given a matrix `M`

of predictors and a corresponding vector of events, compute the Cox proportional hazard model estimate of coefficients. Returns a `CoxModel`

object.

## References

- Cox, D. R. (1972).
*Regression models and life tables (with discussion)*. Journal of the Royal Statistical Society, Series B, 34:187โ220.